Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #14519130 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, Sylow | C33×C9 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle | C3×C9×C3⋊D3 | C22 |
| Frattini | C3 | #10620204 |
| Fitting, hypocenter | C33×C9 | D4 |
| socle | C34 | D12 |
| LCS | G ▷ C3×C9×C3⋊D3 ▷ C33×C9 | |
| UCS | C1 | |
314 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2^3,3^5|b^2=c,g^3=h^2,b^a=bc,d^a=d^2,g^a=g^2h,h^a=h^2,d^b=e^2,e^b=d,f^b=f^2,d^c=d^2,e^c=e^266 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3524);