Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #499×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3232 |
334 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=eg,c^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^82,c^b=ce,f^c=fg,h^d=h^82934 conjugacy classes — view the full character table.
| maximal subgroup of | #3232×D83, C2×#24918632, #36276496, … |
| maximal normal subgroup of | #3232×D83, C2×#24918632, #36276496, … |
| maximal quotient of | #35413901, #35414096, #35414932, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 15679);