Finite Group DatabasebetaFinite Group Databasebeta| order | 25186 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×D257 |
| unambiguous semidirect product | C257⋊(C2×C72) |
| Fitting, socle, Hall | C72×C257 ⋊ C2 |
| derived, Sylow | C257 ⋊ C2×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D257 |
| commutator, cosocle, hypocenter | C257 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C257 | C2 |
| LCS | G ▷ C257 | |
| UCS | C1 ◁ C72 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12593 |
6370 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25186, 6);