Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C8×D4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3297 |
420 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=eg,b^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^82,d^b=de,f^c=fg,h^c=h^821675 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3297×D83, C2×#24919315, #36280895, … |
| maximal normal subgroup of | #3297×D83, C2×#24919315, #36280895, … |
| maximal quotient of | #35419823, #35420657, #35421592, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 16362);