Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#13183527 |
| derived, Hall | #89205 ⋊ C4×C19 |
| Hall | C19×#89205 ⋊ C4 |
| Hall | C72×C19 ⋊ Dic9 |
| Sylow | C72 ⋊ C19×Dic9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | #11725071 |
| commutator, hypocenter | #89205 | C4×C19 |
| Frattini | C2×C3 | C19×#64418 |
| Fitting, socle, prime radical | C2×C3×C72×C19 | D3 |
| cosocle | C2×#89205 | C2×C19 |
| LCS | G ▷ #89205 | |
| UCS | C1 ◁ C2×C19 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4788 |
1482 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 314);