Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #625 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29 |
| direct product | C22×C3×#3798 |
| Sylow | C33 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C4 | D32 |
| commutator, cosocle | C2×C32 | C25×C3 |
| Frattini | C2 | C23×C3×D32 |
| Fitting | C22×C33×C4 | C22 |
| socle | C23×C33 | C23 |
| hypocenter | C32 | C22×C3×#41 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C22×C3×C4 | |
4322 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47598);