Finite Group DatabasebetaFinite Group Databasebeta| order | 33756 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #26014558⋊C3 |
| Fitting, socle, derived, Hall | C29×C97 ⋊ C3×C4 |
| Hall | #26014558 ⋊ C3 |
| Hall | C29×C97⋊C3 ⋊ C4 |
| Hall | C97⋊C3 ⋊ #1181 |
| Sylow | C97 ⋊ C3×#1181 |
| Sylow | C29 ⋊ #87604⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C29×C97 | C3×C4 |
| prime radical | C29⋊(D97⋊C3) | C2 |
| cosocle | D2813 | C2×C3 |
| LCS | G ▷ C29×C97 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2813 |
Polycyclic presentation:
2,3,2,29,97|a^2=c,d^a=d^17,e^a=e^75,e^b=e^35,d^c=d^28,e^c=e^96265 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33756, 15);