Finite Group DatabasebetaFinite Group Databasebeta| order | 23124 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D41×D47 |
| unambiguous semidirect product | (C47×D41)⋊(C2×C3) |
| unambiguous semidirect product | (C41×D47)⋊(C2×C3) |
| unambiguous semidirect product | D1927⋊(C2×C3) |
| Fitting, socle, Hall | C3×C41×C47 ⋊ C22 |
| derived, Hall | C41×C47 ⋊ C22×C3 |
| Hall | C3×C47 ⋊ C2×D41 |
| Hall | C3×C41 ⋊ C2×D47 |
| Sylow | C47 ⋊ C2×C3×D41 |
| Sylow | C41 ⋊ C2×C3×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D41×D47 |
| commutator, cosocle, hypocenter | C41×C47 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C41×C47 | C22 |
| LCS | G ▷ C41×C47 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5781 |
1650 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23124, 12);