Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of D9×AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | Dic9×AGL(1,𝔽7) |
| unambiguous semidirect product | D7⋊(C3×Dic9) |
| unambiguous semidirect product | (C9×AGL(1,𝔽7))⋊C4 |
| derived | C7×C9 ⋊ C2×C3×C4 |
| Hall | C9×ΓL(1,𝔽8) ⋊ C2×C4 |
| Sylow | C7 ⋊ C2×C3×Dic9 |
116 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 252 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D9×AGL(1,𝔽7), AGL(1,𝔽7)×#611 |
| maximal normal subgroup of | C4×D9×AGL(1,𝔽7), AGL(1,𝔽7)×#611 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 109);