Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3×C3⋊(C3⋊(C3⋊D3)) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C36 |
No aliases for this group.
| derived, Sylow | C35 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×C3⋊(C3⋊(C3⋊D3)) |
| commutator, hypocenter | C35 | C2×C4 |
| Fitting, socle, cosocle | C2×C35 | C22 |
| prime radical | C2×C3⋊(C3⋊(C3⋊(C3⋊D3))) | C2 |
| LCS | G ▷ C35 | |
| UCS | C1 ◁ C2 | |
8992 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
2^3,3^5|a^2=c,b^2=c,h^a=h^2,d^b=d^2,e^b=e^2,f^b=f^2,g^b=g^2252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3823);