Finite Group DatabasebetaFinite Group Databasebeta| order | 7264 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C227 ⋊ #103 |
42 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,227|a^2=d,b^2=e,c^2=e,b^a=bc,c^a=ce,f^a=f^226,c^b=ce1144 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #103×D227, C2×#20300212, #28409027, … |
| maximal normal subgroup of | #103×D227, C2×#20300212, #28409027, … |
| maximal quotient of | Q8⋊(C227⋊C8), #28408769, #28408778, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7264, 70);