Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C36 |
| unambiguous semidirect product | (C3×SL(2,𝔽3))⋊H(3,𝔽3) |
| Fitting | C3×Q8×H(3,𝔽3) ⋊ C3 |
| Sylow | Q8 ⋊ C32⋊H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C2×C32 | C32×A4 |
| commutator, cosocle | C32×Q8 | C33 |
| Fitting | C3×Q8×H(3,𝔽3) | C3 |
| hypercenter | C2×C3×H(3,𝔽3) | A4 |
| hypocenter | Q8 | C32⋊H(3,𝔽3) |
| LCS | G ▷ C32×Q8 ▷ Q8 | |
| UCS | C1 ◁ C2×C32 ◁ C2×C3×H(3,𝔽3) | |
623 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 623 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
3^5,2^3|f^2=h,g^2=h,c^a=ce,f^a=fg,g^a=f,c^b=cd,g^f=gh135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1640);