Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C3×C72×Dic57 |
| unambiguous semidirect product | C3⋊(C3×C72×Dic19) |
| derived | C3×C19 ⋊ C3×C4×C72 |
| Hall | C32×C72×C19 ⋊ C4 |
| Hall | C72×C19 ⋊ C3×Dic3 |
| Hall | C32×C72 ⋊ Dic19 |
| Hall | C32×C19 ⋊ C4×C72 |
| Sylow | C19 ⋊ C3×C72×Dic3 |
| Sylow | C32 ⋊ C72×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C72 | D57 |
| commutator, hypocenter | C3×C19 | C3×C4×C72 |
| Frattini | C2 | C3×C72×D57 |
| Fitting, socle, prime radical | C2×C32×C72×C19 | C2 |
| cosocle | C2×C3×C19 | C2×C3×C72 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C2×C3×C72 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11172 |
8820 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 767);