Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C257 ⋊ #106 |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,257|a^2=d,b^2=c,c^2=e,b^a=bc,c^a=ce,f^b=f^2561294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #106×D257, C2×#22551523, #30656773, … |
| maximal normal subgroup of | #106×D257, C2×#22551523, #30656773, … |
| maximal quotient of | #30656487, #30656499, #30656559, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 77);