Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #3141 |
424 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 141 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=f,c^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,d^b=dg,h^b=h^82,d^c=dg,h^c=h^821180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35301905, #35301907, #35301965, … |
| maximal normal subgroup of | #35301905, #35301907, #35301965, … |
| maximal quotient of | #35404620, #35407115, #35408073, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14903);