Finite Group DatabasebetaFinite Group Databasebeta| order | 19572 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×Dic233 |
| unambiguous semidirect product | (C7×Dic233)⋊C3 |
| derived, Hall | C7×C233 ⋊ C3×C4 |
| Hall | C7×Dic233 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C233 ⋊ C4 |
| Sylow | C233 ⋊ C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×Dic233 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | ΓL(1,𝔽8)×D233 |
| commutator, hypocenter | C7×C233 | C3×C4 |
| Fitting, socle, cosocle | C2×C7×C233 | C2×C3 |
| prime radical | C2×ΓL(1,𝔽8)×C233 | C2 |
| LCS | G ▷ C7×C233 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6524 |
1180 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19572, 10);