Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #342×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1899 |
378 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 83 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,b^2=df,c^2=g,b^a=bd,c^a=ce,d^a=dg,d^b=dg,f^b=fg,h^b=h^82,h^c=h^82934 conjugacy classes — view the full character table.
| maximal subgroup of | #1899×D83, C2×#24907920, #35406193, … |
| maximal normal subgroup of | #1899×D83, C2×#24907920, #35406193, … |
| maximal quotient of | #35299779, #35299789, #35299799, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4967);