Finite Group Databasebeta

← Group #101445

Character table — Group #101445

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444444444448888888844444444448888888888884444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-11-11iiii−i−i−i−i1-111-1-111-1-1ii−i−iiiii−i−i−i−i11-1-1ii−i−i11-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-111-11-11iiii−i−i−i−i1-111-1-111-1-1ii−i−iiiii−i−i−i−i-1-111−i−iii-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-111-11-11iiii−i−i−i−i1-1-1-111-1-111ii−i−i−i−i−i−iiiii11-1-1ii−i−i-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-111-11-11iiii−i−i−i−i1-1-1-111-1-111ii−i−i−i−i−i−iiiii-1-111−i−iii11-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-111-11-11−i−i−i−iiiii1-111-1-111-1-1−i−iii−i−i−i−iiiii11-1-1−i−iii11-1-1−i−iii
χ1411111111-1-1-1-1-1-1-1-111-11-11−i−i−i−iiiii1-111-1-111-1-1−i−iii−i−i−i−iiiii-1-111ii−i−i-1-111ii−i−i
χ1511111111-1-1-1-1-1-1-1-111-11-11−i−i−i−iiiii1-1-1-111-1-111−i−iiiiiii−i−i−i−i11-1-1−i−iii-1-111ii−i−i
χ1611111111-1-1-1-1-1-1-1-111-11-11−i−i−i−iiiii1-1-1-111-1-111−i−iiiiiii−i−i−i−i-1-111ii−i−i11-1-1−i−iii
χ17222222222222222222-2-2-2-222222222-2-200000000-2-2-2-2000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000
χ1922222222222-2-2-2-22-2-2222200000000-2-22222-2-2-2-20000000000000000000000000000
χ2022222222222-2-2-2-22-2-2222200000000-2-2-2-2-2-222220000000000000000000000000000
χ2122222222222-2-2-2-22-2-2-2-2-2-200000000220000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2222222222222-2-2-2-22-2-2-2-2-2-20000000022000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-2-22222-2-2-22-22-2000000002-200000000000022-2-2-2-2220000000000000000
χ2422222222-2-2-22222-2-2-22-22-2000000002-2000000000000-2-22222-2-20000000000000000
χ2522222222-2-2-22222-2-2-2-22-2200000000-2222-2-2-2-2220000000000000000000000000000
χ2622222222-2-2-22222-2-2-2-22-2200000000-22-2-22222-2-20000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2222-22-22i2i2i2i−2i−2i−2i−2i-2200000000−2i−2i2i2i000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2222-22-2−2i−2i−2i−2i2i2i2i2i-22000000002i2i−2i−2i000000000000000000000000
χ292222-2-2-2-222-222-2-2-22-2000022-2-222-2-20000000000000000000000000000002−22−22−22−2
χ302222-2-2-2-222-222-2-2-22-2000022-2-222-2-2000000000000000000000000000000−22−22−22−22
χ312222-2-2-2-222-222-2-2-22-20000-2-222-2-2220000000000000000000000000000002−22−2−22−22
χ322222-2-2-2-222-222-2-2-22-20000-2-222-2-222000000000000000000000000000000−22−222−22−2
χ332222-2-2-2-2-2-22-2-22222-200002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000002−2−22i2−i2−i2i2
χ342222-2-2-2-2-2-22-2-22222-200002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000−222−2−i2i2i2−i2
χ352222-2-2-2-2-2-22-2-22222-20000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000002−2−22−i2i2i2−i2
χ362222-2-2-2-2-2-22-2-22222-20000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000−222−2i2−i2−i2i2
χ3722-2-2-22-222-220000-2002-2-22i2−i2i2−i2i2−i2i2−i20000002-22-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ3822-2-2-22-222-220000-2002-2-22i2−i2i2−i2i2−i2i2−i2000000-22-22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ3922-2-2-22-222-220000-2002-2-22−i2i2−i2i2−i2i2−i2i20000002-22-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ4022-2-2-22-222-220000-2002-2-22−i2i2−i2i2−i2i2−i2i2000000-22-22−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ4122-2-2-22-222-220000-200-222-2i2−i2i2−i2i2−i2i2−i2002i−2i2i−2i0000−i2i2−i2i22−2−222−2−220000000000000000
χ4222-2-2-22-222-220000-200-222-2i2−i2i2−i2i2−i2i2−i200−2i2i−2i2i0000−i2i2−i2i2−222−2−222−20000000000000000
χ4322-2-2-22-222-220000-200-222-2−i2i2−i2i2−i2i2−i2i2002i−2i2i−2i0000i2−i2i2−i2−222−2−222−20000000000000000
χ4422-2-2-22-222-220000-200-222-2−i2i2−i2i2−i2i2−i2i200−2i2i−2i2i0000i2−i2i2−i22−2−222−2−220000000000000000
χ4522-2-2-22-22-22-2000020022-2-22−22−2−22−22002i−2i−2i2i0000−222−2−i2i2i2−i2i2−i2−i2i20000000000000000
χ4622-2-2-22-22-22-2000020022-2-22−22−2−22−2200−2i2i2i−2i0000−222−2i2−i2−i2i2−i2i2i2−i20000000000000000
χ4722-2-2-22-22-22-2000020022-2-2−22−222−22−2002i−2i−2i2i00002−2−22i2−i2−i2i2−i2i2i2−i20000000000000000
χ4822-2-2-22-22-22-2000020022-2-2−22−222−22−200−2i2i2i−2i00002−2−22−i2i2i2−i2i2−i2−i2i20000000000000000
χ4922-2-2-22-22-22-20000200-2-2222−22−2−22−220000002-2-222−2−222−22−2−22−220000000000000000
χ5022-2-2-22-22-22-20000200-2-2222−22−2−22−22000000-222-22−2−22−22−222−22−20000000000000000
χ5122-2-2-22-22-22-20000200-2-222−22−222−22−20000002-2-22−222−2−22−222−22−20000000000000000
χ5222-2-2-22-22-22-20000200-2-222−22−222−22−2000000-222-2−222−22−22−2−22−220000000000000000
χ534444-4-4-4-444-4-4-444-4-4400000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-4444-4-44-4400000000000000000000000000000000000000000000000000
χ5544-4-44-44-44-4-4000040000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ5644-4-44-44-44-4-400004000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ5744-4-44-44-4-4440000-400000022−22−2222−222222−2200000000000000000000000000000000000000
χ5844-4-44-44-4-4440000-4000000−222222−2222−22−222200000000000000000000000000000000000000
χ594-44-44-4-440004i−4i4i−4i00000000000000000000000000000000000002i−2i2-2000000000000
χ604-44-44-4-440004i−4i4i−4i0000000000000000000000000000000000000−2i2i-22000000000000
χ614-44-44-4-44000−4i4i−4i4i00000000000000000000000000000000000002i−2i-22000000000000
χ624-44-44-4-44000−4i4i−4i4i0000000000000000000000000000000000000−2i2i2-2000000000000
χ634-44-4-444-40004i−4i−4i4i000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ644-44-4-444-40004i−4i−4i4i00000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ654-44-4-444-4000−4i4i4i−4i000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ664-44-4-444-4000−4i4i4i−4i00000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ678-8-8888-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-8-888000000000000000000000000000000000000000000000000000000000000

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