Finite Group DatabasebetaFinite Group Databasebeta| order | 2380 |
| isoclinism | isoclinic class of D7×D85 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D85 |
| unambiguous semidirect product | (C5×D7)⋊D17 |
| unambiguous semidirect product | (D7×C17)⋊D5 |
| Fitting, socle, derived, Hall | C5×C7×C17 ⋊ C22 |
| Hall | C7×C17 ⋊ C2×D5 |
| Hall | C5×C17 ⋊ C2×D7 |
| Hall | C5×C7 ⋊ C2×D17 |
| Sylow | C17 ⋊ D5×D7 |
| Sylow | C7 ⋊ C2×D85 |
| Sylow | C5 ⋊ D7×D17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C17 | C22 |
| LCS | G ▷ C5×C7×C17 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 595 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D425, C5×D7×D85, D7×C5⋊D85, … |
| maximal normal subgroup of | C5×D7×D85, C7×D7×D85, C11×D7×D85, … |
| maximal quotient of | D7×D425, C5×D7×D85, D7×C5⋊D85, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2380, 26);