Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C22×C8×#272 |
| Fitting | C22×C8×H(3,𝔽3) ⋊ C2 |
| derived, Sylow | H(3,𝔽3) ⋊ C23×C8 |
1859 conjugacy classes of subgroups; only the 397 normal subgroups are shown.
This group has 1859 conjugacy classes of subgroups — too many to draw. Only its 397 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, 20375);