Finite Group DatabasebetaFinite Group Databasebeta| order | 32288 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×#22549054 |
| derived, Sylow | C1009 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #16860937 |
| commutator, hypocenter | C1009 | C22×C8 |
| Frattini | C2 | C22×#16860937 |
| Fitting, socle, prime radical | C23×C1009 | C4 |
| cosocle | Dic1009 | C23 |
| LCS | G ▷ C1009 | |
| UCS | C1 ◁ C23 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32288 |
2048 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32288, 228);