Finite Group DatabasebetaFinite Group Databasebeta| order | 8060 |
| automorphism | Aut(G) order 5803200 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2015 |
| unambiguous semidirect product | C31⋊Dic65 |
| derived, Hall | C5×C13×C31 ⋊ C4 |
| Hall | C13×C31 ⋊ Dic5 |
| Hall | C5×C31 ⋊ Dic13 |
| Hall | C5×C13 ⋊ Dic31 |
| Sylow | C31 ⋊ Dic65 |
| Sylow | C13 ⋊ Dic155 |
| Sylow | C5 ⋊ Dic403 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2015 |
| commutator, hypocenter | C5×C13×C31 | C4 |
| Fitting, socle | C2×C5×C13×C31 | C2 |
| LCS | G ▷ C5×C13×C31 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,13,31,2|a^2=e,b^a=b^4,c^a=c^12,d^a=d^302018 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2015, Dic6045, (C31⋊C3)⋊Dic65, … |
| maximal normal subgroup of | C3×Dic2015, (C31⋊C3)⋊Dic65, #37563759, … |
| maximal quotient of | C3×Dic2015, Dic6045, Dic14105 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8060, 9);