Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #476×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1634 |
218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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=f,c^2=fg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,d^b=df,e^b=eg,h^b=h^82,d^c=dg,e^c=eg805 conjugacy classes — view the full character table.
| maximal subgroup of | #1634×D83, C2×#24906607, #35380297, … |
| maximal normal subgroup of | #1634×D83, C2×#24906607, #35380297, … |
| maximal quotient of | #35293236, #35293246, #35293419, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3654);