Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| isoclinism | isoclinic class of C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5×C7 |
| direct product | C3×C52×C7⋊D7 |
| Fitting, socle, Hall | C3×C52×C72 ⋊ C2 |
| derived, Sylow | C72 ⋊ C2×C3×C52 |
| Hall | C52×C72 ⋊ C2×C3 |
| Hall | C3×C72 ⋊ C2×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C52 | C7⋊D7 |
| commutator, hypocenter | C72 | C2×C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C72 | C2 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C52 | |
320 conjugacy classes of subgroups.
1950 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C52×D72, C3×C52×#5997, C3×C5×D5×C7⋊D7, … |
| maximal normal subgroup of | C3×C52×D72, C3×C52×#5997, C3×C5×D5×C7⋊D7, … |
| maximal quotient of | C3×C52×C7⋊Dic7, C2×C3×C52×C7⋊D7, C52×C9×C7⋊D7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 140);