Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Sylow | C32×H(3,𝔽3) ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #10620191 |
| commutator, Fitting, hypocenter | C32×H(3,𝔽3) | C8 |
| socle | C33 | #622 |
| prime radical | C3⋊D3×H(3,𝔽3) | C4 |
| cosocle | #11758047 | C2 |
| LCS | G ▷ C32×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^3,3^5|a^2=b,b^2=c,d^a=e,e^a=de^2,f^a=fg^2h,g^a=f^2g^2h^2,d^b=de^2,e^b=d^2e^2,f^b=f^2,g^b=g^2,d^c=d^2,e^c=e^2,g^f=gh39 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3474);