Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #336×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1850 |
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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,f^2=g,b^a=bd,c^a=ce,h^a=h^82,h^c=h^821696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1850×D83, C2×#24907642, #35405062, … |
| maximal normal subgroup of | #1850×D83, C2×#24907642, #35405062, … |
| maximal quotient of | #35298233, #35298238, #35298244, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4689);