Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C3×#731 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #4177⋊D3 |
| commutator, Fitting, cosocle | C2×C3×#731 | C22 |
| Frattini | C2×C32 | D3×C3⋊D3 |
| socle | C2×C32 | ((C3⋊D3)⋊C3)⋊C2 |
| hypocenter | C3×#731 | D4 |
| LCS | G ▷ C2×C3×#731 ▷ C3×#731 | |
| UCS | C1 ◁ C2 | |
326 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^3,3^5|a^2=c,f^3=h,b^a=bc,f^a=f^2h^2,g^a=g^2,h^a=h^2,d^b=d^2,e^b=e^2,g^b=g^2h,f^e=fg,g^e=gh57 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1432);