Finite Group DatabasebetaFinite Group Databasebeta| order | 31605 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C7×C43 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×ΓL(1,𝔽8)×C43 |
| unambiguous semidirect product | C7⋊(C3×C5×C7×C43) |
| unambiguous semidirect product | (C5×C7)⋊(C3×C7×C43) |
| Fitting, socle, Hall | C5×C72×C43 ⋊ C3 |
| derived | C7 ⋊ C3×C5×C7×C43 |
| Hall | C72×C43 ⋊ C3×C5 |
| Hall | C5×C72 ⋊ C3×C43 |
| Sylow | C72 ⋊ C3×C5×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7×C43 | ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C7 | C3×C5×C7×C43 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C43 | C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C5×C7×C43 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4515 |
7525 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31605, 15);