Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊(D33⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C3⋊(D33⋊C3) |
| unambiguous semidirect product | #10620215⋊C3 |
| Fitting, socle | C34 ⋊ C2×A4 |
| derived | C3×#1113 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×#1113 | C2×C3 |
| Fitting, socle | C34 | C2×A4 |
| LCS | G ▷ C3×#1113 | |
| UCS | C1 | |
236 conjugacy classes of subgroups; only the 11 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 11 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 12 |
Polycyclic presentation:
2,3,2^2,3^4|e^a=e^2,f^a=f^2,g^a=g^2,h^a=h^2,c^b=cd,d^b=c,f^b=h,g^b=f,h^b=g,f^c=f^2,h^c=h^2,f^d=f^2,g^d=g^230 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3881);