Finite Group DatabasebetaFinite Group Databasebeta| order | 25190 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C5×C11×D229 |
| unambiguous semidirect product | C229⋊(C2×C5×C11) |
| Fitting, socle, Hall | C5×C11×C229 ⋊ C2 |
| derived, Sylow | C229 ⋊ C2×C5×C11 |
| Hall | C11×C229 ⋊ C2×C5 |
| Hall | C5×C229 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C11 | D229 |
| commutator, cosocle, hypocenter | C229 | C2×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C229 | C2 |
| LCS | G ▷ C229 | |
| UCS | C1 ◁ C5×C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12595 |
6380 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25190, 3);