Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C83 ⋊ #2374 |
552 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 185 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=g,b^2=g,c^2=ef,d^2=ef,b^a=be,c^a=cf,d^b=de,h^b=h^82,h^c=h^82,h^d=h^821198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35321161, #35321165, #35321668, … |
| maximal normal subgroup of | #35321161, #35321165, #35321668, … |
| maximal quotient of | #35325868, #35325958, #35325993, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7643);