Finite Group Databasebeta

← Group #101347

Character table — Group #101347

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444442244448888888822444444448888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-11-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ911111111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i11-1-1-11-1-111ii−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i11-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i11-1-1-11-1-111ii−i−iiiii−i−i−i−i-1-111−i−iii−i−iii-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i-1-1-111111-1-1ii−i−i−i−i−i−iiiii11-1-1−i−iiiii−i−i-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i-1-1-111111-1-1ii−i−i−i−i−i−iiiii-1-111ii−i−i−i−iii11-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii11-1-1-11-1-111−i−iii−i−i−i−iiiii11-1-1−i−iii−i−iii11-1-1
χ1411111111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii11-1-1-11-1-111−i−iii−i−i−i−iiiii-1-111ii−i−iii−i−i-1-111
χ1511111111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii-1-1-111111-1-1−i−iiiiiii−i−i−i−i11-1-1ii−i−i−i−iii-1-111
χ1611111111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii-1-1-111111-1-1−i−iiiiiii−i−i−i−i-1-111−i−iiiii−i−i11-1-1
χ172222222222222222-2-222-2-22222222200-200-20000-2-2-2-2000000000000000000000000
χ182222222222222222-2-222-2-2-2-2-2-2-2-2-2-200-200-200002222000000000000000000000000
χ19222222222222-2-2-2-222-2-2220000000022-222-2-2-2-2-20000000000000000000000000000
χ20222222222222-2-2-2-222-2-22200000000-2-2-2-2-2-222220000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-200000000002002000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-20000000000200200000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-2-2-2222222-2-2-2-20000000000-20020000000022-2-2-2-2220000000000000000
χ2422222222-2-2-2-2222222-2-2-2-20000000000-200200000000-2-22222-2-20000000000000000
χ2522222222-2-2-2-22222-2-2-2-22200000000222-2-2-222-2-20000000000000000000000000000
χ2622222222-2-2-2-22222-2-2-2-22200000000-2-2222-2-2-2220000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-22i2i2i2i−2i−2i−2i−2i00200-20000−2i−2i2i2i000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2−2i−2i−2i−2i2i2i2i2i00200-200002i2i−2i−2i000000000000000000000000
χ292222-2-2-2-222-2-200002-2002-222−2−222−2−22-202-2000002−22−22−22−22−22−20000000000000000
χ302222-2-2-2-222-2-200002-2002-222−2−222−2−2-220-22000002−22−2−22−22−22−220000000000000000
χ312222-2-2-2-222-2-200002-2002-2−2−222−2−2222-202-200000−22−22−22−22−22−220000000000000000
χ322222-2-2-2-222-2-200002-2002-2−2−222−2−222-220-2200000−22−222−22−22−22−20000000000000000
χ332222-2-2-2-222-2-20000-2200-2222−2−222−2−20000002i−2i2i−2i−22−22i2−i2−i2i2i2−i2−i2i20000000000000000
χ342222-2-2-2-222-2-20000-2200-2222−2−222−2−2000000−2i2i−2i2i−22−22−i2i2i2−i2−i2i2i2−i20000000000000000
χ352222-2-2-2-222-2-20000-2200-22−2−222−2−2220000002i−2i2i−2i2−22−2−i2i2i2−i2−i2i2i2−i20000000000000000
χ362222-2-2-2-222-2-20000-2200-22−2−222−2−222000000−2i2i−2i2i2−22−2i2−i2−i2i2i2−i2−i2i20000000000000000
χ372222-2-2-2-2-2-22200002-200-22i2i2−i2−i2−i2−i2i2i20000002i−2i−2i2i−i2i2i2−i22−2−22−222−20000000000000000
χ382222-2-2-2-2-2-22200002-200-22i2i2−i2−i2−i2−i2i2i2000000−2i2i2i−2i−i2i2i2−i2−222−22−2−220000000000000000
χ392222-2-2-2-2-2-22200002-200-22−i2−i2i2i2i2i2−i2−i20000002i−2i−2i2ii2−i2−i2i2−222−22−2−220000000000000000
χ402222-2-2-2-2-2-22200002-200-22−i2−i2i2i2i2i2−i2−i2000000−2i2i2i−2ii2−i2−i2i22−2−22−222−20000000000000000
χ412222-2-2-2-2-2-2220000-22002-2i2i2−i2−i2−i2−i2i2i22-20-2200000i2−i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ422222-2-2-2-2-2-2220000-22002-2i2i2−i2−i2−i2−i2i2i2-2202-200000i2−i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ432222-2-2-2-2-2-2220000-22002-2−i2−i2i2i2i2i2−i2−i22-20-2200000−i2i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ442222-2-2-2-2-2-2220000-22002-2−i2−i2i2i2i2i2−i2−i2-2202-200000−i2i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ4522-2-22-2-222i−2i2i−2i2i2i−2i−2i002-2002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000001−i−1+i1+i−1−i0000i2−i22−2
χ4622-2-22-2-222i−2i2i−2i2i2i−2i−2i002-2002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000000000−1+i1−i−1−i1+i0000−i2i2−22
χ4722-2-22-2-222i−2i2i−2i2i2i−2i−2i002-200−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000001−i−1+i1+i−1−i0000−i2i2−22
χ4822-2-22-2-222i−2i2i−2i2i2i−2i−2i002-200−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000000000−1+i1−i−1−i1+i0000i2−i22−2
χ4922-2-22-2-22−2i2i−2i2i−2i−2i2i2i002-2002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000001+i−1−i1−i−1+i0000i2−i2−22
χ5022-2-22-2-22−2i2i−2i2i−2i−2i2i2i002-2002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000−1−i1+i−1+i1−i0000−i2i22−2
χ5122-2-22-2-22−2i2i−2i2i−2i−2i2i2i002-200−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000001+i−1−i1−i−1+i0000−i2i22−2
χ5222-2-22-2-22−2i2i−2i2i−2i−2i2i2i002-200−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000−1−i1+i−1+i1−i0000i2−i2−22
χ5344-4-44-4-444i−4i4i−4i−4i−4i4i4i00-44000000000000000000000000000000000000000000000000
χ5444-4-44-4-44−4i4i−4i4i4i4i−4i−4i00-44000000000000000000000000000000000000000000000000
χ5544-4-4-444-44i−4i−4i4i00000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i00000000000000000000000000000000000000
χ5644-4-4-444-44i−4i−4i4i0000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i00000000000000000000000000000000000000
χ5744-4-4-444-4−4i4i4i−4i00000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i00000000000000000000000000000000000000
χ5844-4-4-444-4−4i4i4i−4i0000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i00000000000000000000000000000000000000
χ594-44-444-4-400004-44-40000000000000000000000000000000000002i−2i2i−2i000000000000
χ604-44-444-4-400004-44-4000000000000000000000000000000000000−2i2i−2i2i000000000000
χ614-44-444-4-40000-44-440000000000000000000000000000000000002i−2i−2i2i000000000000
χ624-44-444-4-40000-44-44000000000000000000000000000000000000−2i2i2i−2i000000000000
χ634-4-444-44-400004i−4i−4i4i000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ644-4-444-44-400004i−4i−4i4i00000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ654-4-444-44-40000−4i4i4i−4i000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ664-4-444-44-40000−4i4i4i−4i00000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ678-88-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-88-88-88000000000000000000000000000000000000000000000000000000000000

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