Finite Group DatabasebetaFinite Group Databasebeta| order | 27580 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C5⋊(D197⋊C7) |
| unambiguous semidirect product | (C2×C5)⋊(D197⋊C7) |
| unambiguous semidirect product | (C2×C197⋊C7)⋊D5 |
| unambiguous semidirect product | (C2×D985)⋊C7 |
| Fitting, socle | C2×C5×C197 ⋊ C2×C7 |
| derived, Hall | C5×C197 ⋊ C22×C7 |
| Hall | C5×C197⋊C7 ⋊ C22 |
| Hall | C2×D985 ⋊ C7 |
| Hall | C197⋊C7 ⋊ C2×D5 |
| Sylow | C197 ⋊ C2×C7×D5 |
| Sylow | C5 ⋊ C2×D197⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊(D197⋊C7) |
| commutator, cosocle, hypocenter | C5×C197 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C197 | C2×C7 |
| LCS | G ▷ C5×C197 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1970 |
196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27580, 22);