Finite Group DatabasebetaFinite Group Databasebeta| order | 5075 |
| isoclinism | isoclinic class of C29⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C7 · Schur multiplier (H2) = C5 |
| direct product | C52×C29⋊C7 |
| unambiguous semidirect product | C29⋊(C52×C7) |
| unambiguous semidirect product | (C5×C29)⋊(C5×C7) |
| unambiguous semidirect product | (C52×C29)⋊C7 |
| Fitting, socle, Hall | C52×C29 ⋊ C7 |
| derived, Sylow | C29 ⋊ C52×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C29⋊C7 |
| commutator, hypocenter | C29 | C52×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C29 | C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C52 | |
32 conjugacy classes of subgroups.
275 conjugacy classes — view the full character table.
| maximal subgroup of | C52⋊C3×C29⋊C7, C3×C52×C29⋊C7, C52×C7×C29⋊C7 |
| maximal normal subgroup of | C52⋊C3×C29⋊C7, C3×C52×C29⋊C7, C52×C7×C29⋊C7 |
| maximal quotient of | C3×C52×C29⋊C7, C52×C29⋊C49, C52×C7×C29⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5075, 4);