Finite Group DatabasebetaFinite Group Databasebeta| order | 880 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #4318⋊C5 |
| Hall | #4318 ⋊ C5 |
| Hall | C11⋊C5 ⋊ M16 |
| Sylow | C11 ⋊ C5×M16 |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 88 |
Polycyclic presentation:
2^2,5,2^2,11|a^2=d,d^2=e,b^a=be,f^a=f^10,f^c=f^958 conjugacy classes — view the full character table.
| maximal subgroup of | #66869⋊C5, #66883⋊C5, #66886⋊C5, … |
| maximal normal subgroup of | #66869⋊C5, #66883⋊C5, #66886⋊C5, … |
| maximal quotient of | #66867⋊C5, C4⋊((C11⋊C5)⋊C8), C22⋊((C11⋊C5)⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(880, 13);