Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #11757735 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#11757735 |
| Fitting | C2×C3×AΣL(1,𝔽27) ⋊ C22 |
| derived, Sylow | C3×AΣL(1,𝔽27) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11757735 |
| commutator, cosocle, hypocenter | C3×AΣL(1,𝔽27) | C23 |
| Frattini | C32 | C2×D3×C3⋊D3 |
| Fitting | C2×C3×AΣL(1,𝔽27) | C22 |
| socle | C2×C32 | ((C3⋊D3)⋊C3)⋊C2 |
| LCS | G ▷ C3×AΣL(1,𝔽27) | |
| UCS | C1 ◁ C2 | |
1225 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 1225 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#11757735, C2×#72221953 |
| maximal normal subgroup of | C2×#72221953 |
| maximal quotient of | D3×#11757735 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2714);