Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #494×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3185 |
358 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 125 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,c^2=fg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,h^b=h^82,d^c=dg,h^d=h^82934 conjugacy classes — view the full character table.
| maximal subgroup of | #35380770, #35380772, #35380830, … |
| maximal normal subgroup of | #35380770, #35380772, #35380830, … |
| maximal quotient of | #35405003, #35408733, #35409645, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 15253);