Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #344×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1932 |
216 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 69 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=f,b^2=df,c^2=d,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^b=h^82,e^c=eg934 conjugacy classes — view the full character table.
| maximal subgroup of | #1932×D83, C2×#24908130, #35406989, … |
| maximal normal subgroup of | #1932×D83, C2×#24908130, #35406989, … |
| maximal quotient of | #35302631, #35302638, #35302645, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5177);