Finite Group Databasebeta

← Group #264813

Character table — Group #264813

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222244444444444444444444444488888888161616161616161616161616161616163232
order12222244444444888844888888888888888888888844444444244444448888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-11-1-1-11-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-111-1-11-1-1-11-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-111-1-11-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1111-11-1-1-1-111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-111-1-111-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1111111-1-111-1-1
χ911111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-11-11-1111-1-1-1-1111-1
χ1011111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11-1111-111-1-111-1-1-11
χ1111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-111-1-111-11
χ1211111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-111-1-11111-1-11-1
χ1311111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1111-1-111-1-1-1-1-11
χ1411111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11-1-1-111-1-1-1-11111111-1
χ1511111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111111-11-11-111-1-1-1-1-1-11-1
χ1611111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-11-11-1-1-1111-1-11111-11
χ17222222-22-2-222-222222-2-22200000000-2-2-2-200000000220022000-2000-2000000000000
χ18222222-22-2-222-222222-2-22200000000-2-2-2-200000000-2-200-2-200020002000000000000
χ19222222-22-2-222-22-2-2-2-2-2-2-2-2000000002222000000002200-2-20002000-2000000000000
χ20222222-22-2-222-22-2-2-2-2-2-2-2-200000000222200000000-2-20022000-20002000000000000
χ21222222-2-2-2-2-2-2-2-2000022002i2i2i2i−2i−2i−2i−2i000000000000002-2002-2000000000000002i−2i00
χ22222222-2-2-2-2-2-2-2-2000022002i2i2i2i−2i−2i−2i−2i00000000000000-2200-2200000000000000−2i2i00
χ23222222-2-2-2-2-2-2-2-200002200−2i−2i−2i−2i2i2i2i2i000000000000002-2002-200000000000000−2i2i00
χ24222222-2-2-2-2-2-2-2-200002200−2i−2i−2i−2i2i2i2i2i00000000000000-2200-22000000000000002i−2i00
χ252222-2-222-2-2-2-22222222-2-2-20000000022-2-200000000000000002002-200-20000000000
χ262222-2-222-2-2-2-22222222-2-2-20000000022-2-20000000000000000-200-220020000000000
χ272222-2-222-2-2-2-222-2-2-2-22-22200000000-2-2220000000000000000200-2-20020000000000
χ282222-2-222-2-2-2-222-2-2-2-22-22200000000-2-2220000000000000000-2002200-20000000000
χ292222-2-22-2-2-2222-20000-22000000000000002222-2-2-2-2002200-2-2002000-200000000000
χ302222-2-22-2-2-2222-20000-22000000000000002222-2-2-2-200-2-2002200-2000200000000000
χ312222-2-22-2-2-2222-20000-2200000000000000-2-2-2-22222002200-2-200-2000200000000000
χ322222-2-22-2-2-2222-20000-2200000000000000-2-2-2-2222200-2-20022002000-200000000000
χ332222-2-2-2222-2-2-222222-22-2-200000000-2-22200000000002-200-220000000000002-20000
χ342222-2-2-2222-2-2-222222-22-2-200000000-2-2220000000000-22002-2000000000000-220000
χ352222-2-2-2222-2-2-22-2-2-2-2-22220000000022-2-200000000002-200-22000000000000-220000
χ362222-2-2-2222-2-2-22-2-2-2-2-22220000000022-2-20000000000-22002-20000000000002-20000
χ3722-2-22-20-2002-2022i2i−2i−2i002i−2ii2i2−i2−i2i2i2−i2−i2000022−2−222−2−22-2002i−2i0000000000i2−i22−2000000
χ3822-2-22-20-2002-2022i2i−2i−2i002i−2ii2i2−i2−i2i2i2−i2−i2000022−2−222−2−2-2200−2i2i0000000000−i2i2−22000000
