Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #324×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1318 |
170 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 170 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,b^a=bc,c^a=ce,e^a=eg,c^b=cg,d^b=deg,h^b=h^82,d^c=dg928 conjugacy classes — view the full character table.
| maximal subgroup of | #1318×D83, C2×#24905394, #35313508, … |
| maximal normal subgroup of | #1318×D83, C2×#24905394, #35313508, … |
| maximal quotient of | #35291026, #35291034, #35291149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2441);