Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of C3⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215×C33 |
| direct product | C25×C3⋊(C3⋊D3) |
| Fitting, socle | C25×C33 ⋊ C2 |
| derived, Sylow | C33 ⋊ C26 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | C3⋊(C3⋊D3) |
| commutator, cosocle, hypocenter | C33 | C26 |
| Frattini | C1 | G |
| Fitting, socle | C25×C33 | C2 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C25 | |
79100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47935);