Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | ΓL(1,𝔽8)×#611 |
| Fitting | C22×C7×C9 ⋊ C2×C3 |
| Hall | C9×ΓL(1,𝔽8) ⋊ D4 |
| Sylow | C7 ⋊ C3×#611 |
116 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 252 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#611, D4×D9×ΓL(1,𝔽8) |
| maximal normal subgroup of | AGL(1,𝔽7)×#611, D4×D9×ΓL(1,𝔽8) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 183);