Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of (C3⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C16 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×(C3⋊(C3⋊C16))⋊C3 |
| derived | C32 ⋊ C22×C3×C16 |
| Sylow | H(3,𝔽3) ⋊ C22×C16 |
419 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 419 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 9173);