Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #1745 |
272 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,b^2=f,c^2=d,e^2=g,b^a=bd,c^a=cg,h^a=h^822680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35290949, #35290950, #35291002, … |
| maximal normal subgroup of | #35290949, #35290950, #35291002, … |
| maximal quotient of | #35294830, #35294837, #35294841, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4259);