Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C7 · Schur multiplier (H2) = C5 |
| direct product | C52×C7×D21 |
| unambiguous semidirect product | C3⋊(C52×C7×D7) |
| unambiguous semidirect product | C7⋊(C52×D3×C7) |
| Fitting, socle, Hall | C3×C52×C72 ⋊ C2 |
| derived | C3×C7 ⋊ C2×C52×C7 |
| Hall | C52×C72 ⋊ D3 |
| Hall | C3×C72 ⋊ C2×C52 |
| Hall | C3×C52 ⋊ C7×D7 |
| Sylow | C72 ⋊ C52×D3 |
| Sylow | C3 ⋊ C52×C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52×C7 | D21 |
| commutator, hypocenter | C3×C7 | C2×C52×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C72 | C2 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C52×C7 | |
176 conjugacy classes of subgroups.
2100 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D3×C7×D7, C52×D7×D21, C52×D21⋊D7, … |
| maximal normal subgroup of | C52×D3×C7×D7, C52×D7×D21, C52×D21⋊D7, … |
| maximal quotient of | C52×C7×Dic21, C2×C52×C7×D21, C52×C7×D63, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 148);