Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | Q8×AGL(1,𝔽11) |
| unambiguous semidirect product | D11⋊(C5×Q8) |
| unambiguous semidirect product | (Q8×D11)⋊C5 |
| Fitting | Q8×C11 ⋊ C2×C5 |
| Hall | Q8×D11 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×Q8 |
| Sylow | C11 ⋊ C2×C5×Q8 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 88 |
55 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×AGL(1,𝔽11), #66968⋊C5, Q16×AGL(1,𝔽11), … |
| maximal normal subgroup of | SD16×AGL(1,𝔽11), #66968⋊C5, Q16×AGL(1,𝔽11), … |
| maximal quotient of | #66940⋊C5, #66949⋊C5, #66941⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 120);