Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊#10620191 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊#10620191 |
| Fitting, socle, derived, Sylow | C35 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C35 | C8 |
| prime radical | C33×C3⋊D3 | C4 |
| cosocle | C3×C3⋊(C3⋊#157) | C2 |
| LCS | G ▷ C35 | |
| UCS | C1 | |
440 conjugacy classes of subgroups; only the 15 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 15 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
Polycyclic presentation:
2^3,3^5|a^2=b,b^2=c,d^a=e,e^a=de^2,f^a=fg^2,g^a=f^2g^2,h^a=h^2,d^b=de^2,e^b=d^2e^2,f^b=f^2,g^b=g^2,d^c=d^2,e^c=e^251 conjugacy classes — view the full character table.
| maximal subgroup of | #72277550 |
| maximal normal subgroup of | #72277550 |
| maximal quotient of | #72277478 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3893);