Finite Group DatabasebetaFinite Group Databasebeta| order | 2380 |
| isoclinism | isoclinic class of D35 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C2 |
| direct product | C2×C17×D35 |
| unambiguous semidirect product | (C2×C5)⋊(D7×C17) |
| unambiguous semidirect product | (C2×C7)⋊(D5×C17) |
| Fitting, socle | C2×C5×C7×C17 ⋊ C2 |
| derived, Hall | C5×C7 ⋊ C22×C17 |
| Hall | C5×C7×C17 ⋊ C22 |
| Hall | C7×C17 ⋊ C2×D5 |
| Hall | C5×C17 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D5×C17 |
| Sylow | C5 ⋊ C2×D7×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | D35 |
| commutator, cosocle, hypocenter | C5×C7 | C22×C17 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C7×C17 | C2 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C2×C17 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1190 |
646 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C17×D175, D5×C17×D35, C2×C17×C5⋊D35, … |
| maximal normal subgroup of | C2×C5×C17×D35, C2×C7×C17×D35, C2×C11×C17×D35, … |
| maximal quotient of | C2×C17×D175, D5×C17×D35, C2×C17×C5⋊D35, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2380, 30);