Finite Group DatabasebetaFinite Group Databasebeta| order | 7264 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C227 ⋊ C2 |
| Sylow | C227 ⋊ #99 |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,227|a^2=d,b^a=bc,c^a=ce,d^b=de,f^b=f^2261141 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #99×D227, C2×#20300202, #28409004, … |
| maximal normal subgroup of | #99×D227, C2×#20300202, #28409004, … |
| maximal quotient of | #28408755, #28408757, #28408765, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7264, 60);