Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #430×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2098 |
210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 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=de,d^2=g,f^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,d^b=dg,e^b=eg,f^b=fg,f^c=fg,h^c=h^82928 conjugacy classes — view the full character table.
| maximal subgroup of | #35317744, #35317749, #35317754, … |
| maximal normal subgroup of | #35317744, #35317749, #35317754, … |
| maximal quotient of | #35309378, #35309383, #35309388, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6062);