Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #11757686⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #11757686⋊C2 |
| unambiguous semidirect product | (#92318⋊C2)⋊C2 |
| Fitting, Sylow | #6903 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle | #92319 | C22 |
| Frattini | C9 | #157⋊D3 |
| Fitting, hypocenter | #6903 | D4 |
| socle | C3 | #157⋊D9 |
| LCS | G ▷ #92319 ▷ #6903 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| minimal degree | μ(G) = 162 |
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
2^3,3^5|b^2=c,f^3=g^2,g^3=h^2,b^a=bc,d^a=d^2,f^a=f^2gh,g^a=g^2h,h^a=h^2,d^b=e^2,e^b=d,d^c=d^2,e^c=e^2,e^d=eh69 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2327);