Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊(C3⋊((C3⋊D3)⋊C3)) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C34 |
| direct product | C22×C3⋊(C3⋊((C3⋊D3)⋊C3)) |
| Fitting | C22×C32×H(3,𝔽3) ⋊ C2 |
| derived | C34 ⋊ C23×C3 |
| Sylow | C32×H(3,𝔽3) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊(C3⋊((C3⋊D3)⋊C3)) |
| commutator, cosocle, hypocenter | C34 | C23×C3 |
| Frattini | C3 | C22×C3×C3⋊(C3⋊D3) |
| Fitting | C22×C32×H(3,𝔽3) | C2 |
| socle | C22×C33 | C3×D3 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C22 | |
3204 conjugacy classes of subgroups; only the 412 normal subgroups are shown.
This group has 3204 conjugacy classes of subgroups — too many to draw. Only its 412 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C3⋊D3×(C3⋊D3)⋊C3, C22×((C3⋊D3)⋊C3)⋊(C3⋊D3), C22×#13091503, … |
| maximal normal subgroup of | C22×C3⋊D3×(C3⋊D3)⋊C3, C22×((C3⋊D3)⋊C3)⋊(C3⋊D3), C22×#13091503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3768);