Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | C32×H(3,𝔽3) ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #10620209 |
| commutator, prime radical, cosocle | C3⋊D3×H(3,𝔽3) | C22 |
| Fitting, hypocenter | C32×H(3,𝔽3) | Q8 |
| socle | C33 | #634 |
| LCS | G ▷ C3⋊D3×H(3,𝔽3) ▷ C32×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
202 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^3,3^5|a^2=c,b^2=c,b^a=bc,d^a=de^2,e^a=d^2e^2,f^a=f^2,g^a=g^2,d^b=e^2,e^b=d,d^c=d^2,e^c=e^2,g^f=gh42 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3552);