Finite Group DatabasebetaFinite Group Databasebeta| order | 33756 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#26014558 |
| Fitting, socle, derived, Hall | C3×C29×C97 ⋊ C4 |
| Hall | C29×C97 ⋊ Dic3 |
| Hall | C3×C97 ⋊ #1181 |
| Sylow | C97 ⋊ C3⋊#1181 |
| Hall | C3×C29 ⋊ #87604 |
| Sylow | C29 ⋊ C3⋊#87604 |
| Sylow | C3 ⋊ #26014558 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C29×C97 | C4 |
| prime radical, cosocle | C3×D2813 | C2 |
| LCS | G ▷ C3×C29×C97 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8439 |
Polycyclic presentation:
2^2,3,29,97|a^2=b,c^a=c^2,d^a=d^17,e^a=e^75,d^b=d^28,e^b=e^962115 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33756, 34);