Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C7⋊#1044) |
| Fitting, socle, derived, Hall | C52×C72 ⋊ C3×C4 |
| Hall | C7⋊(C7⋊#1044) ⋊ C3 |
| Hall | C52×C7×ΓL(1,𝔽8) ⋊ C4 |
| Hall | C7×ΓL(1,𝔽8) ⋊ #1044 |
| Sylow | C72 ⋊ C3×#1044 |
| Sylow | C52 ⋊ ΓL(1,𝔽8)⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C72 | C3×C4 |
| prime radical | C7×ΓL(1,𝔽8)×C5⋊D5 | C2 |
| cosocle | C72×C5⋊D5 | C2×C3 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 | |
160 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,5^2,7^2|a^2=c,d^a=d^2,e^a=e^3,f^a=f^6,g^a=g^6,f^b=f^2,d^c=d^4,e^c=e^4254 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 449);