Finite Group DatabasebetaFinite Group Databasebeta| order | 7820 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D85⋊D23 |
| unambiguous semidirect product | D115⋊D17 |
| unambiguous semidirect product | D391⋊D5 |
| Fitting, socle, derived, Hall | C5×C17×C23 ⋊ C22 |
| Hall | C17×C23 ⋊ C2×D5 |
| Hall | C5×C23 ⋊ C2×D17 |
| Hall | C5×C17 ⋊ C2×D23 |
| Sylow | C23 ⋊ D5×D17 |
| Sylow | C17 ⋊ D5×D23 |
| Sylow | C5 ⋊ D17×D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C17×C23 | C22 |
| LCS | G ▷ C5×C17×C23 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,17,23|d^a=d^16,e^a=e^22,c^b=c^4,d^b=d^16524 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D85⋊D23, D391⋊D15, D115⋊D51, … |
| maximal normal subgroup of | C3×D85⋊D23 |
| maximal quotient of | C3×D85⋊D23, D391⋊D15, D115⋊D51, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7820, 28);