Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | #14584108⋊A4 |
| Fitting, derived, Hall | C22×C19×C49 ⋊ C32 |
| Hall | C19×C49 ⋊ C3×A4 |
| Hall | C22×C49 ⋊ C3×C19⋊C3 |
| Hall | C22×C19 ⋊ C3×C49⋊C3 |
| Sylow | C49 ⋊ A4×C19⋊C3 |
| Sylow | C19 ⋊ A4×C49⋊C3 |
| Sylow | C22 ⋊ C19⋊C3×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C22×C19×C49 | C32 |
| Frattini | C7 | #87705⋊A4 |
| socle | C22×C7×C19 | C3×ΓL(1,𝔽8) |
| LCS | G ▷ C22×C19×C49 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3724 |
Polycyclic presentation:
3^2,2^2,7,19,7|e^7=g^2,e^a=e^2g,f^a=f^11,g^a=g^2,c^b=cd,d^b=c,e^b=e^2g,g^b=g^2484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 184);