Finite Group DatabasebetaFinite Group Databasebeta| order | 25652 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D583 |
| unambiguous semidirect product | (C11×D11)⋊D53 |
| unambiguous semidirect product | (D11×C53)⋊D11 |
| Fitting, socle, derived, Hall | C112×C53 ⋊ C22 |
| Sylow | C112 ⋊ C2×D53 |
| Sylow | C53 ⋊ D112 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C53 | C22 |
| LCS | G ▷ C112×C53 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1166 |
2051 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25652, 26);