Finite Group Databasebeta

← Group #317034

Character table — Group #317034

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222244444444444444444888888888888888888888161616161616161632323232
order12222244444444488888888888888444444448888888888888444488884488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-11-11-111-1-111-1-1
χ61111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1-11-11-1-111-1-111
χ71111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-11-11-111-1-1-1-111
χ81111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-11-11-1-11111-1-1
χ9111111111111111-1-1-1-111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-1111-11-1
χ10111111111111111-1-1-1-111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-1111-1-1-11-11
χ11111111111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-11-11-1-1-111-11-11
χ12111111111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11-1111-1-11-11-1
χ13111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-111111111-1-1-1-11-1-11
χ14111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-11111-1-1-1-11111-111-1
χ15111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-111111111-1-1-1-1-111-1
χ16111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-11111-1-1-1-111111-1-11
χ17222222222-2-22-2-2-2222200000000-2-222-2-2-2-22200000000-20000000000000000
χ18222222222-2-22-2-2-2222200000000-2-2-2-22222-2-200000000-20000000000000000
χ19222222222-2-22-2-2-2-2-2-2-200000000222222-2-2-2-20000000020000000000000000
χ20222222222-2-22-2-2-2-2-2-2-20000000022-2-2-2-222220000000020000000000000000
χ21222222-2-2-2-2-2-2-22200002i2i2i2i−2i−2i−2i−2i0000000000000000000000020-20002i−2i0000
χ22222222-2-2-2-2-2-2-22200002i2i2i2i−2i−2i−2i−2i00000000000000000000000-202000−2i2i0000
χ23222222-2-2-2-2-2-2-2220000−2i−2i−2i−2i2i2i2i2i0000000000000000000000020-2000−2i2i0000
χ24222222-2-2-2-2-2-2-2220000−2i−2i−2i−2i2i2i2i2i00000000000000000000000-2020002i−2i0000
χ252222-2-22-2-2222-2-2222-2-222-2-222-2-2220000000000000000-222-2-2000000000000
χ262222-2-22-2-2222-2-2222-2-2-2-222-2-222220000000000000000-2-2-222000000000000
χ272222-2-22-2-2222-2-22-2-22222-2-222-2-2-2-200000000000000002-2-222000000000000
χ282222-2-22-2-2222-2-22-2-222-2-222-2-222-2-20000000000000000222-2-2000000000000
χ292222-2-22-2-2-2-2222-222-2-200000000-2-2000000002i2i−2i−2i2i2i−2i−2i20000000000000000
χ302222-2-22-2-2-2-2222-222-2-200000000-2-200000000−2i−2i2i2i−2i−2i2i2i20000000000000000
χ312222-2-22-2-2-2-2222-2-2-2220000000022000000002i2i−2i−2i−2i−2i2i2i-20000000000000000
χ322222-2-22-2-2-2-2222-2-2-222000000002200000000−2i−2i2i2i2i2i−2i−2i-20000000000000000
χ332222-2-2-222-2-2-22-2200002i2i−2i−2i−2i−2i2i2i00000000000000000000000020-22i−2i000000
χ342222-2-2-222-2-2-22-2200002i2i−2i−2i−2i−2i2i2i000000000000000000000000-202−2i2i000000
χ352222-2-2-222-2-2-22-220000−2i−2i2i2i2i2i−2i−2i00000000000000000000000020-2−2i2i000000
χ362222-2-2-222-2-2-22-220000−2i−2i2i2i2i2i−2i−2i000000000000000000000000-2022i−2i000000
χ3722-2-22-2-22-20020002i−2i2i−2ii2−i2i2−i2i2−i2i2−i200002-22i−2i002−22−2i2−i2i2−i202−22−2000000000000
χ3822-2-22-2-22-20020002i−2i2i−2ii2−i2i2−i2i2−i2i2−i20000-22−2i2i00−22−22−i2i2−i2i202−22−2000000000000
χ3922-2-22-2-22-20020002i−2i2i−2i−i2i2−i2i2−i2i2−i2i200002-22i−2i00−22−22−i2i2−i2i20−22−22000000000000
χ4022-2-22-2-22-20020002i−2i2i−2i−i2i2−i2i2−i2i2−i2i20000-22−2i2i002−22−2i2−i2i2−i20−22−22000000000000
χ4122-2-22-2-22-2002000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i200002-2−2i2i00−22−22i2−i2i2−i20−22−22000000000000
χ4222-2-22-2-22-2002000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i20000-222i−2i002−22−2−i2i2−i2i20−22−22000000000000
χ4322-2-22-2-22-2002000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i200002-2−2i2i002−22−2−i2i2−i2i202−22−2000000000000
χ4422-2-22-2-22-2002000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i20000-222i−2i00−22−22i2−i2i2−i202−22−2000000000000
χ4522-2-2-22-2-220020002i−2i−2i2ii2−i2−i2i2i2−i2−i2i2002-200002i−2ii2−i2−i2i2−222−202−2−22000000000000
χ4622-2-2-22-2-220020002i−2i−2i2ii2−i2−i2i2i2−i2−i2i200-220000−2i2i−i2i2i2−i22−2−2202−2−22000000000000
χ4722-2-2-22-2-220020002i−2i−2i2i−i2i2i2−i2−i2i2i2−i2002-200002i−2i−i2i2i2−i22−2−220−222−2000000000000
χ4822-2-2-22-2-220020002i−2i−2i2i−i2i2i2−i2−i2i2i2−i200-220000−2i2ii2−i2−i2i2−222−20−222−2000000000000
χ4922-2-2-22-2-22002000−2i2i2i−2ii2−i2−i2i2i2−i2−i2i2002-20000−2i2ii2−i2−i2i22−2−220−222−2000000000000
χ5022-2-2-22-2-22002000−2i2i2i−2ii2−i2−i2i2i2−i2−i2i200-2200002i−2i−i2i2i2−i2−222−20−222−2000000000000
χ5122-2-2-22-2-22002000−2i2i2i−2i−i2i2i2−i2−i2i2i2−i2002-20000−2i2i−i2i2i2−i2−222−202−2−22000000000000
χ5222-2-2-22-2-22002000−2i2i2i−2i−i2i2i2−i2−i2i2i2−i200-2200002i−2ii2−i2−i2i22−2−2202−2−22000000000000
χ53444444-4-4-444-44-4-400000000000000000000000000000000000000000000000
χ544444-4-4-44444-4-44-400000000000000000000000000000000000000000000000
χ5544-4-44-44-4400-4000000022−2222−22−2222−222200000000000000000000000000000000000
χ5644-4-44-44-4400-40000000−2222−222222−2222−2200000000000000000000000000000000000
χ5744-4-4-4444-400-4000000022−22−2222−222222−2200000000000000000000000000000000000
χ5844-4-4-4444-400-40000000−222222−2222−22−222200000000000000000000000000000000000
χ598-88-80000000000000000000000042−42000000000000000000000000000000000
χ608-88-800000000000000000000000−4242000000000000000000000000000000000
χ618-8-88000008i−8i000000000000000000000000000000000000000000000000000
χ628-8-8800000−8i8i000000000000000000000000000000000000000000000000000

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