Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8×C47 · Schur multiplier (H2) = C29 |
| direct product | C2×C47×#3407 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C47 | C24 |
| commutator | C2 | C24×C8×C47 |
| Frattini, cosocle | C8 | C25×C47 |
| socle | C22×C47 | C23×C8 |
| prime radical | C22×#41×C47 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C47 ◁ G | |
2074 conjugacy classes of subgroups.
6392 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 55611);