Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
No aliases for this group.
| derived, Hall | C52×C72 ⋊ C3×C4 |
| Hall | C7⋊(C7⋊#1039) ⋊ C3 |
| Hall | C7×C7⋊(C52⋊C3) ⋊ C4 |
| Sylow | C72 ⋊ #1039⋊C3 |
| Sylow | C52 ⋊ ΓL(1,𝔽8)⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #20301295 |
| commutator, hypocenter | C52×C72 | C3×C4 |
| Fitting, socle, cosocle | C2×C52×C72 | C2×C3 |
| prime radical | C2×C7×C7⋊(C52⋊C3) | C2 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 ◁ C2 | |
120 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,c^b=cd,d^b=c^2d^3,e^b=e^2436 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 353);