Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C19 · Schur multiplier (H2) = C3 |
| direct product | C3×C19×#5997⋊C3 |
| unambiguous semidirect product | #5997⋊(C32×C19) |
| unambiguous semidirect product | (C3×#5997)⋊(C3×C19) |
| Fitting, socle | C3×C72×C19 ⋊ C3×C4 |
| derived, Sylow | C72 ⋊ C32×C4×C19 |
| Hall | C3×C19×#3861 ⋊ C4 |
| Hall | C19×#5997 ⋊ C32 |
| Hall | C72×C19 ⋊ C32×C4 |
| Hall | C3×#3861 ⋊ C4×C19 |
| Hall | #5997 ⋊ C32×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C19 | #5997⋊C3 |
| commutator, hypocenter | C72 | C32×C4×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C19 | C3×C4 |
| prime radical | C3×C19×#64424 | C2 |
| cosocle | C7⋊D7 | C2×C32×C19 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C19 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 798 |
912 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 998);