Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C52×C72 ⋊ C3×C4 |
| Hall | #19096680 ⋊ C3 |
| Hall | C52×#3861 ⋊ C4 |
| Hall | #3861 ⋊ #1043 |
| Sylow | C72 ⋊ C3×#1043 |
| Sylow | C52 ⋊ #5997⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C72 | C3×C4 |
| prime radical | C5⋊(C5⋊#64424) | C2 |
| cosocle | C5⋊(C5⋊(C7⋊D7)) | C2×C3 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 | |
224 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,5^2,7^2|a^2=c,d^a=d^2,e^a=e^2,f^a=f^5g^3,g^a=f^3g^2,f^b=f^2,g^b=g^2,d^c=d^4,e^c=e^4,f^c=f^6,g^c=g^6130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 442);