Finite Group DatabasebetaFinite Group Databasebeta| order | 8484 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C101 · Schur multiplier (H2) = C1 |
| direct product | C4×ΓL(1,𝔽8)×C101 |
| unambiguous semidirect product | (C4×C7)⋊(C3×C101) |
| unambiguous semidirect product | (C4×C7×C101)⋊C3 |
| Fitting, Hall | C4×C7×C101 ⋊ C3 |
| derived, Sylow | C7 ⋊ C3×C4×C101 |
| Hall | C7×C101 ⋊ C3×C4 |
| Hall | C4×C7 ⋊ C3×C101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C101 | ΓL(1,𝔽8) |
| commutator, hypocenter | C7 | C3×C4×C101 |
| Frattini | C2 | C2×ΓL(1,𝔽8)×C101 |
| Fitting | C4×C7×C101 | C3 |
| socle | C2×C7×C101 | C2×C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C4×C101 | |
24 conjugacy classes of subgroups.
2020 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic3×ΓL(1,𝔽8)×C101, C3×C4×ΓL(1,𝔽8)×C101 |
| maximal normal subgroup of | C3×C4×ΓL(1,𝔽8)×C101 |
| maximal quotient of | C4×C7⋊C9×C101, Dic3×ΓL(1,𝔽8)×C101, C3×C4×ΓL(1,𝔽8)×C101 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8484, 2);