Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #1345 |
168 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 37 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,c^2=f,d^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^82,c^b=cf,d^b=def,d^c=dg925 conjugacy classes — view the full character table.
| maximal subgroup of | #1345×D83, C2×#24905466, #35314603, … |
| maximal normal subgroup of | #1345×D83, C2×#24905466, #35314603, … |
| maximal quotient of | #35291089, #35291095, #35291113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2513);