Finite Group DatabasebetaFinite Group Databasebeta| order | 9940 |
| isoclinism | isoclinic class of C71⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2 |
| direct product | C22×C5×C71⋊C7 |
| unambiguous semidirect product | (C22×C5×C71)⋊C7 |
| Fitting, socle, Hall | C22×C5×C71 ⋊ C7 |
| derived, Sylow | C71 ⋊ C22×C5×C7 |
| Hall | C5×C71 ⋊ C22×C7 |
| Hall | C22×C71 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | C71⋊C7 |
| commutator, cosocle, hypocenter | C71 | C22×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C71 | C7 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C22×C5 | |
40 conjugacy classes of subgroups.
340 conjugacy classes — view the full character table.
| maximal subgroup of | C5×A4×C71⋊C7, C2×C5×D3×C71⋊C7, C22×C3×C5×C71⋊C7 |
| maximal normal subgroup of | C5×A4×C71⋊C7, C22×C3×C5×C71⋊C7 |
| maximal quotient of | C2×C5×D3×C71⋊C7, C22×C3×C5×C71⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9940, 32);