Finite Group DatabasebetaFinite Group Databasebeta| order | 23124 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C41 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C41×D47 |
| unambiguous semidirect product | C47⋊(C22×C3×C41) |
| unambiguous semidirect product | (C2×C47)⋊(C2×C3×C41) |
| Fitting, socle | C2×C3×C41×C47 ⋊ C2 |
| derived, Sylow | C47 ⋊ C22×C3×C41 |
| Hall | C3×C41×C47 ⋊ C22 |
| Hall | C41×C47 ⋊ C22×C3 |
| Hall | C3×C47 ⋊ C22×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C41 | D47 |
| commutator, cosocle, hypocenter | C47 | C22×C3×C41 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C41×C47 | C2 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C2×C3×C41 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11562 |
6150 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23124, 22);