Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C36 |
No aliases for this group.
| Fitting | C34×Q8 ⋊ C3 |
| Sylow | Q8 ⋊ C32⋊H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C2×C32 | C32×A4 |
| commutator, cosocle | C32×Q8 | C33 |
| Fitting | C34×Q8 | C3 |
| hypercenter | C2×C34 | A4 |
| hypocenter | Q8 | C32⋊H(3,𝔽3) |
| LCS | G ▷ C32×Q8 ▷ Q8 | |
| UCS | C1 ◁ C2×C32 ◁ C2×C34 | |
779 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
3^5,2^3|f^2=h,g^2=h,b^a=be,c^a=cd,f^a=fg,g^a=f,g^f=gh183 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1667);