Finite Group DatabasebetaFinite Group Databasebeta| order | 36025 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C11 · Schur multiplier (H2) = C5 |
| direct product | C5×C11×C131⋊C5 |
| unambiguous semidirect product | C131⋊(C52×C11) |
| unambiguous semidirect product | (C5×C131)⋊(C5×C11) |
| Fitting, socle | C5×C11×C131 ⋊ C5 |
| derived, Sylow | C131 ⋊ C52×C11 |
| Hall | C11×C131 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C11 | C131⋊C5 |
| commutator, cosocle, hypocenter | C131 | C52×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C131 | C5 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C5×C11 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7205 |
1705 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36025, 10);