Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3×#4174⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| Fitting, derived, Sylow | C3×AΣL(1,𝔽27) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×AΣL(1,𝔽27) | C23 |
| Frattini | C32 | D33 |
| socle | C32 | C2×((C3⋊D3)⋊C3)⋊C2 |
| LCS | G ▷ C3×AΣL(1,𝔽27) | |
| UCS | C1 | |
691 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 691 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 18 |
51 conjugacy classes — view the full character table.
| maximal subgroup of | #72214626, #72244021, D3×#92280⋊C2, … |
| maximal normal subgroup of | D3×(#4174⋊C2)⋊C3, C3×D3×#4174⋊C2 |
| maximal quotient of | D3×#11757735, C3×D3×#4174⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2344);