Finite Group Databasebeta

← Group #488693

Character table — Group #488693

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111122224444444444444444488888816161616161616161616161616161616161616163232
order1222224422444444488888888248888224444444444161616161616161624
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ81111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ911111111-1-11-1-111-1-1-1-1-1-111111-111-1-11-11-11-11-111-1-111-1-111-1-11-1
χ1011111111-1-11-1-111-1-1-1-1-1-111111-111-1-11-11-11-11-1-1-111-1-111-1-111-11
χ1111111111-1-11-1-111-1-1-1-1-1-111111-111-1-1-11-11-11-1111-1-1-1-111-1-1111-1
χ1211111111-1-11-1-111-1-1-1-1-1-111111-111-1-1-11-11-11-11-1-11111-1-111-1-1-11
χ1311111111-1-11-1-1-1-111-1-1-1-11111-11-1-1111-11-1-11-1111-1-111-1-1-1-111-11
χ1411111111-1-11-1-1-1-111-1-1-1-11111-11-1-1111-11-1-11-11-1-111-1-11111-1-11-1
χ1511111111-1-11-1-1-1-111-1-1-1-11111-11-1-111-11-111-11-111-1-1-1-11111-1-1-11
χ1611111111-1-11-1-1-1-111-1-1-1-11111-11-1-111-11-111-11-1-1-11111-1-1-1-1111-1
χ1722222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000
χ1922222222-2-22-2-222-2-22222-2-2-2-22-2-2-2220000000000000000000000
χ2022222222-2-22-2-2-2-2222222-2-2-2-2-2222-2-20000000000000000000000
χ21222222-2-222-2-2-2222200000000-2-200000000000000002−22−22−22−200
χ22222222-2-222-2-2-2222200000000-2-20000000000000000−22−22−22−2200
χ23222222-2-222-2-2-2-2-2-2-2000000002200000000000000002−22−2−22−2200
χ24222222-2-222-2-2-2-2-2-2-200000000220000000000000000−22−222−22−200
χ25222222-2-2-2-2-22222-2-200000000-2200000000000000002−2−222−2−2200
χ26222222-2-2-2-2-22222-2-200000000-220000000000000000−222−2−222−200
χ27222222-2-2-2-2-222-2-222000000002-200000000000000002−2−22−222−200
χ28222222-2-2-2-2-222-2-222000000002-20000000000000000−222−22−2−2200
χ292222-2-2222-2-22-2000022-2-222-2-2000000000022-2-200000000000000
χ302222-2-2222-2-22-2000022-2-222-2-20000000000-2-22200000000000000
χ312222-2-2222-2-22-20000-2-222-2-2220000002-2-22000000000000000000
χ322222-2-2222-2-22-20000-2-222-2-222000000-222-2000000000000000000
χ332222-2-222-22-2-22000022-2-2-2-22200000022-2-2000000000000000000
χ342222-2-222-22-2-22000022-2-2-2-222000000-2-222000000000000000000
χ352222-2-222-22-2-220000-2-22222-2-200000000002-2-2200000000000000
χ362222-2-222-22-2-220000-2-22222-2-20000000000-222-200000000000000
χ374444-4-4-4-44-44-440000000000000000000000000000000000000000
χ384444-4-4-4-4-4444-40000000000000000000000000000000000000000
χ3944-4-44-40000000004i−4i000022−2222−2200002i2−2i20000000000000000000000
χ4044-4-44-40000000004i−4i0000−2222−22220000−2i22i20000000000000000000000
χ4144-4-44-4000000000−4i4i000022−2222−220000−2i22i20000000000000000000000
χ4244-4-44-4000000000−4i4i0000−2222−222200002i2−2i20000000000000000000000
χ4344-4-4-4400000004i−4i00000022−22−2222002i2−2i2000000000000000000000000
χ4444-4-4-4400000004i−4i000000−222222−2200−2i22i2000000000000000000000000
χ4544-4-4-440000000−4i4i00000022−22−222200−2i22i2000000000000000000000000
χ4644-4-4-440000000−4i4i000000−222222−22002i2−2i2000000000000000000000000
χ474-44-4004-4000000000004i−4i0000000000000000002-22i−2i0000000000
χ484-44-4004-4000000000004i−4i000000000000000000-22−2i2i0000000000
χ494-44-4004-400000000000−4i4i0000000000000000002-2−2i2i0000000000
χ504-44-4004-400000000000−4i4i000000000000000000-222i−2i0000000000
χ518-88-800-88000000000000000000000000000000000000000000000
χ528-8-88000000000000042−420000000000000000000000000000000000
χ538-8-880000000000000−42420000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).