Finite Group DatabasebetaFinite Group Databasebeta| order | 33396 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊#13089712 |
| derived, Hall | C23×C112⋊C3 ⋊ C4 |
| Hall | C112×C23 ⋊ Dic3 |
| Hall | C112⋊C3 ⋊ Dic23 |
| Sylow | C112 ⋊ Dic69 |
| Sylow | C23 ⋊ #13089712 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C23⋊#10624391 |
| commutator, hypocenter | C23×C112⋊C3 | C4 |
| Fitting, socle | C2×C112×C23 | D3 |
| prime radical, cosocle | C2×C23×C112⋊C3 | C2 |
| LCS | G ▷ C23×C112⋊C3 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3036 |
Polycyclic presentation:
2,3,23,11^2,2|a^2=f,b^a=b^2,c^a=c^22,d^a=d^2e^10,e^a=d^3e^9,d^b=d^2e^10,e^b=d^7e^81022 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33396, 45);