Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5×C7 |
| direct product | C2×C52⋊#3862 |
| unambiguous semidirect product | (C2×C52)⋊#3862 |
| Fitting, socle, Hall | C2×C52×C72 ⋊ C3 |
| derived, Hall | C52×C72 ⋊ C2×C3 |
| Hall | C2×C72 ⋊ C52⋊C3 |
| Hall | C2×C52 ⋊ #3862 |
| Sylow | C72 ⋊ C2×C52⋊C3 |
| Sylow | C52 ⋊ C2×#3862 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C52⋊#3862 |
| commutator, hypocenter | C52×C72 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C72 | C3 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 ◁ C2 | |
80 conjugacy classes of subgroups.
822 conjugacy classes — view the full character table.
| maximal subgroup of | #28413165, #28413171, #28413173, … |
| maximal normal subgroup of | #28413165, #28413171, #28413173, … |
| maximal quotient of | C4×C52⋊#3862, C22×C52⋊#3862, C2×C52⋊#89205, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 138);