Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #1753 |
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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=e,b^2=f,c^2=e,e^2=g,b^a=bd,c^a=cg,h^a=h^82,h^b=h^82,h^c=h^821696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1753×D83, C2×#24907249, #35401990, … |
| maximal normal subgroup of | #1753×D83, C2×#24907249, #35401990, … |
| maximal quotient of | #35294884, #35294890, #35294895, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4296);