Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #2036 |
316 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 87 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,c^2=dg,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^82,c^b=cf,e^c=eg1180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2036×D83, C2×#24908666, #35431882, … |
| maximal normal subgroup of | #2036×D83, C2×#24908666, #35431882, … |
| maximal quotient of | #35307707, #35307714, #35307797, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5713);