Finite Group DatabasebetaFinite Group Databasebeta| order | 10620 |
| automorphism | Aut(G) order 7391520 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2655 |
| unambiguous semidirect product | C9⋊Dic295 |
| unambiguous semidirect product | C59⋊Dic45 |
| derived, Hall | C5×C9×C59 ⋊ C4 |
| Hall | C9×C59 ⋊ Dic5 |
| Hall | C5×C59 ⋊ Dic9 |
| Sylow | C59 ⋊ Dic45 |
| Hall | C5×C9 ⋊ Dic59 |
| Sylow | C9 ⋊ Dic295 |
| Sylow | C5 ⋊ Dic531 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2655 |
| commutator, hypocenter | C5×C9×C59 | C4 |
| Frattini | C2×C3 | D885 |
| Fitting, cosocle | C2×C5×C9×C59 | C2 |
| socle, prime radical | C2×C3×C5×C59 | D3 |
| LCS | G ▷ C5×C9×C59 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,59,2,3|a^2=e,b^3=f^2,b^a=b^2f,c^a=c^4,d^a=d^58,f^a=f^22658 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic5310, Dic7965, Dic13275 |
| maximal normal subgroup of | Dic5310 |
| maximal quotient of | Dic7965, Dic13275 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10620, 8);