Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C83 ⋊ #1312 |
92 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=c,b^2=d,c^2=e,d^2=f,f^2=g,b^a=be,h^a=h^822704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1312×D83, C2×#24905382, #35313392, … |
| maximal normal subgroup of | #1312×D83, C2×#24905382, #35313392, … |
| maximal quotient of | #35291021, #35291231, #35291736, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2429);