Finite Group DatabasebetaFinite Group Databasebeta| order | 8428 |
| automorphism | Aut(G) order 7433496 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4214 |
| direct product | C2×D2107 |
| unambiguous semidirect product | (C2×C43)⋊D49 |
| unambiguous semidirect product | (C2×C49)⋊D43 |
| Fitting | C2×C43×C49 ⋊ C2 |
| derived, Hall | C43×C49 ⋊ C22 |
| Sylow | C49 ⋊ C2×D43 |
| Sylow | C43 ⋊ C2×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2107 |
| commutator, hypocenter | C43×C49 | C22 |
| Frattini | C7 | C2×D301 |
| Fitting | C2×C43×C49 | C2 |
| socle | C2×C7×C43 | D7 |
| LCS | G ▷ C43×C49 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
2110 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#27162354, C2×#27162353, C2×(C49⋊C3)⋊D43, … |
| maximal normal subgroup of | C2×#27162354, C2×#27162353, C2×(C49⋊C3)⋊D43, … |
| maximal quotient of | D3×D2107, C2×C3×D2107, C2×D6321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8428, 13);