Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C7⋊#3874 |
| unambiguous semidirect product | C7⋊(C7×#3874) |
| Fitting, socle, Hall | C52×C72 ⋊ D3 |
| derived | C7×C52⋊C3 ⋊ C2×C7 |
| Hall | C72×C52⋊C3 ⋊ C2 |
| Hall | C52⋊C3 ⋊ C7×D7 |
| Sylow | C72 ⋊ #3874 |
| Sylow | C52 ⋊ C7×D21 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C7⋊#3874 |
| commutator, hypocenter | C7×C52⋊C3 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C72 | D3 |
| LCS | G ▷ C7×C52⋊C3 | |
| UCS | C1 ◁ C7 | |
66 conjugacy classes of subgroups.
322 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#3874⋊D7, C7×((C5⋊D5)⋊C3)⋊D7, #28413342, … |
| maximal normal subgroup of | C7×#3874⋊D7, C7×((C5⋊D5)⋊C3)⋊D7, #28413342, … |
| maximal quotient of | C7×C7⋊#64470, C2×C7×C7⋊#3874, C7×C7⋊#90646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 107);