Finite Group DatabasebetaFinite Group Databasebeta| order | 25652 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C53 · Schur multiplier (H2) = C2 |
| direct product | D112×C53 |
| unambiguous semidirect product | (C11×D11)⋊(C2×C53) |
| unambiguous semidirect product | (C11⋊D11)⋊(C2×C53) |
| Fitting, socle, Hall | C112×C53 ⋊ C22 |
| derived, Sylow | C112 ⋊ C22×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | D112 |
| commutator, cosocle, hypocenter | C112 | C22×C53 |
| Frattini | C1 | G |
| Fitting, socle | C112×C53 | C22 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C53 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1166 |
2597 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25652, 25);