Finite Group DatabasebetaFinite Group Databasebeta| order | 7820 |
| isoclinism | isoclinic class of #66772 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×#66772 |
| Fitting, socle, Hall | C5×C17×C23 ⋊ C4 |
| derived, Hall | C5×C17 ⋊ C4×C23 |
| Hall | C17×C23 ⋊ Dic5 |
| Hall | C5×C23 ⋊ #595 |
| Sylow | C17 ⋊ Dic5×C23 |
| Sylow | C5 ⋊ C23×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #66772 |
| commutator, hypocenter | C5×C17 | C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C23 | C4 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 ◁ C23 | |
24 conjugacy classes of subgroups.
644 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C23×#66772, C23×C3⋊#66772 |
| maximal normal subgroup of | C3×C23×#66772 |
| maximal quotient of | C3×C23×#66772, C23×C3⋊#66772 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7820, 22);