Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #1043⋊(C49⋊C3) |
| Fitting, derived, Hall | C52×C49 ⋊ C3×C4 |
| Hall | C49×#1043 ⋊ C3 |
| Hall | C52⋊(C49⋊C3) ⋊ C4 |
| Hall | #1043 ⋊ C49⋊C3 |
| Sylow | C49 ⋊ #1043⋊C3 |
| Sylow | C52 ⋊ C4×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C52×C49 | C3×C4 |
| Frattini | C7 | #1043⋊ΓL(1,𝔽8) |
| socle | C52×C7 | C4×ΓL(1,𝔽8) |
| prime radical | (C5⋊D5)⋊(C49⋊C3) | C2 |
| cosocle | C49×C5⋊D5 | C2×C3 |
| LCS | G ▷ C52×C49 | |
| UCS | C1 | |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,5^2,7^2|a^2=c,f^7=g^2,d^a=d^3,e^a=e^3,d^b=de^2,e^b=de^3,f^b=f^2g,g^b=g^2,d^c=d^4,e^c=e^4174 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 123);