Finite Group DatabasebetaFinite Group Databasebeta| order | 31575 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52 · Schur multiplier (H2) = C5 |
| direct product | C3×C5×C421⋊C5 |
| unambiguous semidirect product | (C3×C421)⋊C52 |
| unambiguous semidirect product | (C3×C5×C421)⋊C5 |
| Fitting, socle | C3×C5×C421 ⋊ C5 |
| derived, Sylow | C421 ⋊ C3×C52 |
| Hall | C3×C421 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C421⋊C5 |
| commutator, cosocle, hypocenter | C421 | C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C421 | C5 |
| LCS | G ▷ C421 | |
| UCS | C1 ◁ C3×C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6315 |
1335 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31575, 7);