Finite Group DatabasebetaFinite Group Databasebeta| order | 8484 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×Dic101 |
| unambiguous semidirect product | (C7×Dic101)⋊C3 |
| derived, Hall | C7×C101 ⋊ C3×C4 |
| Hall | C7×Dic101 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C101 ⋊ C4 |
| Sylow | C101 ⋊ C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×Dic101 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | ΓL(1,𝔽8)×D101 |
| commutator, hypocenter | C7×C101 | C3×C4 |
| Fitting, socle | C2×C7×C101 | C2×C3 |
| LCS | G ▷ C7×C101 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
520 conjugacy classes — view the full character table.
| maximal subgroup of | C3×ΓL(1,𝔽8)×Dic101, ΓL(1,𝔽8)×Dic303 |
| maximal normal subgroup of | C3×ΓL(1,𝔽8)×Dic101 |
| maximal quotient of | C7⋊C9×Dic101, C3×ΓL(1,𝔽8)×Dic101, ΓL(1,𝔽8)×Dic303 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8484, 10);