Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C49⋊C3)⋊#1042 |
| unambiguous semidirect product | (C49⋊#1042)⋊C3 |
| Fitting, derived, Hall | C52×C49 ⋊ C3×C4 |
| Hall | C49⋊#1042 ⋊ C3 |
| Hall | C52×C49⋊C3 ⋊ C4 |
| Hall | C49⋊C3 ⋊ #1042 |
| Sylow | C49 ⋊ C3×#1042 |
| Sylow | C52 ⋊ (C49⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C52×C49 | C3×C4 |
| Frattini | C7 | ΓL(1,𝔽8)⋊#1042 |
| socle | C52×C7 | ΓL(1,𝔽8)⋊C4 |
| prime radical | C5×D5×C49⋊C3 | C2 |
| cosocle | C5×D5×C49 | C2×C3 |
| LCS | G ▷ C52×C49 | |
| UCS | C1 | |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,5^2,7^2|a^2=c,f^7=g^6,d^a=d^2,e^a=e^4,f^a=f^6g,g^a=g^6,f^b=f^2g^3,g^b=g^2,d^c=d^4199 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 111);