Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #1923 |
292 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,b^2=df,c^2=d,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 | #1923×D83, C2×#24908071, #35406692, … |
| maximal normal subgroup of | #1923×D83, C2×#24908071, #35406692, … |
| maximal quotient of | #35302579, #35302586, #35302593, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5118);