Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C9 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×A4×C27⋊C3 |
| Fitting | C23×C27⋊C3 ⋊ C3 |
| Sylow | C23 ⋊ C3×C27⋊C3 |
288 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72229223, C2×A4×#6875, C2×A4⋊(D27⋊C3) |
| maximal normal subgroup of | C2×A4×#6875, C2×A4⋊(D27⋊C3) |
| maximal quotient of | C2×#72229223 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2776);