Finite Group DatabasebetaFinite Group Databasebeta| order | 33396 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C23⋊#13089721 |
| Fitting, socle, Hall | C112×C23 ⋊ Dic3 |
| derived, Hall | C23×C112⋊C3 ⋊ C4 |
| Hall | C112⋊C3 ⋊ Dic23 |
| Sylow | C112 ⋊ Dic69 |
| Sylow | C23 ⋊ #13089721 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C23×C112⋊C3 | C4 |
| Fitting, socle | C112×C23 | Dic3 |
| prime radical, cosocle | C23×(C11⋊D11)⋊C3 | C2 |
| LCS | G ▷ C23×C112⋊C3 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1518 |
Polycyclic presentation:
2^2,3,23,11^2|a^2=b,c^a=c^2,d^a=d^22,e^a=e^10f^7,f^a=e^6f,e^b=e^10,f^b=f^10,e^c=e^5f^7,f^c=e^5f^5302 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33396, 80);