Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Hall | C112×C13 ⋊ Dic5 |
| derived, Hall | C13×#10597245 ⋊ C4 |
| Hall | #10597245 ⋊ #261 |
| Sylow | C112 ⋊ #63118 |
| Sylow | C13 ⋊ #14559049 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C13×#10597245 | C4 |
| Fitting, socle | C112×C13 | Dic5 |
| prime radical, cosocle | D13×#10597245 | C2 |
| LCS | G ▷ C13×#10597245 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 286 |
Polycyclic presentation:
2^2,5,13,11^2|a^2=b,c^a=c^4,d^a=d^5,e^a=e^4f^2,f^a=e^9f^7,d^b=d^12,e^c=e^3f^9,f^c=f^4149 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 90);