Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×#41×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1906 |
332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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,e^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^82,d^b=dg,e^b=eg,f^b=fg,d^c=dg,e^c=eg,f^c=fg1672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1906×D83, C2×#24907964, #35406315, … |
| maximal normal subgroup of | #1906×D83, C2×#24907964, #35406315, … |
| maximal quotient of | #35299871, #35299878, #35299885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5011);