Finite Group Databasebeta

← Group #116204

Character table — Group #116204

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222222224444444444444444444444161616161616161616161616161616161616161616161616
order12222222222222444444442244448888888888888888444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ9111111-1-1-1-1-111-1-1-111-1-1-1-11-1111-1iiiiiiii−i−i−i−i−i−i−i−i1-11-111-1-1ii−i−ii−i11-1-1ii−i−ii−i
χ10111111-1-1-1-1-111-1-1-111-1-1-1-11-1111-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1-1-111ii−i−i−ii-1-111−i−iii−ii
χ11111111-1-1-1-1-111-1-1-111-1-1-1-11-1111-1iiiiiiii−i−i−i−i−i−i−i−i-11-1111-1-1−i−iiii−i-1-111−i−iiii−i
χ12111111-1-1-1-1-111-1-1-111-1-1-1-11-1111-1iiiiiiii−i−i−i−i−i−i−i−i-11-11-1-111−i−iii−ii11-1-1ii−i−i−ii
χ13111111-1-1-1-1-111-1-1-111-1-1-1-11-1111-1−i−i−i−i−i−i−i−iiiiiiiii1-11-111-1-1−i−iii−ii11-1-1−i−iii−ii
χ14111111-1-1-1-1-111-1-1-111-1-1-1-11-1111-1−i−i−i−i−i−i−i−iiiiiiiii1-11-1-1-111−i−iiii−i-1-111ii−i−ii−i
χ15111111-1-1-1-1-111-1-1-111-1-1-1-11-1111-1−i−i−i−i−i−i−i−iiiiiiiii-11-1111-1-1ii−i−i−ii-1-111ii−i−i−ii
χ16111111-1-1-1-1-111-1-1-111-1-1-1-11-1111-1−i−i−i−i−i−i−i−iiiiiiiii-11-11-1-111ii−i−ii−i11-1-1−i−iiii−i
χ1722222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000000000000000002i−2i00000000−2i2i
χ1822222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000−2i2i000000002i−2i
χ19222222222-2-2-2-222222-2-2-2-2-2-22-2-2200000000000000000000000000000000002i−2i2i−2i00
χ20222222222-2-2-2-222222-2-2-2-2-2-22-2-220000000000000000000000000000000000−2i2i−2i2i00
χ21222222222-2-2-2-22-2-2-2-22222-2-2-222-2000000000000000022-2-200000000000000000000
χ22222222222-2-2-2-22-2-2-2-22222-2-2-222-20000000000000000-2-22200000000000000000000
χ23222222-2-2-222-2-2-222-2-2-2-2-2-2-22-222200000000000000002-2-2200000000000000000000
χ24222222-2-2-222-2-2-222-2-2-2-2-2-2-22-22220000000000000000-222-200000000000000000000
χ25222222-2-2-222-2-2-2-2-2222222-222-2-2-200000000000000000000000000000000002-2-2200
χ26222222-2-2-222-2-2-2-2-2222222-222-2-2-20000000000000000000000000000000000-222-200
χ27222222-2-2-2-2-222-222-2-222222-2-2-2-2200000000000000000000000000002200000000-2-2
χ28222222-2-2-2-2-222-222-2-222222-2-2-2-220000000000000000000000000000-2-20000000022
χ292222-2-222-222-2-2-2222222-2-22-2-22-2-20000000000000000000000002i−2i2i−2i000000000000
χ302222-2-222-222-2-2-2222222-2-22-2-22-2-2000000000000000000000000−2i2i−2i2i000000000000
χ312222-2-222-222-2-2-2-2-2-2-2-2-2222-22-2220000000000000000000000000000002i−2i2i−2i000000
χ322222-2-222-222-2-2-2-2-2-2-2-2-2222-22-222000000000000000000000000000000−2i2i−2i2i000000
χ332222-2-222-2-2-222-22222-2-222-22-2-22-2000000000000000000002-22-20000000000000000
χ342222-2-222-2-2-222-22222-2-222-22-2-22-200000000000000000000-22-220000000000000000
χ352222-2-222-2-2-222-2-2-2-2-222-2-2-2222-222i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ362222-2-222-2-2-222-2-2-2-2-222-2-2-2222-22−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ372222-2-2-2-222222222-2-2-2-222-2-222-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000
χ382222-2-2-2-222222222-2-2-2-222-2-222-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000
χ392222-2-2-2-2222222-2-22222-2-2-2-2-2-222000000000000000000002-2-220000000000000000
χ402222-2-2-2-2222222-2-22222-2-2-2-2-2-22200000000000000000000-222-20000000000000000
χ412222-2-2-2-22-2-2-2-2222-2-222-2-2222-22-20000000000000000000000000000002i−2i−2i2i000000
χ422222-2-2-2-22-2-2-2-2222-2-222-2-2222-22-2000000000000000000000000000000−2i2i2i−2i000000
χ432222-2-2-2-22-2-2-2-22-2-222-2-22222-22-220000000000000000000000002-2-22000000000000
χ442222-2-2-2-22-2-2-2-22-2-222-2-22222-22-22000000000000000000000000-222-2000000000000
χ4544-4-4000044-44-4-40000000000000000002222−22−222222−22−220000000000000000000000000000
χ4644-4-4000044-44-4-4000000000000000000−22−222222−22−2222220000000000000000000000000000
χ4744-4-400004-44-44-4000000000000002222−22−22000000002222−22−22000000000000000000000000
χ4844-4-400004-44-44-400000000000000−22−22222200000000−22−222222000000000000000000000000
χ4944-4-40000-44-4-444000000000000002i22i2−2i2−2i200000000−2i2−2i22i22i2000000000000000000000000
χ5044-4-40000-44-4-44400000000000000−2i2−2i22i22i2000000002i22i2−2i2−2i2000000000000000000000000
χ5144-4-40000-4-444-440000000000000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000
χ5244-4-40000-4-444-44000000000000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000
χ534-44-4004-40000004i−4i4i−4i00000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ544-44-4004-40000004i−4i4i−4i0000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ554-44-4004-4000000−4i4i−4i4i00000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ564-44-4004-4000000−4i4i−4i4i0000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ574-44-400-440000004i−4i−4i4i00000000002ζ−2ζ2ζ−2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ584-44-400-440000004i−4i−4i4i0000000000−2ζ2ζ−2ζ2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ594-44-400-44000000−4i4i4i−4i00000000002ζ3−2ζ32ζ3−2ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ604-44-400-44000000−4i4i4i−4i0000000000−2ζ32ζ3−2ζ32ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ614-4-444-40000000000004-44-40000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ624-4-444-40000000000004-44-4000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ634-4-444-4000000000000-44-440000002-2-222-2-22-222-2-222-2000000000000000000000000
χ644-4-444-4000000000000-44-44000000-222-2-222-22-2-222-2-22000000000000000000000000
χ654-4-44-440000000000004-4-440000002-2-22-222-22-2-22-222-2000000000000000000000000
χ664-4-44-440000000000004-4-44000000-222-22-2-22-222-22-2-22000000000000000000000000
χ674-4-44-44000000000000-444-40000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ684-4-44-44000000000000-444-4000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000

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