Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C47 · Schur multiplier (H2) = C24 |
| direct product | C47×#32700 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C47 | #2760 |
| commutator, Frattini, cosocle | C24 | C24×C47 |
| prime radical | C47×#2021 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C47 ◁ C24×C47 ◁ G | |
778 conjugacy classes of subgroups.
1598 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 25688);