Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #474×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3319 |
414 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=eg,b^2=g,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,h^b=h^82,f^c=fg,h^d=h^82808 conjugacy classes — view the full character table.
| maximal subgroup of | #3319×D83, C2×#24919616, #36281171, … |
| maximal normal subgroup of | #3319×D83, C2×#24919616, #36281171, … |
| maximal quotient of | #35419956, #35420714, #35421477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 16663);