Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C5×C232⋊C3 ⋊ C4 |
| Hall | C5×C232 ⋊ Dic3 |
| Hall | C232⋊C3 ⋊ Dic5 |
| Sylow | C232 ⋊ Dic15 |
| Sylow | C5 ⋊ #20263650 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊#15691772 |
| commutator, hypocenter | C5×C232⋊C3 | C4 |
| Fitting, socle | C2×C5×C232 | D3 |
| prime radical, cosocle | C2×C5×C232⋊C3 | C2 |
| LCS | G ▷ C5×C232⋊C3 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1380 |
Polycyclic presentation:
2,3,5,23^2,2|a^2=f,b^a=b^2,c^a=c^4,e^a=d^2e^22,d^b=d^7e^4,e^b=d^3e^15964 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 32);