Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊(((C22⋊C27)⋊C2)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C3⋊(((C22⋊C27)⋊C2)⋊C3) |
| derived | C3×C22⋊C27 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C22⋊C27 | C2×C3 |
| Frattini | C9 | C3×C3⋊S4 |
| Fitting | C22×C32×C9 | D3 |
| socle | C22×C32 | C3×D9 |
| LCS | G ▷ C3×C22⋊C27 | |
| UCS | C1 | |
219 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 219 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) = 162 |
Polycyclic presentation:
2,3^5,2^2|c^3=e,e^3=f,c^a=c^2e^2f^2,d^a=d^2,e^a=e^2f^2,f^a=f^2,g^a=gh,c^b=cf^2,g^c=h,h^c=gh99 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2430);