Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C17 ⋊ #359 |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^6,17|a^2=d,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^13,c^b=ce,e^b=ef,g^b=g^16,g^d=g^1650 conjugacy classes — view the full character table.
| maximal subgroup of | D17⋊#359, C2×#11763724, #14545098, … |
| maximal normal subgroup of | D17⋊#359, C2×#11763724, #14545098, … |
| maximal quotient of | #14543739, #14543740, #14543775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1464);