Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| isoclinism | isoclinic class of #3874 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×#3874 |
| Fitting, socle, Hall | C52×C72 ⋊ D3 |
| derived, Hall | C52⋊C3 ⋊ C2×C72 |
| Hall | C72×C52⋊C3 ⋊ C2 |
| Sylow | C52 ⋊ D3×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | #3874 |
| commutator, hypocenter | C52⋊C3 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C52×C72 | D3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C72 | |
120 conjugacy classes of subgroups.
637 conjugacy classes — view the full character table.
| maximal subgroup of | C72×#3874⋊C2, C7×#3874⋊D7, #3874⋊(C7⋊D7), … |
| maximal normal subgroup of | C72×#3874⋊C2, C7×#3874⋊D7, #3874⋊(C7⋊D7), … |
| maximal quotient of | C72×#64470, C2×C72×#3874, C72×#90646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 106);