Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C17 ⋊ C4 |
| Sylow | C17 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 136 |
Polycyclic presentation:
2^6,17|a^2=d,b^a=bc,c^a=ce,e^a=ef,g^a=g^13,d^b=de,g^b=g^16,d^c=df,g^d=g^1653 conjugacy classes — view the full character table.
| maximal subgroup of | D17⋊AΣL(1,𝔽16), C2×#11763710, #14545037, … |
| maximal normal subgroup of | D17⋊AΣL(1,𝔽16), C2×#11763710, #14545037, … |
| maximal quotient of | #14543709, #14543728, #14543763, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1450);