Finite Group DatabasebetaFinite Group Databasebeta| order | 8428 |
| isoclinism | isoclinic class of D43 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×Dic43 |
| derived, Sylow | C43 ⋊ C4×C49 |
| Hall | C43×C49 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C49 | D43 |
| commutator, hypocenter | C43 | C4×C49 |
| Frattini | C2×C7 | C7×D43 |
| Fitting | C2×C43×C49 | C2 |
| socle | C2×C7×C43 | C2×C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2×C49 | |
18 conjugacy classes of subgroups.
2254 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C49×(C43⋊C3)⋊C4, C49⋊C3×Dic43, #38760205, … |
| maximal normal subgroup of | C49×(C43⋊C3)⋊C4, C49⋊C3×Dic43, #38760205, … |
| maximal quotient of | C3×C49×Dic43, C49×Dic129 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8428, 5);