Finite Group DatabasebetaFinite Group Databasebeta| order | 33568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×#22554218 |
| Fitting, socle | C22×C1049 ⋊ C8 |
| derived, Sylow | C1049 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #22554218 |
| commutator, hypocenter | C1049 | C22×C8 |
| Frattini | C1 | G |
| Fitting, socle | C22×C1049 | C8 |
| prime radical | C22×D1049 | C4 |
| cosocle | #16862310 | C23 |
| LCS | G ▷ C1049 | |
| UCS | C1 ◁ C22 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4196 |
556 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33568, 244);