Finite Group DatabasebetaFinite Group Databasebeta| order | 5075 |
| isoclinism | isoclinic class of C29⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×C29⋊C7 |
| unambiguous semidirect product | C29⋊(C7×C25) |
| unambiguous semidirect product | (C25×C29)⋊C7 |
| Fitting, Hall | C25×C29 ⋊ C7 |
| derived, Sylow | C29 ⋊ C7×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | C29⋊C7 |
| commutator, hypocenter | C29 | C7×C25 |
| Frattini | C5 | C5×C29⋊C7 |
| Fitting | C25×C29 | C7 |
| socle | C5×C29 | C5×C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C25 | |
12 conjugacy classes of subgroups.
275 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C25×C29⋊C7, C7×C25×C29⋊C7 |
| maximal normal subgroup of | C3×C25×C29⋊C7, C7×C25×C29⋊C7 |
| maximal quotient of | C3×C25×C29⋊C7, C25×C29⋊C49, C7×C25×C29⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5075, 2);