Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #11925890⋊D13 |
| Fitting, socle, Hall | C112×C13 ⋊ C2×D5 |
| derived, Hall | C13×#10597245 ⋊ C22 |
| Hall | #10597245 ⋊ C2×D13 |
| Sylow | C112 ⋊ D5×D13 |
| Sylow | C13 ⋊ #11925890⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C13×#10597245 | C22 |
| Fitting, socle | C112×C13 | C2×D5 |
| LCS | G ▷ C13×#10597245 | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 286 |
Polycyclic presentation:
2^2,5,13,11^2|c^a=c^4,d^a=d^12,e^a=e^4f^2,f^a=e^9f^7,c^b=c^4,e^b=e^7f^9,f^b=e^2f^4,e^c=e^3f^9,f^c=f^4215 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 99);