Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #1599 |
266 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 53 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=g,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,e^b=eg,h^b=h^82,d^c=dg925 conjugacy classes — view the full character table.
| maximal subgroup of | #35317155, #35317156, #35317166, … |
| maximal normal subgroup of | #35317155, #35317156, #35317166, … |
| maximal quotient of | #35293130, #35293143, #35293174, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3449);