Finite Group DatabasebetaFinite Group Databasebeta| order | 8620 |
| automorphism | Aut(G) order 7413200 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2155 |
| unambiguous semidirect product | C431⋊Dic5 |
| derived, Hall | C5×C431 ⋊ C4 |
| Sylow | C431 ⋊ Dic5 |
| Sylow | C5 ⋊ Dic431 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2155 |
| commutator, hypocenter | C5×C431 | C4 |
| Fitting, socle | C2×C5×C431 | C2 |
| LCS | G ▷ C5×C431 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,431,2|a^2=d,b^a=b^4,c^a=c^4302158 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2155, Dic6465, Dic4310, … |
| maximal normal subgroup of | C3×Dic2155, Dic4310 |
| maximal quotient of | C3×Dic2155, Dic6465, Dic15085 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8620, 6);