Finite Group DatabasebetaFinite Group Databasebeta| order | 31095 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C3×C5×C691⋊C3 |
| unambiguous semidirect product | (C5×C691)⋊C32 |
| unambiguous semidirect product | (C3×C5×C691)⋊C3 |
| Fitting, socle | C3×C5×C691 ⋊ C3 |
| derived, Sylow | C691 ⋊ C32×C5 |
| Hall | C5×C691 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C691⋊C3 |
| commutator, cosocle, hypocenter | C691 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C691 | C3 |
| LCS | G ▷ C691 | |
| UCS | C1 ◁ C3×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10365 |
3495 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31095, 8);