[
    {
        "id": "osp-13627",
        "type": "article-journal",
        "title": "Two Groups 2^3.〖PSL〗_2 (7) and 2^3:〖PSL〗_2 (7) of Order 1344",
        "author": [
            {
                "family": "Koca",
                "given": "Mehmet"
            },
            {
                "family": "Koç",
                "given": "Ramazan"
            },
            {
                "family": "Koca",
                "given": "Nazife Özdeş"
            }
        ],
        "URL": "https://omanscience.com/en/articles/two-groups-2-3-psl-2-7-and-2-3-psl-2-7-of-order-1344",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2019
                ]
            ]
        },
        "container-title": "Sultan Qaboos University Journal for Science",
        "volume": "24",
        "issue": "1",
        "page": "57",
        "DOI": "10.24200/squjs.vol24iss1pp57-70",
        "publisher": "Sultan Qaboos University",
        "ISSN": "2308-3921",
        "abstract": "We analyze the group structures of two groups of order 1344 which are respectively non-split and split extensions of the elementary Abelian group of order 8 by its automorphism group 𝑃𝑆𝐿 2 (7).Two groups have the same number of conjugacy classes and the set of dimensions of irreducible representations is equal.The group 2 3 .𝑃𝑆𝐿 2 (7) is a finite subgroup of the Lie Group 𝐺 2 preserving the set of octonions ±𝑒 𝑖 , (𝑖 = 1,2, … ,7) representing a 7dimensional octahedron.Its three maximal subgroups 2 3 : 7: 3, 2 3 .𝑆 4 and 4. 𝑆 4 : 2 correspond to the finite subgroups of the Lie groups 𝐺 2 , 𝑆𝑂(4) and 𝑆𝑈(3) respectively.The group 2 3 : 𝑃𝑆𝐿 2 (7) representing the split extension possesses five maximal subgroups 2 3 : 7: 3, 2 3 : 𝑆 4 , 4: 𝑆 4 : 2 and two non-conjugate Klein's group 𝑃𝑆𝐿 2 (7).The character tables of the groups and their maximal subgroups, tensor products and decompositions of their irreducible representations under the relevant maximal subgroups are identified.Possible implications in physics are discussed."
    }
]