Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | #6879 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92191⋊C2 |
| commutator, Fitting, cosocle | C2×#6879 | C22 |
| Frattini | C2×C3×C9 | D32 |
| socle | C2×C3 | #4178⋊C2 |
| hypocenter | #6879 | D4 |
| LCS | G ▷ C2×#6879 ▷ #6879 | |
| UCS | C1 ◁ C2 | |
129 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 129 conjugacy classes of subgroups — too many to draw. Only its 20 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|e^3=g^2h,f^3=h^2,b^a=bc,e^a=e^2gh^2,f^a=f^2h,g^a=g^2,h^a=h^2,d^b=d^2,f^b=f^2g,g^b=gh,h^b=h^2,e^d=ef,f^d=fg,g^d=gh49 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 216);