Finite Group DatabasebetaFinite Group Databasebeta| order | 33732 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C937 ⋊ C4×C9 |
| Hall | #22554625 ⋊ C4 |
| Hall | Dic937 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #22554625⋊C2 |
| commutator, hypocenter | C937 | C4×C9 |
| Fitting, socle | C2×C937 | C2×C9 |
| prime radical, cosocle | C2×C937⋊C3 | C2×C3 |
| LCS | G ▷ C937 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3748 |
Polycyclic presentation:
2,3^2,937,2|a^2=e,b^3=c,d^a=d^936,d^b=d^499,d^c=d^614140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33732, 20);