Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72×C25 · Schur multiplier (H2) = C7 |
| direct product | D3×C72×C25 |
| unambiguous semidirect product | C3⋊(C2×C72×C25) |
| Fitting, Hall | C3×C72×C25 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C72×C25 |
| Hall | C3×C72 ⋊ C2×C25 |
| Hall | C3×C25 ⋊ C2×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72×C25 | D3 |
| commutator, hypocenter | C3 | C2×C72×C25 |
| Frattini | C5 | C5×D3×C72 |
| Fitting | C3×C72×C25 | C2 |
| socle | C3×C5×C72 | C2×C5 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C72×C25 | |
120 conjugacy classes of subgroups.
3675 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C7×D7×C25, D3×C25×C7⋊D7, D3×C72×D25, … |
| maximal normal subgroup of | D3×C7×D7×C25, D3×C25×C7⋊D7, D3×C72×D25, … |
| maximal quotient of | C72×Dic3×C25, C2×D3×C72×C25, C72×D9×C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 69);