Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #432×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1551 |
252 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 77 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=e,c^2=g,d^2=g,e^2=fg,b^a=bd,c^a=cf,d^a=df,h^a=h^82,d^b=dg,e^b=efg,h^b=h^821180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35296543, #35296547, #35296555, … |
| maximal normal subgroup of | #35296543, #35296547, #35296555, … |
| maximal quotient of | #35292417, #35292447, #35292560, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3206);