Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| isoclinism | isoclinic class of C7⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×C7×C7⋊AGL(1,𝔽5) |
| Fitting, socle, Hall | C3×C52×C72 ⋊ C4 |
| derived | C5×C7 ⋊ C3×C4×C5×C7 |
| Hall | C52×C72 ⋊ C3×C4 |
| Hall | C3×C72 ⋊ C5×AGL(1,𝔽5) |
| Hall | C3×C52 ⋊ C7×Dic7 |
| Sylow | C72 ⋊ C3×C5×AGL(1,𝔽5) |
| Sylow | C52 ⋊ C3×C7×Dic7 |
164 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1785 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 638);