Finite Group DatabasebetaFinite Group Databasebeta| order | 33220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #30658862⋊C2 |
| unambiguous semidirect product | #30658868⋊C2 |
| unambiguous semidirect product | #30658874⋊C2 |
| Fitting, socle, derived, Hall | C11×C151 ⋊ C22×C5 |
| Hall | #22552173 ⋊ C22 |
| Hall | D11×D151 ⋊ C5 |
| Sylow | C151 ⋊ C2×AGL(1,𝔽11) |
| Sylow | C11 ⋊ C2×D151⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C151 | C22×C5 |
| LCS | G ▷ C11×C151 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1661 |
Polycyclic presentation:
2^2,5,11,151|e^a=e^150,d^b=d^10,d^c=d^4,e^c=e^19127 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33220, 36);