Finite Group DatabasebetaFinite Group Databasebeta| order | 32012 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D53×D151 |
| unambiguous semidirect product | (D53×C151)⋊C2 |
| unambiguous semidirect product | (C53×D151)⋊C2 |
| unambiguous semidirect product | D8003⋊C2 |
| Fitting, socle, derived, Hall | C53×C151 ⋊ C22 |
| Sylow | C151 ⋊ C2×D53 |
| Sylow | C53 ⋊ C2×D151 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C53×C151 | C22 |
| LCS | G ▷ C53×C151 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8003 |
2156 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32012, 8);