Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×SD32×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3416 |
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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=g,e^2=fg,f^2=g,b^a=be,e^a=ef,f^a=fg,e^b=ef,f^b=fg,d^c=dg,h^d=h^82934 conjugacy classes — view the full character table.
| maximal subgroup of | #35561147, #35561149, #35561164, … |
| maximal normal subgroup of | #35561147, #35561149, #35561164, … |
| maximal quotient of | #35557311, #35557318, #35557449, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17652);