Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #4178⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×#4178⋊C2 |
| Fitting | C4×#732 ⋊ C22 |
| derived, Sylow | #732 ⋊ C22×C4 |
294 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | C4×(#4178⋊C2)⋊C3, D4×#4178⋊C2, AGL(1,𝔽5)×#4178⋊C2 |
| maximal normal subgroup of | C4×(#4178⋊C2)⋊C3, D4×#4178⋊C2 |
| maximal quotient of | AGL(1,𝔽5)×#4178⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 866);