Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #568×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1910 |
344 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 89 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=dfg,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^82,e^b=eg,d^c=dg,f^c=fg1423 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35320175, #35320178, #35320196, … |
| maximal normal subgroup of | #35320175, #35320178, #35320196, … |
| maximal quotient of | #35299909, #35299914, #35299929, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5037);