Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5×C7 |
| direct product | C52⋊C3×C7⋊D7 |
| Fitting, socle, derived, Hall | C52×C72 ⋊ C2×C3 |
| Hall | C72×C52⋊C3 ⋊ C2 |
| Hall | C52×C7⋊D7 ⋊ C3 |
| Sylow | C72 ⋊ C2×C52⋊C3 |
| Sylow | C52 ⋊ C3×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C72 | C2×C3 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
286 conjugacy classes — view the full character table.
| maximal subgroup of | C7⋊D7×#3874, #28413349, #28413352, … |
| maximal normal subgroup of | C7⋊D7×#3874, #28413349, #28413352, … |
| maximal quotient of | C52⋊C3×C7⋊Dic7, C2×C52⋊C3×C7⋊D7, C7⋊D7×C52⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 131);