Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22⋊C16×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2113 |
228 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 79 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=e,e^2=f,f^2=g,b^a=bd,c^b=cg,h^c=h^821696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2113×D83, C2×#24909075, #35557079, … |
| maximal normal subgroup of | #2113×D83, C2×#24909075, #35557079, … |
| maximal quotient of | #35313467, #35313539, #35313607, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6122);