Finite Group DatabasebetaFinite Group Databasebeta| order | 8416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C263 ⋊ #107 |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,263|a^2=d,b^2=ce,c^2=e,b^a=bc,c^a=ce,f^b=f^2621324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #107×D263, C2×#22554403, #30681973, … |
| maximal normal subgroup of | #107×D263, C2×#22554403, #30681973, … |
| maximal quotient of | #30681690, #30681700, #30681763, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8416, 79);