Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C22⋊C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3002 |
764 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^82,e^b=eg,h^b=h^821678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35299512, #35299514, #35376512, … |
| maximal normal subgroup of | #35299512, #35299514, #35376512, … |
| maximal quotient of | #35376514, #35376565, #35376616, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13732);