Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #6290 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×#88807 |
| Sylow | C33 ⋊ C22×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D3×C3⋊D3 |
| commutator | C2×C33 | C23×C4 |
| Frattini | C22 | C22×D3×C3⋊D3 |
| Fitting, socle, prime radical | C24×C33 | C22 |
| cosocle | C22×C33 | C24 |
| hypocenter | C33 | C22×C4⋊C4 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C24 | |
3452 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 44096);