Finite Group DatabasebetaFinite Group Databasebeta| order | 32288 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C8×#16860937 |
| Fitting | C8×C1009 ⋊ C4 |
| derived, Sylow | C1009 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #16860937 |
| commutator, hypocenter | C1009 | C4×C8 |
| Frattini | C4 | C2×#16860937 |
| Fitting | C8×C1009 | C4 |
| socle | C2×C1009 | C42 |
| prime radical | C2×D1009 | C2×C4 |
| cosocle | C4×D1009 | C22 |
| LCS | G ▷ C1009 | |
| UCS | C1 ◁ C8 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8072 |
2048 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32288, 198);