Finite Group DatabasebetaFinite Group Databasebeta| order | 8420 |
| automorphism | Aut(G) order 7072800 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2105 |
| derived, Hall | C5×C421 ⋊ C4 |
| Sylow | C421 ⋊ Dic5 |
| Sylow | C5 ⋊ Dic421 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2105 |
| commutator, hypocenter | C5×C421 | C4 |
| Fitting, socle | C2×C5×C421 | C2 |
| LCS | G ▷ C5×C421 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,421,2|a^2=d,b^a=b^4,c^a=c^4202108 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2105, Dic6315, Dic2105⋊C3, … |
| maximal normal subgroup of | C3×Dic2105, Dic2105⋊C3, Dic4210 |
| maximal quotient of | C3×Dic2105, Dic6315, Dic14735 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8420, 6);