Finite Group DatabasebetaFinite Group Databasebeta| order | 32008 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#30630749 |
| unambiguous semidirect product | D4001⋊C4 |
| Fitting, socle | C2×C4001 ⋊ C4 |
| derived, Sylow | C4001 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #30630749 |
| commutator, hypocenter | C4001 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C4001 | C4 |
| prime radical | C2×D4001 | C2 |
| cosocle | D4001 | C22 |
| LCS | G ▷ C4001 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8002 |
2008 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32008, 14);