Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×(C5⋊AGL(1,𝔽7))⋊D7 |
| unambiguous semidirect product | (C5⋊AGL(1,𝔽7))⋊(C5×D7) |
| unambiguous semidirect product | (ΓL(1,𝔽8)⋊D7)⋊(C5×D5) |
| Fitting, socle, Hall | C52×C72 ⋊ C22×C3 |
| derived | C5×C72 ⋊ C22×C3×C5 |
| Hall | C5×D35⋊D7 ⋊ 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, hypercenter | C5 | (C5⋊AGL(1,𝔽7))⋊D7 |
| commutator, cosocle, hypocenter | C5×C72 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C72 | C22×C3 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C5 | |
208 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
395 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 422);