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 | #22554623 ⋊ C4 |
| Hall | #16836713 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #16836713⋊C3 |
| commutator, hypocenter | C937 | C4×C9 |
| Fitting, socle | C3×C937 | C3×C4 |
| prime radical, cosocle | C3×D937 | C2×C3 |
| LCS | G ▷ C937 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8433 |
Polycyclic presentation:
2,3,2,937,3|a^2=c,b^3=e,d^a=d^741,d^b=d^614,d^c=d^936270 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33732, 8);