Finite Group DatabasebetaFinite Group Databasebeta| order | 8608 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q8×C269 ⋊ C4 |
| Sylow | C269 ⋊ #104 |
44 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,269|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^187,c^b=ce,f^b=f^268,f^d=f^268349 conjugacy classes — view the full character table.
| maximal subgroup of | D269⋊#104, C2×#22575518, #31771602, … |
| maximal normal subgroup of | D269⋊#104, C2×#22575518, #31771602, … |
| maximal quotient of | #31771453, Q8⋊#14524137, #31771457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8608, 211);