Finite Group DatabasebetaFinite Group Databasebeta| order | 33572 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C11⋊#89137) |
| unambiguous semidirect product | C11⋊(C7⋊#89137) |
| Fitting, socle, derived, Hall | C7×C11×C109 ⋊ C4 |
| Hall | C11×C109 ⋊ Dic7 |
| Hall | C7×C109 ⋊ Dic11 |
| Sylow | C109 ⋊ Dic77 |
| Hall | C7×C11 ⋊ #89137 |
| Sylow | C11 ⋊ C7⋊#89137 |
| Sylow | C7 ⋊ C11⋊#89137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C11×C109 | C4 |
| prime radical, cosocle | C7×C11×D109 | C2 |
| LCS | G ▷ C7×C11×C109 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8393 |
Polycyclic presentation:
2^2,7,11,109|a^2=b,c^a=c^6,d^a=d^10,e^a=e^76,e^b=e^1082159 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33572, 15);