Finite Group DatabasebetaFinite Group Databasebeta| order | 32428 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C67 · Schur multiplier (H2) = C2 |
| direct product | C2×C67×D121 |
| unambiguous semidirect product | C121⋊(C22×C67) |
| unambiguous semidirect product | (C2×C121)⋊(C2×C67) |
| Fitting | C2×C67×C121 ⋊ C2 |
| derived, Sylow | C121 ⋊ C22×C67 |
| Hall | C67×C121 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C67 | D121 |
| commutator, cosocle, hypocenter | C121 | C22×C67 |
| Frattini | C11 | C2×D11×C67 |
| Fitting | C2×C67×C121 | C2 |
| socle | C2×C11×C67 | D11 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C2×C67 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16214 |
8308 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32428, 12);