Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of ((C3⋊D3)⋊C3)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×#6199 |
| derived, Sylow | H(3,𝔽3) ⋊ C24×C4 |
5515 conjugacy classes of subgroups; only the 1051 normal subgroups are shown.
This group has 5515 conjugacy classes of subgroups — too many to draw. Only its 1051 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30879);