Finite Group DatabasebetaFinite Group Databasebeta| order | 32008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D4001 |
| Fitting | C22×C4001 ⋊ C2 |
| Sylow | C4001 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D4001 |
| commutator, socle, cosocle | C2×C4001 | C22 |
| Fitting | C22×C4001 | C2 |
| hypercenter | C22 | D4001 |
| hypocenter | C4001 | D4 |
| LCS | G ▷ C2×C4001 ▷ C4001 | |
| UCS | C1 ◁ C2 ◁ C22 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16004 |
Polycyclic presentation:
2^3,4001|b^a=bc,d^b=d^40008005 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32008, 9);