Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D5×C5⋊AGL(1,𝔽7) |
| unambiguous semidirect product | (C5×D5)⋊(C7×AGL(1,𝔽7)) |
| unambiguous semidirect product | (D5×ΓL(1,𝔽8))⋊(C7×D5) |
| unambiguous semidirect product | (D5×D35)⋊(C3×C7) |
| Fitting, socle, Hall | C52×C72 ⋊ C22×C3 |
| derived | C52×C7 ⋊ C22×C3×C7 |
| Hall | C7×D5×D35 ⋊ C3 |
| Hall | C52×C7×ΓL(1,𝔽8) ⋊ C22 |
| Hall | C7×ΓL(1,𝔽8) ⋊ D52 |
| Sylow | C72 ⋊ C3×D52 |
| Sylow | C52 ⋊ C2×C7×AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D5×C5⋊AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C52×C7 | C22×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C72 | C22×C3 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C7 | |
202 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
476 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 488);