Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q8×C257 ⋊ C4 |
| Sylow | C257 ⋊ #104 |
44 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,257|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^241,c^b=ce,f^b=f^256,f^d=f^256334 conjugacy classes — view the full character table.
| maximal subgroup of | D257⋊#104, C2×#22551657, #30657734, … |
| maximal normal subgroup of | D257⋊#104, C2×#22551657, #30657734, … |
| maximal quotient of | #30657585, Q8⋊#14523346, #30657589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 211);