Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊((C3⋊D3)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C33 |
| direct product | C2×C3×C3⋊((C3⋊Dic3)⋊C3) |
| unambiguous semidirect product | (C2×C3)⋊(C3×(C3⋊Dic3)⋊C3) |
| derived | C33 ⋊ C2×C32×C4 |
| Sylow | C32×H(3,𝔽3) ⋊ C2×C4 |
1521 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 1521 conjugacy classes of subgroups — too many to draw. Only its 238 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3344);