Finite Group DatabasebetaFinite Group Databasebeta| order | 36925 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C7 · Schur multiplier (H2) = C5 |
| direct product | C5×C7×C211⋊C5 |
| unambiguous semidirect product | (C7×C211)⋊C52 |
| unambiguous semidirect product | (C5×C7×C211)⋊C5 |
| Fitting, socle | C5×C7×C211 ⋊ C5 |
| derived, Sylow | C211 ⋊ C52×C7 |
| Hall | C7×C211 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | C211⋊C5 |
| commutator, cosocle, hypocenter | C211 | C52×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C211 | C5 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C5×C7 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7385 |
1645 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36925, 8);