Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #1315 |
116 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^82,c^b=cg,d^b=deg1186 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291768, #35291769, #35291771, … |
| maximal normal subgroup of | #35291768, #35291769, #35291771, … |
| maximal quotient of | #35291031, #35291033, #35291035, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2436);