Finite Group DatabasebetaFinite Group Databasebeta| order | 32008 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×D4001 |
| Fitting | C4×C4001 ⋊ C2 |
| derived, Sylow | C4001 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D4001 |
| commutator, hypocenter | C4001 | C2×C4 |
| Frattini | C2 | C2×D4001 |
| Fitting | C4×C4001 | C2 |
| socle, cosocle | C2×C4001 | C22 |
| prime radical | C2×D4001 | C2 |
| LCS | G ▷ C4001 | |
| UCS | C1 ◁ C4 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16004 |
8008 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32008, 7);