Finite Group DatabasebetaFinite Group Databasebeta| order | 22764 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C4×#19151018 |
| Fitting, Hall | C4×C7×C271 ⋊ C3 |
| derived, Hall | C7×C271 ⋊ C3×C4 |
| Hall | C4×C271 ⋊ ΓL(1,𝔽8) |
| Sylow | C271 ⋊ C4×ΓL(1,𝔽8) |
| Hall | C4×C7 ⋊ C271⋊C3 |
| Sylow | C7 ⋊ C4×C271⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #19151018 |
| commutator, hypocenter | C7×C271 | C3×C4 |
| Frattini | C2 | C2×#19151018 |
| Fitting | C4×C7×C271 | C3 |
| socle, cosocle | C2×C7×C271 | C2×C3 |
| prime radical | C2×#19151018 | C2 |
| LCS | G ▷ C7×C271 | |
| UCS | C1 ◁ C4 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7588 |
2540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22764, 4);