Finite Group DatabasebetaFinite Group Databasebeta| order | 31476 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C43×C61 ⋊ C3×C4 |
| Hall | C43×#6923 ⋊ C3 |
| Hall | #21463500 ⋊ C4 |
| Hall | #6923 ⋊ C43⋊C3 |
| Sylow | C61 ⋊ C4×C43⋊C3 |
| Sylow | C43 ⋊ #6923⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C43×C61 | C3×C4 |
| prime radical | #30628679 | C2 |
| cosocle | C43×D61 | C2×C3 |
| LCS | G ▷ C43×C61 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2623 |
Polycyclic presentation:
2,3,2,43,61|a^2=c,e^a=e^50,d^b=d^36,e^b=e^47,e^c=e^60283 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31476, 34);