Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #6855 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #10619734 |
| commutator, prime radical, cosocle | #92197 | C22 |
| Frattini, socle | C33 | PSU(3,𝔽2) |
| Fitting, hypocenter | #6855 | Q8 |
| LCS | G ▷ #92197 ▷ #6855 | |
| UCS | C1 ◁ C3 | |
53 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^3,3^5|a^2=c,b^2=c,d^3=g^2h^2,e^3=g,b^a=bc,d^a=de^2f,e^a=d^2e^2f^2,f^a=fh^2,g^a=h,h^a=g^2,d^b=e,e^b=d^2gh,f^b=fg^2,g^b=gh,h^b=gh^2,d^c=d^2gh,e^c=e^2g^2,f^c=fgh^2,g^c=g^2,h^c=h^2,e^d=efg^2h27 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 807);