Finite Group DatabasebetaFinite Group Databasebeta| order | 10220 |
| automorphism | Aut(G) order 8830080 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2555 |
| unambiguous semidirect product | C7⋊Dic365 |
| derived, Hall | C5×C7×C73 ⋊ C4 |
| Hall | C7×C73 ⋊ Dic5 |
| Hall | C5×C73 ⋊ Dic7 |
| Sylow | C73 ⋊ Dic35 |
| Hall | C5×C7 ⋊ Dic73 |
| Sylow | C7 ⋊ Dic365 |
| Sylow | C5 ⋊ Dic511 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2555 |
| commutator, hypocenter | C5×C7×C73 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C5×C7×C73 | C2 |
| LCS | G ▷ C5×C7×C73 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,7,73,2|a^2=e,b^a=b^4,c^a=c^6,d^a=d^722558 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2555, Dic7665, #44501282, … |
| maximal normal subgroup of | C3×Dic2555, #44501282, ΓL(1,𝔽8)⋊Dic365, … |
| maximal quotient of | C3×Dic2555, Dic7665, Dic12775 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10220, 8);