Finite Group DatabasebetaFinite Group Databasebeta| order | 33056 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×#22551925 |
| Fitting, socle | C22×C1033 ⋊ C8 |
| derived, Sylow | C1033 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #22551925 |
| commutator, hypocenter | C1033 | C22×C8 |
| Frattini | C1 | G |
| Fitting, socle | C22×C1033 | C8 |
| prime radical | C22×D1033 | C4 |
| cosocle | #16861757 | C23 |
| LCS | G ▷ C1033 | |
| UCS | C1 ◁ C22 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4132 |
548 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33056, 244);