Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #465×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3246 |
392 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,f^c=fg,h^d=h^82934 conjugacy classes — view the full character table.
| maximal subgroup of | #3246×D83, C2×#24918774, #36277230, … |
| maximal normal subgroup of | #3246×D83, C2×#24918774, #36277230, … |
| maximal quotient of | #35414279, #35414286, #35414775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 15821);