Finite Group DatabasebetaFinite Group Databasebeta| order | 22428 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×ΓL(1,𝔽8)×#67063 |
| unambiguous semidirect product | (C7×#67063)⋊C32 |
| unambiguous semidirect product | (C3×C7×#67063)⋊C3 |
| Fitting, socle | C3×C7×C89 ⋊ C3×C4 |
| derived, Hall | C7×C89 ⋊ C32×C4 |
| Hall | C3×ΓL(1,𝔽8)×C89 ⋊ C4 |
| Hall | C7×#67063 ⋊ C32 |
| Sylow | C89 ⋊ C3×C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C32×#67063 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | ΓL(1,𝔽8)×#67063 |
| commutator, hypocenter | C7×C89 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C89 | C3×C4 |
| prime radical | C3×ΓL(1,𝔽8)×D89 | C2 |
| cosocle | C7×D89 | C2×C32 |
| LCS | G ▷ C7×C89 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1869 |
390 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22428, 64);