Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C32 |
| direct product | C2×#11722577 |
| Fitting | C2×C32×H(5,𝔽2) ⋊ C3 |
| Sylow | C2×H(5,𝔽2) ⋊ H(3,𝔽3) |
1213 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 1213 conjugacy classes of subgroups — too many to draw. Only its 169 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
182 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72220368, C2×#10593663⋊C3, C2×#13164635, … |
| maximal normal subgroup of | C2×#72220368, C2×#10593663⋊C3, C2×#13164635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30922);