Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C49⋊#3874 |
| Fitting, Hall | C52×C49 ⋊ D3 |
| derived, Hall | C49×C52⋊C3 ⋊ C2 |
| Hall | C52⋊C3 ⋊ D49 |
| Sylow | C49 ⋊ #3874 |
| Sylow | C52 ⋊ D147 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C49×C52⋊C3 | C2 |
| Frattini | C7 | C7⋊#3874 |
| Fitting | C52×C49 | D3 |
| socle | C52×C7 | D21 |
| LCS | G ▷ C49×C52⋊C3 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,5^2,7|c^7=f^6,b^a=b^2,c^a=c^6f,d^a=d^2e,e^a=d^2e^3,f^a=f^6,d^b=d^2e^4,e^b=d^2e^2277 conjugacy classes — view the full character table.
| maximal subgroup of | #3874⋊D49, ((C5⋊D5)⋊C3)⋊D49, D49×#3874, … |
| maximal normal subgroup of | #3874⋊D49, ((C5⋊D5)⋊C3)⋊D49, D49×#3874, … |
| maximal quotient of | C49⋊#64470, C2×C49⋊#3874, C49⋊#90646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 15);