Finite Group DatabasebetaFinite Group Databasebeta| order | 7820 |
| automorphism | Aut(G) order 5505280 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1955 |
| unambiguous semidirect product | C23⋊Dic85 |
| derived, Hall | C5×C17×C23 ⋊ C4 |
| Hall | C17×C23 ⋊ Dic5 |
| Hall | C5×C23 ⋊ Dic17 |
| Hall | C5×C17 ⋊ Dic23 |
| Sylow | C23 ⋊ Dic85 |
| Sylow | C17 ⋊ Dic115 |
| Sylow | C5 ⋊ Dic391 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1955 |
| commutator, hypocenter | C5×C17×C23 | C4 |
| Fitting, socle | C2×C5×C17×C23 | C2 |
| LCS | G ▷ C5×C17×C23 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,17,23,2|a^2=e,b^a=b^4,c^a=c^16,d^a=d^221958 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic1955, Dic5865, Dic3910, … |
| maximal normal subgroup of | C3×Dic1955, Dic3910 |
| maximal quotient of | C3×Dic1955, Dic5865, Dic13685 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7820, 8);