Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C112×C13 ⋊ C4×C5 |
| Hall | C13×#10597245 ⋊ C4 |
| Hall | C11×C11⋊#261 ⋊ C5 |
| Hall | #10597245 ⋊ #261 |
| Sylow | C112 ⋊ C5×#261 |
| Sylow | C13 ⋊ #14559055 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C112×C13 | C4×C5 |
| prime radical | D13×#10597245 | C2 |
| cosocle | C112×D13 | C2×C5 |
| LCS | G ▷ C112×C13 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1430 |
Polycyclic presentation:
2,5,2,11^2,13|a^2=c,e^a=e^10,f^a=f^5,d^b=d^4,e^b=e^3,f^c=f^12137 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 131);