Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C11 |
| unambiguous semidirect product | D65⋊(C11⋊D11) |
| Fitting, socle, derived, Hall | C5×C112×C13 ⋊ C22 |
| Hall | C112×C13 ⋊ C2×D5 |
| Hall | C5×C112 ⋊ C2×D13 |
| Sylow | C112 ⋊ D5×D13 |
| Hall | C5×C13 ⋊ C2×C11⋊D11 |
| Sylow | C13 ⋊ D5×C11⋊D11 |
| Sylow | C5 ⋊ D13×C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C112×C13 | C22 |
| LCS | G ▷ C5×C112×C13 | |
| UCS | C1 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7865 |
Polycyclic presentation:
2^2,5,11^2,13|d^a=d^10,e^a=e^10,f^a=f^12,c^b=c^4,d^b=d^10,e^b=e^102072 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 219);