Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3175 |
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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=fg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^82,d^b=dg,h^b=h^821180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35559516, #35559518, #35559561, … |
| maximal normal subgroup of | #35559516, #35559518, #35559561, … |
| maximal quotient of | #35404972, #35408678, #35408682, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 15151);