Finite Group DatabasebetaFinite Group Databasebeta| order | 7820 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C23 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×C23×D17 |
| unambiguous semidirect product | C17⋊(C22×C5×C23) |
| unambiguous semidirect product | (C2×C17)⋊(C2×C5×C23) |
| Fitting, socle | C2×C5×C17×C23 ⋊ C2 |
| derived, Sylow | C17 ⋊ C22×C5×C23 |
| Hall | C5×C17×C23 ⋊ C22 |
| Hall | C17×C23 ⋊ C22×C5 |
| Hall | C5×C17 ⋊ C22×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C23 | D17 |
| commutator, hypocenter | C17 | C22×C5×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C17×C23 | C2 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C5×C23 | |
40 conjugacy classes of subgroups.
2300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×C23×D17, C2×C3×C5×C23×D17, C2×C5×C23×D51 |
| maximal normal subgroup of | C2×C3×C5×C23×D17 |
| maximal quotient of | C5×D3×C23×D17, C2×C3×C5×C23×D17, C2×C5×C23×D51 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7820, 34);