χ3922-2-22-20-2002-2022i2i−2i−2i002i−2i−i2−i2i2i2−i2−i2i2i20000−2−222−2−2222-2002i−2i0000000000−i2i2−22000000
χ4022-2-22-20-2002-2022i2i−2i−2i002i−2i−i2−i2i2i2−i2−i2i2i20000−2−222−2−222-2200−2i2i0000000000i2−i22−2000000
χ4122-2-22-20-2002-202−2i−2i2i2i00−2i2ii2i2−i2−i2i2i2−i2−i20000−2−222−2−2222-200−2i2i0000000000i2−i2−22000000
χ4222-2-22-20-2002-202−2i−2i2i2i00−2i2ii2i2−i2−i2i2i2−i2−i20000−2−222−2−222-22002i−2i0000000000−i2i22−2000000
χ4322-2-22-20-2002-202−2i−2i2i2i00−2i2i−i2−i2i2i2−i2−i2i2i2000022−2−222−2−22-200−2i2i0000000000−i2i22−2000000
χ4422-2-22-20-2002-202−2i−2i2i2i00−2i2i−i2−i2i2i2−i2−i2i2i2000022−2−222−2−2-22002i−2i0000000000i2−i2−22000000
χ454444444-444-4-44-40000-4-4000000000000000000000000000000000000000000000000
χ464444-4-4-4-44444-4-400004-4000000000000000000000000000000000000000000000000
χ4744-4-44-40400-440-4000000002222−22−22−22−22222200000000000000000000000000000000000000
χ4844-4-44-40400-440-400000000−22−2222222222−22−2200000000000000000000000000000000000000
χ4944-4-4-4404004-40-4000000000000000000002222−22−22−22−22222200000000000000000000000000
χ5044-4-4-4404004-40-400000000000000000000−22−2222222222−22−2200000000000000000000000000
χ5144-4-4-440-400-44044i4i−4i−4i00−4i4i0000000000000000000000000000000000000000000000
χ5244-4-4-440-400-4404−4i−4i4i4i004i−4i0000000000000000000000000000000000000000000000
χ534-44-400400000-4022−2222−2200002-22-22-22-222−220022−2222−22000000000000000000000000000000
χ544-44-400400000-4022−2222−220000-22-22-22-2222−2200−2222−2222000000000000000000000000000000
χ554-44-400400000-40−2222−222200002-22-22-22-2−222200−2222−2222000000000000000000000000000000
χ564-44-400400000-40−2222−22220000-22-22-22-22−22220022−2222−22000000000000000000000000000000
χ574-44-400-4000004022−2222−2200002i−2i2i−2i−2i2i−2i2i−22220000002i2−2i22i2−2i200000000000000000000000000
χ584-44-400-4000004022−2222−220000−2i2i−2i2i2i−2i2i−2i−2222000000−2i22i2−2i22i200000000000000000000000000
χ594-44-400-40000040−2222−222200002i−2i2i−2i−2i2i−2i2i22−22000000−2i22i2−2i22i200000000000000000000000000
χ604-44-400-40000040−2222−22220000−2i2i−2i2i2i−2i2i−2i22−220000002i2−2i22i2−2i200000000000000000000000000
χ614-4-4400004i−4i00002i2−2i2−2i22i200002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30022−222-2-22−2i2i2i−2i00000000000000000000000000
χ624-4-4400004i−4i00002i2−2i2−2i22i20000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30022−22-222-22i−2i−2i2i00000000000000000000000000
χ634-4-4400004i−4i0000−2i22i22i2−2i200002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300−2222-222-22i−2i−2i2i00000000000000000000000000
χ644-4-4400004i−4i0000−2i22i22i2−2i20000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300−22222-2-22−2i2i2i−2i00000000000000000000000000
χ654-4-440000−4i4i00002i2−2i2−2i22i200002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00−22222-2-222i−2i−2i2i00000000000000000000000000
χ664-4-440000−4i4i00002i2−2i2−2i22i20000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00−2222-222-2−2i2i2i−2i00000000000000000000000000
χ674-4-440000−4i4i0000−2i22i22i2−2i200002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0022−22-222-2−2i2i2i−2i00000000000000000000000000
χ684-4-440000−4i4i0000−2i22i22i2−2i20000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0022−222-2-222i−2i−2i2i00000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.