Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C83 ⋊ #2254 |
128 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=d,c^2=efg,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^c=h^82940 conjugacy classes — view the full character table.
| maximal subgroup of | #35318364, #35318365, #35318366, … |
| maximal normal subgroup of | #35318364, #35318365, #35318366, … |
| maximal quotient of | #35320840, #35322436, #35323004, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6790);