Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #157⋊(C3⋊(C3⋊D3)) |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C33 |
| unambiguous semidirect product | #157⋊(C3⋊(C3⋊D3)) |
| Fitting, socle, Sylow | C35 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C33×C3⋊D3 | C22 |
| Fitting, socle, hypocenter | C35 | D4 |
| LCS | G ▷ C33×C3⋊D3 ▷ C35 | |
| UCS | C1 | |
1508 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^3,3^5|b^2=c,b^a=bc,d^a=d^2,f^a=f^2,g^a=g^2,h^a=h^2,d^b=e^2,e^b=d,d^c=d^2,e^c=e^287 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3919);