Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #4339⋊C5 |
| Fitting | C2×C4×C11 ⋊ C2×C5 |
| Hall | #4339 ⋊ C5 |
| Hall | C11⋊C5 ⋊ #41 |
| Sylow | C11 ⋊ C5×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×AGL(1,𝔽11) |
| commutator, socle, cosocle | C2×C11 | C23×C5 |
| Frattini | C2 | C22×AGL(1,𝔽11) |
| Fitting | C2×C4×C11 | C2×C5 |
| hypercenter | C2×C4 | AGL(1,𝔽11) |
| hypocenter | C11 | C5×#41 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 88 |
Polycyclic presentation:
2^3,5,2,11|b^2=e,c^a=ce,f^a=f^10,f^d=f^958 conjugacy classes — view the full character table.
| maximal subgroup of | #66869⋊C5, #66889⋊C5, #66954⋊C5, … |
| maximal normal subgroup of | #66869⋊C5, #66889⋊C5, #66954⋊C5, … |
| maximal quotient of | C4×(C11⋊C5)⋊Q8, #66923⋊C5, #66925⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 117);