Finite Group DatabasebetaFinite Group Databasebeta| order | 37066 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D431⋊C43 |
| unambiguous semidirect product | (C431⋊C43)⋊C2 |
| Fitting, socle, derived, Sylow | C431 ⋊ C2×C43 |
| Hall | C431⋊C43 ⋊ C2 |
| Hall | D431 ⋊ C43 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C431 | C2×C43 |
| LCS | G ▷ C431 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 431 |
Polycyclic presentation:
2,43,431|c^a=c^430,c^b=c^491 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37066, 1);