Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #1348 |
116 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|a^2=d,b^2=g,c^2=fg,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,h^a=h^82,c^b=cf,d^b=defg,e^b=eg,f^b=fg931 conjugacy classes — view the full character table.
| maximal subgroup of | #1348×D83, C2×#24905475, #35314631, … |
| maximal normal subgroup of | #1348×D83, C2×#24905475, #35314631, … |
| maximal quotient of | #35291080, #35291083, #35291116, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2522);