Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
No aliases for this group.
| Fitting, socle, Hall | C52×C72 ⋊ Dic3 |
| derived, Hall | C72×C52⋊C3 ⋊ C4 |
| Hall | C52⋊C3 ⋊ #5997 |
| Sylow | C72 ⋊ #64470 |
| Sylow | C52 ⋊ C3⋊#5997 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C72×C52⋊C3 | C4 |
| Fitting, socle | C52×C72 | Dic3 |
| prime radical, cosocle | C52⋊C3×C7⋊D7 | C2 |
| LCS | G ▷ C72×C52⋊C3 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,7^2,5^2|a^2=b,c^a=c^2,d^a=d^3e^5,e^a=d^5e^4,f^a=f^2g,g^a=f^2g^3,d^b=d^6,e^b=e^6,f^c=f^2g^4,g^c=f^2g^2158 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 531);