Finite Group DatabasebetaFinite Group Databasebeta| order | 25454 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C13⋊(D89⋊C11) |
| unambiguous semidirect product | (C89⋊C11)⋊D13 |
| unambiguous semidirect product | D1157⋊C11 |
| Fitting, socle, derived, Hall | C13×C89 ⋊ C2×C11 |
| Hall | C13×C89⋊C11 ⋊ C2 |
| Hall | D1157 ⋊ C11 |
| Hall | C89⋊C11 ⋊ D13 |
| Sylow | C89 ⋊ C11×D13 |
| Sylow | C13 ⋊ D89⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C89 | C2×C11 |
| LCS | G ▷ C13×C89 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1157 |
Polycyclic presentation:
2,11,13,89|c^a=c^12,d^a=d^88,d^b=d^64140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25454, 12);