Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Fitting, derived, Hall | C52×C49 ⋊ C2×C3 |
| Hall | C49×C52⋊C3 ⋊ C2 |
| Hall | C5⋊D245 ⋊ C3 |
| Hall | C52⋊C3 ⋊ D49 |
| Sylow | C49 ⋊ (C5⋊D5)⋊C3 |
| Sylow | C52 ⋊ C3×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C52×C49 | C2×C3 |
| Frattini | C7 | #11760384 |
| socle | C52×C7 | C3×D7 |
| LCS | G ▷ C52×C49 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5^2,7^2|e^7=f^6,c^a=c^4,d^a=d^4,e^a=e^6f,f^a=f^6,c^b=cd,d^b=c^2d^3274 conjugacy classes — view the full character table.
| maximal subgroup of | #3874⋊D49, D49×(C5⋊D5)⋊C3, C2×#20301201, … |
| maximal normal subgroup of | #3874⋊D49, D49×(C5⋊D5)⋊C3, C2×#20301201, … |
| maximal quotient of | #28412873, C2×#20301201, #36347607, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 24);