Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C3 |
No aliases for this group.
| derived, Sylow | #6855 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | C9⋊D9 |
| commutator, hypocenter | #6855 | C8 |
| Frattini | C33×C4 | C3⋊D3 |
| Fitting, cosocle | C4×#6855 | C2 |
| socle, prime radical | C2×C33 | C3⋊Dic3 |
| LCS | G ▷ #6855 | |
| UCS | C1 ◁ C3×C4 | |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
Polycyclic presentation:
2^3,3^5|a^2=b,b^2=c,d^3=h,e^3=g,d^a=d^2h^2,e^a=e^2g^2,g^a=g^2,h^a=h^2,e^d=ef216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 51);