Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C83⋊C32) |
| Sylow | C83 ⋊ C4⋊C32 |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=c,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^822704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊(C83⋊C32), #35291843, #35291845, … |
| maximal normal subgroup of | D4⋊(C83⋊C32), #35291843, #35291845, … |
| maximal quotient of | #35292070, #35292077, #35292091, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2706);