Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C83 ⋊ #2956 |
458 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 217 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=f,c^2=f,e^2=g,f^2=g,b^a=be,e^a=eg,h^a=h^82,e^b=eg,d^c=dg,h^c=h^82946 conjugacy classes — view the full character table.
| maximal subgroup of | #35425270, #35425274, #35425279, … |
| maximal normal subgroup of | #35425270, #35425274, #35425279, … |
| maximal quotient of | #35373843, #35373854, #35374034, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13420);