Finite Group DatabasebetaFinite Group Databasebeta| order | 7100 |
| isoclinism | isoclinic class of C71⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C22×C5×C71⋊C5 |
| unambiguous semidirect product | (C22×C71)⋊C52 |
| unambiguous semidirect product | (C22×C5×C71)⋊C5 |
| Fitting, socle | C22×C5×C71 ⋊ C5 |
| derived, Sylow | C71 ⋊ C22×C52 |
| Hall | C22×C71 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | C71⋊C5 |
| commutator, hypocenter | C71 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C71 | C5 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C22×C5 | |
80 conjugacy classes of subgroups.
380 conjugacy classes — view the full character table.
| maximal subgroup of | C5×A4×C71⋊C5, C2×C5×D3×C71⋊C5, C22×C3×C5×C71⋊C5 |
| maximal normal subgroup of | C5×A4×C71⋊C5, C22×C3×C5×C71⋊C5 |
| maximal quotient of | C2×C5×D3×C71⋊C5, C22×C3×C5×C71⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7100, 33);