Finite Group DatabasebetaFinite Group Databasebeta| order | 32428 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C112 · Schur multiplier (H2) = C11 |
| direct product | C11×Dic67⋊C11 |
| unambiguous semidirect product | Dic67⋊C112 |
| unambiguous semidirect product | (C67⋊C11)⋊(C4×C11) |
| unambiguous semidirect product | (C11×Dic67)⋊C11 |
| derived, Sylow | C67 ⋊ C4×C112 |
| Hall | C11×C67⋊C11 ⋊ C4 |
| Hall | Dic67 ⋊ C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D67⋊C11 |
| commutator, hypocenter | C67 | C4×C112 |
| Frattini | C2 | C11×D67⋊C11 |
| Fitting, socle | C2×C11×C67 | C2×C11 |
| prime radical | C2×C11×C67⋊C11 | C2 |
| cosocle | C2×C67 | C2×C112 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C2×C11 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2948 |
550 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32428, 15);