Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C19 · Schur multiplier (H2) = C2 |
| direct product | C19×#11725071⋊C2 |
| unambiguous semidirect product | #11725071⋊(C2×C19) |
| derived, Hall | #89205 ⋊ C22×C19 |
| Hall | C19×#89205 ⋊ C22 |
| Hall | C72×C19 ⋊ C2×D9 |
| Sylow | C72 ⋊ C2×D9×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | #11725071⋊C2 |
| commutator, cosocle, hypocenter | #89205 | C22×C19 |
| Frattini | C3 | C19×#64418⋊C2 |
| Fitting, socle | C3×C72×C19 | C2×D3 |
| LCS | G ▷ #89205 | |
| UCS | C1 ◁ C19 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1197 |
627 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 390);