Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| isoclinism | isoclinic class of D105 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×D105 |
| unambiguous semidirect product | C3⋊(C5×C7×D35) |
| unambiguous semidirect product | C5⋊(C5×C7×D21) |
| unambiguous semidirect product | C7⋊(C5×C7×D15) |
| Fitting, socle, Hall | C3×C52×C72 ⋊ C2 |
| derived | C3×C5×C7 ⋊ C2×C5×C7 |
| Hall | C52×C72 ⋊ D3 |
| Hall | C3×C72 ⋊ C5×D5 |
| Hall | C3×C52 ⋊ C7×D7 |
| Sylow | C72 ⋊ C5×D15 |
| Sylow | C52 ⋊ C7×D21 |
| Sylow | C3 ⋊ C5×C7×D35 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | D105 |
| commutator, hypocenter | C3×C5×C7 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C72 | C2 |
| LCS | G ▷ C3×C5×C7 | |
| UCS | C1 ◁ C5×C7 | |
128 conjugacy classes of subgroups.
1890 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C7×D7×D15, C5×D7×D105, C5×#15668837, … |
| maximal normal subgroup of | C5×C7×D7×D15, C5×D7×D105, C5×#15668837, … |
| maximal quotient of | C5×C7×Dic105, C2×C5×C7×D105, C5×C7×D315, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 151);