Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210×C4 |
| direct product | C2×#20247026 |
| Fitting | C22×#121×C47 ⋊ C2 |
| Sylow | C47 ⋊ C2×#2433 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D47 |
| commutator, cosocle | C23×C47 | C25 |
| Frattini | C23 | C24×D47 |
| Fitting | C22×#121×C47 | C2 |
| socle | C24×C47 | C24 |
| hypercenter | C22×#121 | D47 |
| hypocenter | C47 | C2×#2433 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C24 ◁ C22×#121 | |
9422 conjugacy classes of subgroups.
1364 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 337390);