Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #338×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2069 |
216 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=de,b^2=d,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^82,c^b=cf,f^b=fg,h^b=h^82,d^c=dg,h^c=h^82925 conjugacy classes — view the full character table.
| maximal subgroup of | #2069×D83, C2×#24908862, #35433129, … |
| maximal normal subgroup of | #2069×D83, C2×#24908862, #35433129, … |
| maximal quotient of | #35309034, #35309048, #35309062, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5909);