Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C22⋊C16×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1315 |
116 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 37 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=d,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=ce,c^b=cg,d^b=deg,h^b=h^821678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1315×D83, C2×#24905388, #35313474, … |
| maximal normal subgroup of | #1315×D83, C2×#24905388, #35313474, … |
| maximal quotient of | #35291030, #35291032, #35291034, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2435);