Finite Group DatabasebetaFinite Group Databasebeta| order | 32428 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D737 |
| unambiguous semidirect product | (C11×D11)⋊D67 |
| unambiguous semidirect product | (D11×C67)⋊D11 |
| Fitting, socle, derived, Hall | C112×C67 ⋊ C22 |
| Sylow | C112 ⋊ C2×D67 |
| Sylow | C67 ⋊ D112 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C67 | C22 |
| LCS | G ▷ C112×C67 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1474 |
2590 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32428, 34);