Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of (C3⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C8 · Schur multiplier (H2) = C26×C3 |
| direct product | C23×(C3⋊(C3⋊C8))⋊C3 |
| derived | C32 ⋊ C23×C3×C8 |
| Sylow | H(3,𝔽3) ⋊ C23×C8 |
1419 conjugacy classes of subgroups; only the 692 normal subgroups are shown.
This group has 1419 conjugacy classes of subgroups — too many to draw. Only its 692 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, 19610);