Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#30660650 |
| Fitting, socle | C2×C72×C19 ⋊ C2×C9 |
| derived, Hall | C72×C19 ⋊ C22×C9 |
| Hall | #22552719 ⋊ C22 |
| Hall | C2×C19×C7⋊D7 ⋊ C9 |
| Hall | C2×C7⋊D7 ⋊ #4296 |
| Sylow | C72 ⋊ C22×#4296 |
| Sylow | C19 ⋊ C2×#11725077 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #30660650 |
| commutator, hypocenter | C72×C19 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C19 | C2×C9 |
| prime radical | C2×C19⋊C3×C7⋊D7 | C3 |
| cosocle | C72×C19⋊C3 | C22×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C2 | |
300 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1862 |
188 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 970);