Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #2873 |
564 conjugacy classes of subgroups; only the 373 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 373 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,b^2=f,e^2=g,d^a=dg,h^a=h^82,c^b=cg1708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35301737, #35301740, #35301742, … |
| maximal normal subgroup of | #35301737, #35301740, #35301742, … |
| maximal quotient of | #35369988, #35370012, #35370041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 12929);