Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #1676 |
144 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 61 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=fg,b^2=df,c^2=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^82,e^c=eg1669 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35318296, #35318298, #35318303, … |
| maximal normal subgroup of | #35318296, #35318298, #35318303, … |
| maximal quotient of | #35297463, #35300550, #35302766, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3914);