Finite Group DatabasebetaFinite Group Databasebeta| order | 8416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C263 ⋊ C2 |
| Sylow | C263 ⋊ #99 |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,263|a^2=d,b^a=bc,c^a=ce,d^b=de,f^b=f^2621321 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #99×D263, C2×#22554384, #30681910, … |
| maximal normal subgroup of | #99×D263, C2×#22554384, #30681910, … |
| maximal quotient of | #30681661, #30681663, #30681671, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8416, 60);