Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | #585×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3027 |
772 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|d^2=g,b^a=be,c^a=cf,d^a=dg,h^a=h^82,f^b=fg,e^c=eg1423 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35323386, #35323389, #35323391, … |
| maximal normal subgroup of | #35323386, #35323389, #35323391, … |
| maximal quotient of | #35378375, #35378382, #35378389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13912);