Finite Group DatabasebetaFinite Group Databasebeta| order | 19068 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×Dic227 |
| unambiguous semidirect product | C227⋊(C4×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C7×Dic227)⋊C3 |
| derived, Hall | C7×C227 ⋊ C3×C4 |
| Hall | C7×Dic227 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C227 ⋊ C4 |
| Sylow | C227 ⋊ C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×Dic227 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | ΓL(1,𝔽8)×D227 |
| commutator, hypocenter | C7×C227 | C3×C4 |
| Fitting, socle, cosocle | C2×C7×C227 | C2×C3 |
| prime radical | C2×ΓL(1,𝔽8)×C227 | C2 |
| LCS | G ▷ C7×C227 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6356 |
1150 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19068, 10);