Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊(C11⋊AGL(1,𝔽5)) |
| Fitting | C22×C5×C11 ⋊ C4 |
| Hall | C5×C11 ⋊ C22⋊C4 |
| Sylow | C11 ⋊ C22⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C22⋊Dic11 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 220 |
Polycyclic presentation:
2^4,5,11|a^2=c,b^a=bd,e^a=e^3,f^a=f^10,e^c=e^494 conjugacy classes — view the full character table.
| maximal subgroup of | #13182580, #13182581, #13182645, … |
| maximal normal subgroup of | #13182580, #13182581, #13182645, … |
| maximal quotient of | #13182645, #13182648, #13182651, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 148);