Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C8×Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3360 |
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^82,d^b=de,f^c=fg,h^c=h^821675 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35394016, #35394023, #35394091, … |
| maximal normal subgroup of | #35394016, #35394023, #35394091, … |
| maximal quotient of | #35421002, #35421202, #35423362, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17161);