Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #542×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3263 |
346 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,f^c=fg,h^c=h^82928 conjugacy classes — view the full character table.
| maximal subgroup of | #3263×D83, C2×#24918928, #36277384, … |
| maximal normal subgroup of | #3263×D83, C2×#24918928, #36277384, … |
| maximal quotient of | #35414372, #35414378, #35414820, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 15975);