Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C3 |
| direct product | Q8×#638⋊C3 |
| Fitting | C22×Q8×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ D4×Q8 |
1136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
155 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 19724);