Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #413×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2888 |
756 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 209 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,f^2=g,b^a=be,e^a=eg,f^b=fg,d^c=dg,h^c=h^82,h^d=h^82943 conjugacy classes — view the full character table.
| maximal subgroup of | #35321967, #35321969, #35321971, … |
| maximal normal subgroup of | #35321967, #35321969, #35321971, … |
| maximal quotient of | #35370219, #35370221, #35370234, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 12987);