Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊(C3⋊((C3⋊D3)⋊C3)) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C34 |
| direct product | C2×C3⋊(C3⋊((C3⋊Dic3)⋊C3)) |
| unambiguous semidirect product | (C2×C3)⋊(C3⋊((C3⋊Dic3)⋊C3)) |
| derived | C34 ⋊ C2×C3×C4 |
| Sylow | C32×H(3,𝔽3) ⋊ C2×C4 |
1972 conjugacy classes of subgroups; only the 396 normal subgroups are shown.
This group has 1972 conjugacy classes of subgroups — too many to draw. Only its 396 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 648 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3391);