Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C16×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2232 |
150 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|c^2=d,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^82,e^c=ef,f^c=fg,h^c=h^821669 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35317606, #35317607, #35317618, … |
| maximal normal subgroup of | #35317606, #35317607, #35317618, … |
| maximal quotient of | #35320693, #35320905, #35321340, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6691);