Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #11757439⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #11757439⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C22×#733 | C2×C3 |
| Frattini | C3×C9 | D3×A4 |
| socle | C22×C3 | #4178 |
| LCS | G ▷ C22×#733 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2,3,2^2,3^4|b^3=g,e^3=h^2,f^3=h^2,e^a=e^2h,f^a=f^2h,h^a=h^2,c^b=d,d^b=cd,e^b=efg^2,f^b=fh,f^e=fgh^2,g^e=gh36 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 921);