Finite Group DatabasebetaFinite Group Databasebeta| order | 22428 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×Dic267 |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽8)×Dic89) |
| unambiguous semidirect product | (C7×Dic267)⋊C3 |
| derived | C3×C7×C89 ⋊ C3×C4 |
| Hall | C3×ΓL(1,𝔽8)×C89 ⋊ C4 |
| Hall | C7×C89 ⋊ C3×Dic3 |
| Sylow | C89 ⋊ Dic3×ΓL(1,𝔽8) |
| Hall | C3×ΓL(1,𝔽8) ⋊ Dic89 |
| Sylow | C7 ⋊ C3×Dic267 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | ΓL(1,𝔽8)×D267 |
| commutator, hypocenter | C3×C7×C89 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C7×C89 | C2×C3 |
| prime radical | C2×C3×ΓL(1,𝔽8)×C89 | C2 |
| LCS | G ▷ C3×C7×C89 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7476 |
1350 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22428, 48);