Finite Group DatabasebetaFinite Group Databasebeta| order | 31262 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊D2233 |
| unambiguous semidirect product | C11⋊(C7⋊D203) |
| unambiguous semidirect product | C29⋊(C7⋊D77) |
| Fitting, socle, derived, Hall | C72×C11×C29 ⋊ C2 |
| Hall | C72×C29 ⋊ D11 |
| Hall | C72×C11 ⋊ D29 |
| Hall | C11×C29 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ D319 |
| Sylow | C29 ⋊ C7⋊D77 |
| Sylow | C11 ⋊ C7⋊D203 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C11×C29 | C2 |
| LCS | G ▷ C72×C11×C29 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15631 |
Polycyclic presentation:
2,7^2,11,29|b^a=b^6,c^a=c^6,d^a=d^10,e^a=e^287817 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31262, 32);