Finite Group DatabasebetaFinite Group Databasebeta| order | 8628 |
| automorphism | Aut(G) order 6194904 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2157 |
| unambiguous semidirect product | C3⋊Dic719 |
| unambiguous semidirect product | C719⋊Dic3 |
| derived, Hall | C3×C719 ⋊ C4 |
| Sylow | C719 ⋊ Dic3 |
| Sylow | C3 ⋊ Dic719 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2157 |
| commutator, hypocenter | C3×C719 | C4 |
| Fitting, socle | C2×C3×C719 | C2 |
| LCS | G ▷ C3×C719 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,719,2|a^2=d,b^a=b^2,c^a=c^7182160 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic6471, C3⋊Dic2157, C3×Dic2157, … |
| maximal normal subgroup of | C3×Dic2157, Dic4314 |
| maximal quotient of | Dic6471, C3⋊Dic2157, C3×Dic2157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8628, 4);