Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #11757810⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2×C32 |
| unambiguous semidirect product | #11757810⋊C2 |
| Fitting | C22×#733 ⋊ D3 |
| derived | #11757810 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #11757810 | C2 |
| Frattini | C32 | C3⋊(C3⋊S4) |
| Fitting | C22×#733 | D3 |
| socle | C22×C3 | C3⋊#272 |
| LCS | G ▷ #11757810 | |
| UCS | C1 | |
277 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 277 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2,3^5,2^2|b^3=f,c^3=f,d^3=f,b^a=b^2f^2,c^a=c^2f^2,d^a=d^2f^2,e^a=ef^2,f^a=f^2,g^a=gh,g^b=h,h^b=gh,d^c=de,e^d=ef43 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2499);