Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
| direct product | C3×C19⋊#10596885 |
| Fitting, socle | C3×C72×C19 ⋊ Dic3 |
| derived | C19×#3862 ⋊ C3×C4 |
| Hall | C3×C19×#3862 ⋊ C4 |
| Hall | C72×C19 ⋊ C3×Dic3 |
| Hall | C3×#3862 ⋊ Dic19 |
| Sylow | C72 ⋊ C3×Dic57 |
| Sylow | C19 ⋊ C3×#10596885 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C19⋊#10596885 |
| commutator, hypocenter | C19×#3862 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C19 | Dic3 |
| prime radical | C3×C19×#64425 | C2 |
| cosocle | C19×#64425 | C2×C3 |
| LCS | G ▷ C19×#3862 | |
| UCS | C1 ◁ C3 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 798 |
408 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 997);