Finite Group DatabasebetaFinite Group Databasebeta| order | 25146 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C2×C11×#11765919 |
| Fitting, socle, Hall | C2×C11×C127 ⋊ C9 |
| derived, Sylow | C127 ⋊ C2×C9×C11 |
| Hall | C11×C127 ⋊ C2×C9 |
| Hall | C2×C127 ⋊ C9×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | #11765919 |
| commutator, hypocenter | C127 | C2×C9×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C127 | C9 |
| prime radical | C2×C11×C127⋊C3 | C3 |
| cosocle | C127⋊C3 | C2×C3×C11 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C2×C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2794 |
506 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25146, 17);