Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C7 |
| direct product | C3×(C19⋊C3)⋊#5997 |
| unambiguous semidirect product | (C19⋊C3)⋊(C3×#5997) |
| Fitting, socle | C3×C72×C19 ⋊ C3×C4 |
| derived, Hall | C72×C19 ⋊ C32×C4 |
| Hall | C3×C72×C19⋊C3 ⋊ C4 |
| Hall | C19⋊#5997 ⋊ C32 |
| Hall | C3×C19⋊C3 ⋊ #5997 |
| Sylow | C72 ⋊ C3×(C19⋊C3)⋊C4 |
| Sylow | C19 ⋊ C32×#5997 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C19⋊C3)⋊#5997 |
| commutator, hypocenter | C72×C19 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C19 | C3×C4 |
| prime radical | C3×C19⋊C3×C7⋊D7 | C2 |
| cosocle | C19×C7⋊D7 | C2×C32 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C3 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 798 |
378 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 993);