Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C72 · Schur multiplier (H2) = C7 |
| direct product | C5×C72×D15 |
| unambiguous semidirect product | C3⋊(C5×C72×D5) |
| unambiguous semidirect product | C5⋊(C5×D3×C72) |
| Fitting, socle, Hall | C3×C52×C72 ⋊ C2 |
| derived | C3×C5 ⋊ C2×C5×C72 |
| Hall | C52×C72 ⋊ D3 |
| Hall | C3×C72 ⋊ C5×D5 |
| Hall | C3×C52 ⋊ C2×C72 |
| Sylow | C52 ⋊ D3×C72 |
| Sylow | C3 ⋊ C5×C72×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C72 | D15 |
| commutator, hypocenter | C3×C5 | C2×C5×C72 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C72 | C2 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C5×C72 | |
200 conjugacy classes of subgroups.
2205 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C7×D7×D15, C5×D15×C7⋊D7, C5×D3×C72×D5, … |
| maximal normal subgroup of | C5×C7×D7×D15, C5×D15×C7⋊D7, C5×D3×C72×D5, … |
| maximal quotient of | C5×C72×Dic15, C2×C5×C72×D15, C5×C72×D45, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 150);