Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #498×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3184 |
446 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 446 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|c^2=fg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^82,c^b=cg,h^b=h^82,d^c=dg,h^d=h^82934 conjugacy classes — view the full character table.
| maximal subgroup of | #35380737, #35380739, #35380797, … |
| maximal normal subgroup of | #35380737, #35380739, #35380797, … |
| maximal quotient of | #35405000, #35408714, #35409654, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 15249);