Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| isoclinism | isoclinic class of C5⋊(C7⋊D7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C7 |
| direct product | C3×C5×C5⋊(C7⋊D7) |
| unambiguous semidirect product | C5⋊(C3×C5×C7⋊D7) |
| Fitting, socle, Hall | C3×C52×C72 ⋊ C2 |
| derived | C5×C72 ⋊ C2×C3×C5 |
| Hall | C52×C72 ⋊ C2×C3 |
| Hall | C3×C72 ⋊ C5×D5 |
| Hall | C3×C52 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ C3×C5×D5 |
| Sylow | C52 ⋊ C3×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C5⋊(C7⋊D7) |
| commutator, hypocenter | C5×C72 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C72 | C2 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C3×C5 | |
200 conjugacy classes of subgroups.
1860 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 143);