Finite Group DatabasebetaFinite Group Databasebeta| order | 31460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊Dic715 |
| derived, Hall | C5×C112×C13 ⋊ C4 |
| Hall | C112×C13 ⋊ Dic5 |
| Hall | C5×C112 ⋊ Dic13 |
| Sylow | C112 ⋊ Dic65 |
| Hall | C5×C13 ⋊ C11⋊Dic11 |
| Sylow | C13 ⋊ C11⋊Dic55 |
| Sylow | C5 ⋊ C11⋊Dic143 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(C11⋊D143) |
| commutator, hypocenter | C5×C112×C13 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C5×C112×C13 | C2 |
| LCS | G ▷ C5×C112×C13 | |
| UCS | C1 ◁ C2 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31460 |
Polycyclic presentation:
2,5,11^2,13,2|a^2=f,b^a=b^4,c^a=c^10,d^a=d^10,e^a=e^127868 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31460, 78);