Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×M32×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3414 |
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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=g,e^2=fg,f^2=g,b^a=be,c^a=cg,e^a=ef,f^a=fg,h^a=h^82,e^b=ef,f^b=fg,h^b=h^821672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35321523, #35321525, #35321544, … |
| maximal normal subgroup of | #35321523, #35321525, #35321544, … |
| maximal quotient of | #35557310, #35557443, #35557716, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17646);