Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C11 |
No aliases for this group.
| derived, Hall | C112×C13 ⋊ C4×C5 |
| Hall | C13×#10597245 ⋊ C4 |
| Hall | C11⋊Dic143 ⋊ C5 |
| Hall | #10597245 ⋊ Dic13 |
| Sylow | C112 ⋊ C5×Dic13 |
| Sylow | C13 ⋊ #14559052 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C13⋊#11925893 |
| commutator, hypocenter | C112×C13 | C4×C5 |
| Fitting, socle, cosocle | C2×C112×C13 | C2×C5 |
| prime radical | C2×C13×#10597245 | C2 |
| LCS | G ▷ C112×C13 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2860 |
Polycyclic presentation:
2,5,11^2,13,2|a^2=f,c^a=c^10,d^a=d^10,e^a=e^12,c^b=c^4,d^b=d^3392 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 54);