Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #1939 |
260 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,b^2=f,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^82,h^b=h^821696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35298316, #35298317, #35298323, … |
| maximal normal subgroup of | #35298316, #35298317, #35298323, … |
| maximal quotient of | #35302942, #35302947, #35302952, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5229);