Finite Group DatabasebetaFinite Group Databasebeta| order | 18963 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C43 · Schur multiplier (H2) = C3 |
| direct product | ΓL(1,𝔽8)2×C43 |
| unambiguous semidirect product | (C7×ΓL(1,𝔽8))⋊(C3×C43) |
| unambiguous semidirect product | #3861⋊(C3×C43) |
| unambiguous semidirect product | #3862⋊(C3×C43) |
| Fitting, socle, Hall | C72×C43 ⋊ C32 |
| derived, Sylow | C72 ⋊ C32×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | ΓL(1,𝔽8)2 |
| commutator, cosocle, hypocenter | C72 | C32×C43 |
| Frattini | C1 | G |
| Fitting, socle | C72×C43 | C32 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C43 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 903 |
1075 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#64418⋊C3, #49181660, ΓL(1,𝔽8)2×D43, … |
| maximal normal subgroup of | C43×#64418⋊C3, #49181660, ΓL(1,𝔽8)2×D43, … |
| maximal quotient of | C2×ΓL(1,𝔽8)2×C43 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18963, 40);