Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #14516414 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | #6862 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, prime radical, cosocle | #92204 | C22 |
| Frattini | C33 | PSU(3,𝔽2) |
| Fitting, hypocenter | #6862 | Q8 |
| socle | C32 | SU(3,𝔽2) |
| LCS | G ▷ #92204 ▷ #6862 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2^3,3^5|a^2=c,b^2=c,d^3=h^2,e^3=g^2h,b^a=bc,d^a=de^2f,e^a=d^2e^2f^2h,f^a=fg,g^a=h,h^a=g^2,d^b=e,e^b=d^2h,f^b=fgh^2,g^b=gh,h^b=gh^2,d^c=d^2h,e^c=e^2gh^2,f^c=fgh,g^c=g^2,h^c=h^2,e^d=efg^2h,f^d=fgh,f^e=fg^219 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 808);