Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | #64418⋊(C5⋊D5) |
| Fitting, socle, Hall | C52×C72 ⋊ C2×D3 |
| derived, Hall | C52×#3862 ⋊ C22 |
| Hall | #3862 ⋊ C2×C5⋊D5 |
| Sylow | C72 ⋊ D3×C5⋊D5 |
| Sylow | C52 ⋊ #64418⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C52×#3862 | C22 |
| Fitting, socle | C52×C72 | C2×D3 |
| LCS | G ▷ C52×#3862 | |
| UCS | C1 | |
272 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^2,3,5^2,7^2|c^a=c^2,d^a=d^4,e^a=e^4,f^a=g,g^a=f,c^b=c^2,f^b=g^6,g^b=f^6,f^c=f^2,g^c=g^4259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 483);