Finite Group DatabasebetaFinite Group Databasebeta| order | 36995 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×C151⋊C5 |
| unambiguous semidirect product | C151⋊(C5×C72) |
| unambiguous semidirect product | (C7×C151)⋊(C5×C7) |
| unambiguous semidirect product | (C72×C151)⋊C5 |
| Fitting, socle, Hall | C72×C151 ⋊ C5 |
| derived, Sylow | C151 ⋊ C5×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | C151⋊C5 |
| commutator, cosocle, hypocenter | C151 | C5×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C151 | C5 |
| LCS | G ▷ C151 | |
| UCS | C1 ◁ C72 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7399 |
1715 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36995, 4);