Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #470×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3054 |
500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|b^2=e,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^82,c^b=cg,h^b=h^82,h^d=h^82688 conjugacy classes — view the full character table.
| maximal subgroup of | #35314553, #35314566, #35558301, … |
| maximal normal subgroup of | #35314553, #35314566, #35558301, … |
| maximal quotient of | #35386920, #35386948, #35386990, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14121);