Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C9⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C22×C34 |
| direct product | C22×C3×C22⋊H(3,𝔽3) |
| Fitting | C24×C33 ⋊ C3 |
| Sylow | C24 ⋊ C3×H(3,𝔽3) |
1092 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | #72220499, C22×C3⋊((C3⋊D3)⋊A4), C3×#11722398, … |
| maximal normal subgroup of | #72220499, C22×C3⋊((C3⋊D3)⋊A4), C3×#11722398, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3051);