Finite Group DatabasebetaFinite Group Databasebeta| order | 31476 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #30628679⋊C2 |
| unambiguous semidirect product | #30628683⋊C2 |
| unambiguous semidirect product | #30628687⋊C2 |
| Fitting, socle, derived, Hall | C43×C61 ⋊ C22×C3 |
| Hall | D43×D61 ⋊ C3 |
| Hall | #21463500 ⋊ C22 |
| Sylow | C61 ⋊ C2×D43⋊C3 |
| Sylow | C43 ⋊ C2×D61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C43×C61 | C22×C3 |
| LCS | G ▷ C43×C61 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2623 |
Polycyclic presentation:
2^2,3,43,61|e^a=e^60,d^b=d^42,d^c=d^36,e^c=e^47256 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31476, 30);