Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #1296 |
188 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=e,c^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^82,c^b=cg1678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1296×D83, C2×#24905347, #35294489, … |
| maximal normal subgroup of | #1296×D83, C2×#24905347, #35294489, … |
| maximal quotient of | #35290956, #35290972, #35290973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2394);