Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #2064 |
208 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 69 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=de,b^2=d,c^2=g,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^82,c^b=cf,d^c=dg,f^c=fg,h^c=h^821174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2064×D83, C2×#24908829, #35432948, … |
| maximal normal subgroup of | #2064×D83, C2×#24908829, #35432948, … |
| maximal quotient of | #35308927, #35308941, #35308955, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5876);