Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×C4×#272 |
| Fitting | C23×C4×H(3,𝔽3) ⋊ C2 |
| derived, Sylow | H(3,𝔽3) ⋊ C24×C4 |
7491 conjugacy classes of subgroups; only the 1389 normal subgroups are shown.
This group has 7491 conjugacy classes of subgroups — too many to draw. Only its 1389 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 31039);