Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #2217 |
164 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|b^2=dfg,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^b=h^82940 conjugacy classes — view the full character table.
| maximal subgroup of | #2217×D83, C2×#24909557, #35558838, … |
| maximal normal subgroup of | #2217×D83, C2×#24909557, #35558838, … |
| maximal quotient of | #35318618, #35318669, #35318737, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6604);