Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | #410×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3027 |
772 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 145 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=eg,h^c=h^82931 conjugacy classes — view the full character table.
| maximal subgroup of | #35323388, #35323390, #35323393, … |
| maximal normal subgroup of | #35323388, #35323390, #35323393, … |
| maximal quotient of | #35378376, #35378377, #35378383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13913);