Finite Group DatabasebetaFinite Group Databasebeta| order | 25092 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C41 · Schur multiplier (H2) = C2×C3 |
| direct product | C3⋊D3×D17×C41 |
| unambiguous semidirect product | (C3×D17)⋊(D3×C41) |
| Fitting, socle, Hall | C32×C17×C41 ⋊ C22 |
| derived, Hall | C32×C17 ⋊ C22×C41 |
| Hall | C17×C41 ⋊ C2×C3⋊D3 |
| Hall | C32×C41 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×C3⋊D3×C41 |
| Sylow | C32 ⋊ C2×D17×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | C3⋊D3×D17 |
| commutator, cosocle, hypocenter | C32×C17 | C22×C41 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C41 | C22 |
| LCS | G ▷ C32×C17 | |
| UCS | C1 ◁ C41 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6273 |
2460 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25092, 97);