Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of ((C3⋊D3)⋊C27)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #92206⋊C4 |
| derived, Sylow | C32⋊C27 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | ((C3⋊D3)⋊C27)⋊C2 |
| commutator, hypocenter | C32⋊C27 | C2×C4 |
| Frattini | C2×C3×C9 | D32 |
| Fitting, cosocle | C2×C32⋊C27 | C22 |
| socle | C2×C32 | D3×D9 |
| prime radical | C2×#92206 | C2 |
| LCS | G ▷ C32⋊C27 | |
| UCS | C1 ◁ C2 | |
162 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^3,3^5|a^2=c,b^2=c,e^3=g,g^3=h,e^a=e^2g^2h^2,f^a=f^2,g^a=g^2h^2,h^a=h^2,d^b=d^2,f^b=f^2,e^d=ef102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 158);