Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Fitting, socle, derived, Hall | C52×C72 ⋊ C2×C3 |
| Hall | C7×C7⋊(C52⋊C3) ⋊ C2 |
| Hall | C7×C5⋊D35 ⋊ C3 |
| Sylow | C72 ⋊ (C5⋊D5)⋊C3 |
| Sylow | C52 ⋊ D7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C72 | C2×C3 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5^2,7^2|c^a=c^4,d^a=d^4,f^a=f^6,c^b=cd,d^b=c^2d^3,e^b=e^2221 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 121);