Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #1401 |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^82,c^b=cg,d^b=dg1696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1401×D83, C2×#24905605, #35324613, … |
| maximal normal subgroup of | #1401×D83, C2×#24905605, #35324613, … |
| maximal quotient of | #35291745, #35291805, D4⋊(C83⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2652);