Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #1325 |
134 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 37 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=d,b^2=eg,c^2=g,d^2=f,b^a=bc,c^a=ce,e^a=eg,d^b=deg,h^b=h^82,d^c=dg928 conjugacy classes — view the full character table.
| maximal subgroup of | #1325×D83, C2×#24905408, #35313559, … |
| maximal normal subgroup of | #1325×D83, C2×#24905408, #35313559, … |
| maximal quotient of | #35291040, #35291047, #35291200, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2455);