Finite Group DatabasebetaFinite Group Databasebeta| order | 8428 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D43×D49 |
| unambiguous semidirect product | (C43×D49)⋊C2 |
| unambiguous semidirect product | (C49×D43)⋊C2 |
| unambiguous semidirect product | D2107⋊C2 |
| Fitting, derived, Hall | C43×C49 ⋊ C22 |
| Sylow | C49 ⋊ C2×D43 |
| Sylow | C43 ⋊ C2×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C43×C49 | C22 |
| Frattini | C7 | D7×D43 |
| socle | C7×C43 | C2×D7 |
| LCS | G ▷ C43×C49 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
598 conjugacy classes — view the full character table.
| maximal subgroup of | #27162348⋊C2, #27162347⋊C2, D43×D49⋊C3, … |
| maximal normal subgroup of | #27162348⋊C2, #27162347⋊C2, D43×D49⋊C3, … |
| maximal quotient of | C3×D43×D49, D43×D147, D49×D129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8428, 10);