Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C7 |
| direct product | C3×C7⋊D175 |
| unambiguous semidirect product | C25⋊(C3×C7⋊D7) |
| Fitting, Hall | C3×C72×C25 ⋊ C2 |
| derived, Hall | C72×C25 ⋊ C2×C3 |
| Hall | C3×C72 ⋊ D25 |
| Hall | C3×C25 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ C3×D25 |
| Sylow | C25 ⋊ C3×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C7⋊D175 |
| commutator, hypocenter | C72×C25 | C2×C3 |
| Frattini | C5 | C3×C5⋊(C7⋊D7) |
| Fitting | C3×C72×C25 | C2 |
| socle | C3×C5×C72 | D5 |
| LCS | G ▷ C72×C25 | |
| UCS | C1 ◁ C3 | |
120 conjugacy classes of subgroups.
1842 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#19096644, C3×D25×C7⋊D7, C3×D7×D175, … |
| maximal normal subgroup of | C3×#19096644, C3×D25×C7⋊D7, C3×D7×D175, … |
| maximal quotient of | C3×C7⋊Dic175, C2×C3×C7⋊D175, C9×C7⋊D175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 68);