Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊(C7⋊#64470) |
| derived, Hall | C72×C52⋊C3 ⋊ C4 |
| Hall | C52×C72 ⋊ Dic3 |
| Hall | C52⋊C3 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ #64470 |
| Sylow | C52 ⋊ C3⋊(C7⋊Dic7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊(C7⋊#3874) |
| commutator, hypocenter | C72×C52⋊C3 | C4 |
| Fitting, socle | C2×C52×C72 | D3 |
| prime radical, cosocle | C2×C72×C52⋊C3 | C2 |
| LCS | G ▷ C72×C52⋊C3 | |
| UCS | C1 ◁ C2 | |
180 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7^2,5^2,2|a^2=g,b^a=b^2,c^a=c^6,d^a=d^6,e^a=e^2f,f^a=e^2f^3,e^b=e^2f^4,f^b=e^2f^2554 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 343);