Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #344×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1829 |
272 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 73 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=d,f^2=g,b^a=bd,c^a=ce,d^a=dg,f^b=fg,h^b=h^82,e^c=eg931 conjugacy classes — view the full character table.
| maximal subgroup of | #1829×D83, C2×#24907573, #35404274, … |
| maximal normal subgroup of | #1829×D83, C2×#24907573, #35404274, … |
| maximal quotient of | #35297862, #35297868, #35297919, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4620);