Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #1372 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=ceg,c^2=eg,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,h^b=h^821192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1372×D83, C2×#24905536, #35315986, … |
| maximal normal subgroup of | #1372×D83, C2×#24905536, #35315986, … |
| maximal quotient of | #35291145, #35291273, #35292086, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2583);