Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C23 |
| direct product | C22⋊C4×#1094 |
| Sylow | C22×C22⋊C4 ⋊ 3−1+2 |
878 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | #217×#1094, SL(2,ℤ/4)×#1094 |
| maximal quotient of | #217×#1094 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18227);