Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #1088⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #1088⋊D9 |
| Fitting, Sylow | C9×H(3,𝔽3) ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle | C9×#272 | C22 |
| Frattini, socle | C32 | #157⋊D3 |
| Fitting, hypocenter | C9×H(3,𝔽3) | D4 |
| LCS | G ▷ C9×#272 ▷ C9×H(3,𝔽3) | |
| UCS | C1 | |
228 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 22 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:
2^3,3^5|b^2=c,f^3=g^2,b^a=bc,d^a=d^2,f^a=f^2g,g^a=g^2,h^a=h^2,d^b=e^2,e^b=d,d^c=d^2,e^c=e^2,e^d=eh69 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2323);