Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D9⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×#92265 |
| Fitting | C4×#6900 ⋊ C2 |
| Sylow | #6900 ⋊ C2×C4 |
261 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #72219876, C4×#92265⋊C2, #72219888, … |
| maximal normal subgroup of | #72219876, C4×#92265⋊C2, #72219888, … |
| maximal quotient of | #72219962, AGL(1,𝔽5)×#92265 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1726);