Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4×D4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3105 |
454 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^82,f^c=fg1678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35299615, #35299621, #35374370, … |
| maximal normal subgroup of | #35299615, #35299621, #35374370, … |
| maximal quotient of | #35404409, #35407343, #35407387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14557);