Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | (ΓL(1,𝔽8)⋊D7)⋊(C5⋊D5) |
| Fitting, socle, derived, Hall | C52×C72 ⋊ C22×C3 |
| Hall | (C7⋊D7)⋊(C5⋊D5) ⋊ C3 |
| Hall | C52×C7×ΓL(1,𝔽8) ⋊ C22 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C2×C5⋊D5 |
| Sylow | C72 ⋊ C2×C3×C5⋊D5 |
| Sylow | C52 ⋊ D7×AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C72 | C22×C3 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 | |
336 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 73 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|d^a=d^4,e^a=e^4,f^a=f^6,f^b=f^6,g^b=g^6,f^c=f^2299 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 480);