Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #11757417⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #11757417⋊C2 |
| derived | C22⋊C27 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C22⋊C27 | C2×C9 |
| Frattini | C3×C9 | C3×S4 |
| Fitting | C22×C9⋊C9 | D3 |
| socle | C22×C3 | D9⋊C9 |
| prime radical | ((C22⋊C27)⋊C2)⋊C3 | C3 |
| cosocle | #66353 | C2×C3 |
| LCS | G ▷ C22⋊C27 | |
| UCS | C1 | |
87 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2,3^5,2^2|b^3=c,d^3=e,e^3=f,d^a=d^2e^2f^2,e^a=e^2f^2,f^a=f^2,g^a=gh,d^b=de,e^b=ef,d^c=df,g^d=h,h^d=gh61 conjugacy classes — view the full character table.
| maximal subgroup of | #72228977, C2×#11757417⋊C2, #72229397 |
| maximal normal subgroup of | C2×#11757417⋊C2 |
| maximal quotient of | C2×#11757417⋊C2, #72229362, #72229397 |
| automorphism group of | (C22⋊C27)⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 823);