Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | D47×#2544 |
| Fitting | C47×#2544 ⋊ C2 |
| Sylow | C47 ⋊ C2×#2544 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D47 |
| commutator, socle, cosocle | C23×C47 | C25 |
| Fitting | C47×#2544 | C2 |
| prime radical | C2×#127×D47 | C2 |
| hypercenter | #2544 | D47 |
| hypocenter | C47 | C2×#2544 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ #2544 | |
4174 conjugacy classes of subgroups.
950 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 340724);