Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2490 |
560 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=eg,b^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^82,c^b=cg1678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35472474, #35472478, #35472534, … |
| maximal normal subgroup of | #35472474, #35472478, #35472534, … |
| maximal quotient of | #35326344, #35326885, #35327494, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 8862);