Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D3×#1088⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| Fitting, Sylow | C3×H(3,𝔽3) ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle | C3×#272 | C23 |
| Frattini | C3 | D3×GO+(4,𝔽2) |
| Fitting, hypocenter | C3×H(3,𝔽3) | C2×D4 |
| socle | C32 | C2×GO+(4,𝔽2) |
| LCS | G ▷ C3×#272 ▷ C3×H(3,𝔽3) | |
| UCS | C1 | |
338 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 31 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
39 conjugacy classes — view the full character table.
| maximal subgroup of | #72228602, D3×(((C3⋊D3)⋊C3)⋊C2)⋊D3, #72259834 |
| maximal quotient of | D3×(((C3⋊D3)⋊C3)⋊C2)⋊D3, #72259834, #72260000 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2909);