Finite Group DatabasebetaFinite Group Databasebeta| order | 33666 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C31×C181 ⋊ C2×C3 |
| Hall | #30682780 ⋊ C2 |
| Hall | C31×D181 ⋊ C3 |
| Hall | D181 ⋊ C31⋊C3 |
| Sylow | C181 ⋊ C2×C31⋊C3 |
| Sylow | C31 ⋊ D181⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C181 | C2×C3 |
| LCS | G ▷ C31×C181 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5611 |
Polycyclic presentation:
2,3,31,181|d^a=d^180,c^b=c^25,d^b=d^48956 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33666, 15);