Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C83 ⋊ #1442 |
520 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=e,c^2=d,b^a=bd,c^a=ce,h^a=h^82,c^b=cf,h^b=h^82,h^c=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35298456, #35298457, #35298470, … |
| maximal normal subgroup of | #35298456, #35298457, #35298470, … |
| maximal quotient of | #35292329, #35292331, #35312589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2769);