Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C5 |
| direct product | C7×#11760384 |
| Fitting, socle, Hall | C52×C72 ⋊ C2×C3 |
| derived | C52×C7 ⋊ C2×C3×C7 |
| Hall | C72×C52⋊C3 ⋊ C2 |
| Hall | C7×C5⋊D35 ⋊ C3 |
| Hall | C52⋊C3 ⋊ C7×D7 |
| Sylow | C72 ⋊ (C5⋊D5)⋊C3 |
| Sylow | C52 ⋊ C3×C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #11760384 |
| commutator, hypocenter | C52×C7 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C72 | C2×C3 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C7 | |
66 conjugacy classes of subgroups.
301 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#3874⋊D7, #28413343, C7×D7×(C5⋊D5)⋊C3, … |
| maximal normal subgroup of | C7×#3874⋊D7, #28413343, C7×D7×(C5⋊D5)⋊C3, … |
| maximal quotient of | C7×#14523572, C2×C7×#11760384, C7×#15691245, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 113);