Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C43 · Schur multiplier (H2) = C43 |
| direct product | C3×C4×Dic32 |
| derived | C32 ⋊ C3×C43 |
| Sylow | C33 ⋊ C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C4 | D32 |
| commutator, hypocenter | C32 | C3×C43 |
| Frattini | C23 | C2×C3×D32 |
| Fitting | C22×C33×C4 | C22 |
| socle, prime radical | C23×C33 | C23 |
| cosocle | C23×C32 | C23×C3 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C22×C3×C4 | |
1410 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
432 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 24235);