Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C11 · Schur multiplier (H2) = C4 |
| direct product | C4×C11×AGL(1,𝔽5) |
| Fitting | C4×C5×C11 ⋊ C4 |
| derived, Sylow | C5 ⋊ C42×C11 |
| Hall | C5×C11 ⋊ C42 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 220 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×C11⋊C8, #13182557, #13182564, … |
| maximal normal subgroup of | AGL(1,𝔽5)×C11⋊C8, #13182557, #13182564, … |
| maximal quotient of | C8×C11×AGL(1,𝔽5), C11×#3992, C4×C11×#170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 137);