Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C9 |
No aliases for this group.
| Sylow | Q8 ⋊ #6898 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C2×C32 | C32×A4 |
| commutator, cosocle | C32×Q8 | C33 |
| Fitting | Q8×C32⋊C9 | C3 |
| prime radical | C2×C33 | C3×A4 |
| hypercenter | C2×C32⋊C9 | A4 |
| hypocenter | Q8 | #6898 |
| LCS | G ▷ C32×Q8 ▷ Q8 | |
| UCS | C1 ◁ C2×C32 ◁ C2×C32⋊C9 | |
173 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 173 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 648 |
Polycyclic presentation:
3^5,2^3|a^3=e,b^3=d,f^2=h,g^2=h,c^a=cd,f^a=fg,g^a=f,c^b=ce^2,g^f=gh135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1575);