Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C7⋊#1039) |
| derived, Hall | C52×C72 ⋊ C3×C4 |
| Hall | C7⋊(C7⋊#1039) ⋊ C3 |
| Hall | C52×C7×ΓL(1,𝔽8) ⋊ C4 |
| Hall | C7×ΓL(1,𝔽8) ⋊ #1039 |
| Sylow | C72 ⋊ C3×#1039 |
| Sylow | C52 ⋊ ΓL(1,𝔽8)⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(C5⋊(ΓL(1,𝔽8)⋊D7)) |
| commutator, hypocenter | C52×C72 | C3×C4 |
| Fitting, socle, cosocle | C2×C52×C72 | C2×C3 |
| prime radical | C2×C52×C7×ΓL(1,𝔽8) | C2 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 ◁ C2 | |
240 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5^2,7^2,2|a^2=g,c^a=c^4,d^a=d^4,e^a=e^6,f^a=f^6,e^b=e^2884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 336);