Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C83 ⋊ #1744 |
296 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,b^2=f,c^2=d,e^2=g,b^a=bd,h^a=h^822704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C83⋊#7014, #35290937, #35290959, … |
| maximal normal subgroup of | C83⋊#7014, #35290937, #35290959, … |
| maximal quotient of | #35294827, #35294829, #35294833, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4256);