Finite Group DatabasebetaFinite Group Databasebeta| order | 8416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C263 ⋊ #101 |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,263|a^2=d,b^2=e,d^2=e,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 | #101×D263, C2×#22554388, #30681919, … |
| maximal normal subgroup of | #101×D263, C2×#22554388, #30681919, … |
| maximal quotient of | #30681663, #30681679, #30681683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8416, 64);