Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Hall | C52×C72 ⋊ D3 |
| derived, Hall | C52⋊#3862 ⋊ C2 |
| Sylow | C72 ⋊ #3874 |
| Sylow | C52 ⋊ #64418 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C52⋊#3862 | C2 |
| Fitting, socle | C52×C72 | D3 |
| LCS | G ▷ C52⋊#3862 | |
| UCS | C1 | |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5^2,7^2|b^a=b^2,d^a=cd^4,e^a=f,f^a=e,c^b=c^3d^3,d^b=c^4d,e^b=e^2,f^b=f^4258 conjugacy classes — view the full character table.
| maximal subgroup of | #28413344, #28413345, #28413350, … |
| maximal normal subgroup of | #28413344, #28413345, #28413350, … |
| maximal quotient of | #28413165, C2×#20301286, #36347818, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 109);