Finite Group DatabasebetaFinite Group Databasebeta| order | 32428 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D67×D121 |
| unambiguous semidirect product | (C67×D121)⋊C2 |
| unambiguous semidirect product | (C121×D67)⋊C2 |
| unambiguous semidirect product | D8107⋊C2 |
| Fitting, derived, Hall | C67×C121 ⋊ C22 |
| Sylow | C121 ⋊ C2×D67 |
| Sylow | C67 ⋊ C2×D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C67×C121 | C22 |
| Frattini | C11 | D11×D67 |
| socle | C11×C67 | C2×D11 |
| LCS | G ▷ C67×C121 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8107 |
2170 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32428, 10);