Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C4×#1084 |
| derived, Sylow | H(3,𝔽3) ⋊ C22×C42 |
2739 conjugacy classes of subgroups; only the 957 normal subgroups are shown.
This group has 2739 conjugacy classes of subgroups — too many to draw. Only its 957 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, 20470);