Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×D4×C269 ⋊ C4 |
| Sylow | C269 ⋊ #353 |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2152 |
Polycyclic presentation:
2^6,269|a^2=d,c^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^187,c^b=cf,d^b=def,d^c=df,g^d=g^268683 conjugacy classes — view the full character table.
| maximal subgroup of | #46826004, #46826005 |
| maximal normal subgroup of | #46826004, #46826005 |
| maximal quotient of | #46825813, #46825828, #46825863, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1453);