Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| isoclinism | isoclinic class of D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×D75 |
| unambiguous semidirect product | C3⋊(C72×D25) |
| unambiguous semidirect product | C25⋊(D3×C72) |
| Fitting, Hall | C3×C72×C25 ⋊ C2 |
| derived, Hall | C3×C25 ⋊ C2×C72 |
| Hall | C72×C25 ⋊ D3 |
| Hall | C3×C72 ⋊ D25 |
| Sylow | C25 ⋊ D3×C72 |
| Sylow | C3 ⋊ C72×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D75 |
| commutator, hypocenter | C3×C25 | C2×C72 |
| Frattini | C5 | C72×D15 |
| Fitting | C3×C72×C25 | C2 |
| socle | C3×C5×C72 | D5 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C72 | |
120 conjugacy classes of subgroups.
1911 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D7×D75, C7⋊D7×D75, D3×C72×D25, … |
| maximal normal subgroup of | C7×D7×D75, C7⋊D7×D75, D3×C72×D25, … |
| maximal quotient of | C72×Dic75, C2×C72×D75, C72×D225, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 72);