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 | C52×#3862 ⋊ C4 |
| Hall | #3862 ⋊ #1043 |
| Sylow | C72 ⋊ C3⋊#1043 |
| Sylow | C52 ⋊ #10596885 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C52×#3862 | C4 |
| Fitting, socle | C52×C72 | Dic3 |
| prime radical, cosocle | C5⋊(C5⋊#64425) | C2 |
| LCS | G ▷ C52×#3862 | |
| UCS | C1 | |
144 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5^2,7^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^2,f^a=g,g^a=f^6,d^b=d^4,e^b=e^4,f^b=f^6,g^b=g^6,f^c=f^2,g^c=g^4124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 441);