Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #3713 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×#63568 |
| Sylow | C33 ⋊ C2×#104 |
1074 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#10590393, C2×C3×#10591522, C2×C3×#10591510 |
| maximal normal subgroup of | C2×C3×#10590393, C2×C3×#10591522, C2×C3×#10591510 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 24202);