Finite Group DatabasebetaFinite Group Databasebeta| order | 31605 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C7 |
| direct product | C5×C43⋊#3862 |
| unambiguous semidirect product | C43⋊(C5×#3862) |
| unambiguous semidirect product | (C5×C43)⋊#3862 |
| Fitting, socle, Hall | C5×C72×C43 ⋊ C3 |
| derived, Hall | C72×C43 ⋊ C3×C5 |
| Hall | C5×C72 ⋊ C43⋊C3 |
| Hall | C5×C43 ⋊ #3862 |
| Sylow | C72 ⋊ C5×C43⋊C3 |
| Sylow | C43 ⋊ C5×#3862 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C43⋊#3862 |
| commutator, cosocle, hypocenter | C72×C43 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C43 | C3 |
| LCS | G ▷ C72×C43 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4515 |
3525 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31605, 22);