Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C4×#22552710 |
| derived, Hall | C72×C19 ⋊ C4×C9 |
| Hall | C4×C72×C19 ⋊ C9 |
| Hall | C4×C72 ⋊ #4294 |
| Hall | C4×C19 ⋊ #89204 |
| Sylow | C72 ⋊ C4×#4294 |
| Sylow | C19 ⋊ C4×#89204 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | #14584116 |
| commutator, hypocenter | C72×C19 | C4×C9 |
| Frattini | C2×C3 | C2×#14584116 |
| Fitting | C3×C4×C72×C19 | C3 |
| socle, prime radical, cosocle | C2×C3×C72×C19 | C2×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C3×C4 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33516 |
3756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 322);