Finite Group DatabasebetaFinite Group Databasebeta| order | 7525 |
| isoclinism | isoclinic class of C43⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C7 · Schur multiplier (H2) = C5 |
| direct product | C52×C43⋊C7 |
| unambiguous semidirect product | C43⋊(C52×C7) |
| unambiguous semidirect product | (C5×C43)⋊(C5×C7) |
| unambiguous semidirect product | (C52×C43)⋊C7 |
| Fitting, socle, Hall | C52×C43 ⋊ C7 |
| derived, Sylow | C43 ⋊ C52×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C43⋊C7 |
| commutator, hypocenter | C43 | C52×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C43 | C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C52 | |
32 conjugacy classes of subgroups.
325 conjugacy classes — view the full character table.
| maximal subgroup of | C52×D43⋊C7, C5×C5⋊(D43⋊C7), C5×D5×C43⋊C7, … |
| maximal normal subgroup of | C52×D43⋊C7, C5×C5⋊(D43⋊C7), C5×D5×C43⋊C7, … |
| maximal quotient of | C2×C52×C43⋊C7, C3×C52×C43⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7525, 4);