Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of #4245⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#4248⋊C3 |
| unambiguous semidirect product | #4248⋊C32 |
| unambiguous semidirect product | (C3×#4248)⋊C3 |
| Hall | C32×ΓL(1,𝔽8) ⋊ Q8 |
| Sylow | C7 ⋊ C32×Dic6 |
192 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | #72246906, C3×Dic6×AGL(1,𝔽7), #72246915, … |
| maximal normal subgroup of | #72246906, C3×Dic6×AGL(1,𝔽7), #72246915, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 607);