Finite Group DatabasebetaFinite Group Databasebeta| order | 8428 |
| automorphism | Aut(G) order 7433496 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2107 |
| unambiguous semidirect product | C43⋊Dic49 |
| unambiguous semidirect product | C49⋊Dic43 |
| derived, Hall | C43×C49 ⋊ C4 |
| Sylow | C49 ⋊ Dic43 |
| Sylow | C43 ⋊ Dic49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2107 |
| commutator, hypocenter | C43×C49 | C4 |
| Frattini | C2×C7 | D301 |
| Fitting | C2×C43×C49 | C2 |
| socle | C2×C7×C43 | D7 |
| LCS | G ▷ C43×C49 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,43,2,7|a^2=d,b^7=e^6,b^a=b^6e,c^a=c^42,e^a=e^62110 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C43⋊C3)⋊Dic49, (C49⋊C3)⋊Dic43, #38760211, … |
| maximal normal subgroup of | (C43⋊C3)⋊Dic49, (C49⋊C3)⋊Dic43, #38760211, … |
| maximal quotient of | C3×Dic2107, Dic6321, Dic14749 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8428, 6);