Finite Group Databasebeta

← Group #115015

Character table — Group #115015

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222222224444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444442444448888888888888888222244448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ911111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-11-11-111-1-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1-111-1-11-1-111−i−iiiii−i−i−i−iii
χ1111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-111-1-111-1-1-111−i−iii−i−iiiii−i−i
χ1211111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11-11-1111-1-1ii−i−i−i−iii−i−iii
χ1311111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-11-11-111-1-1−i−iii−i−iii−i−iii
χ1411111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1-111-1-11-1-111ii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-111-1-111-1-1-111ii−i−iii−i−i−i−iii
χ1611111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11-11-1111-1-1−i−iiiii−i−iii−i−i
χ172222222222222-2-2-2-2-2-2-22-22-2-2-22-20000000000000000000000000000000000002i−2i2i−2i
χ182222222222222-2-2-2-2-2-2-22-22-2-2-22-2000000000000000000000000000000000000−2i2i−2i2i
χ1922222222-2-2-2-2-22-2-22222-222-2-2-2-220000000000000000000000000000000000002-2-22
χ2022222222-2-2-2-2-22-2-22222-222-2-2-2-22000000000000000000000000000000000000-222-2
χ21222222-2-2222-2-22-2-222-2-222-222-2-2-200000000000000000000000000002-22-200000000
χ22222222-2-2222-2-22-2-222-2-222-222-2-2-20000000000000000000000000000-22-2200000000
χ23222222-2-2222-2-2-222-2-2222-2-2-2-22-2200000000000000002-200-22000000000000000000
χ24222222-2-2222-2-2-222-2-2222-2-2-2-22-220000000000000000-22002-2000000000000000000
χ25222222-2-2-2-2-22222222-2-2-22-2-2-222-200000000000000002200-2-2000000000000000000
χ26222222-2-2-2-2-22222222-2-2-22-2-2-222-20000000000000000-2-20022000000000000000000
χ27222222-2-2-2-2-222-2-2-2-2-222-2-2-222-22200000000000000000000000000002i−2i−2i2i00000000
χ28222222-2-2-2-2-222-2-2-2-2-222-2-2-222-2220000000000000000000000000000−2i2i2i−2i00000000
χ292222-2-22222-2-2-2222-2-222-22-22-2-22-20000000000000000002-200-220000000000000000
χ302222-2-22222-2-2-2222-2-222-22-22-2-22-2000000000000000000-22002-20000000000000000
χ312222-2-22222-2-2-2-2-2-222-2-2-2-2-2-222222i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ322222-2-22222-2-2-2-2-2-222-2-2-2-2-2-22222−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ332222-2-222-2-22222-2-2-2-22222-2-222-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000
χ342222-2-222-2-22222-2-2-2-22222-2-222-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000
χ352222-2-222-2-2222-22222-2-22-2-22-2-2-220000000000000000002200-2-20000000000000000
χ362222-2-222-2-2222-22222-2-22-2-22-2-2-22000000000000000000-2-200220000000000000000
χ372222-2-2-2-222-2222-2-2-2-2-2-2-2222-22-22000000000000000000000000000000002i−2i2i−2i0000
χ382222-2-2-2-222-2222-2-2-2-2-2-2-2222-22-2200000000000000000000000000000000−2i2i−2i2i0000
χ392222-2-2-2-222-222-2222222-2-22-22-2-2-20000000000000000000000002-22-2000000000000
χ402222-2-2-2-222-222-2222222-2-22-22-2-2-2000000000000000000000000-22-22000000000000
χ412222-2-2-2-2-2-22-2-2222-2-2-2-2222-22-2220000000000000000000000002-2-22000000000000
χ422222-2-2-2-2-2-22-2-2222-2-2-2-2222-22-222000000000000000000000000-222-2000000000000
χ432222-2-2-2-2-2-22-2-2-2-2-222222-222-222-2000000000000000000000000000000002-2-220000
χ442222-2-2-2-2-2-22-2-2-2-2-222222-222-222-200000000000000000000000000000000-222-20000
χ4544-4-400004i−4i00004-4004i−4i000000002ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ3000000000000000000000000
χ4644-4-400004i−4i00004-4004i−4i00000000−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3000000000000000000000000
χ4744-4-400004i−4i0000-4400−4i4i000000002ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ000000000000000000000000
χ4844-4-400004i−4i0000-4400−4i4i00000000−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ000000000000000000000000
χ4944-4-40000−4i4i00004-400−4i4i000000002ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ000000000000000000000000
χ5044-4-40000−4i4i00004-400−4i4i00000000−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ000000000000000000000000
χ5144-4-40000−4i4i0000-44004i−4i000000002ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ3000000000000000000000000
χ5244-4-40000−4i4i0000-44004i−4i00000000−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ3000000000000000000000000
χ534-44-4004-40044-40000000-4000000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000000000
χ544-44-4004-40044-40000000-400000000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000000000
χ554-44-4004-400-4-44000000040000000000022−2222−22−2222−22220000000000000000000000000000
χ564-44-4004-400-4-440000000400000000000−2222−222222−2222−220000000000000000000000000000
χ574-44-400-44004-440000000-400000002i2−2i22i2−2i2000000002i2−2i22i2−2i2000000000000000000000000
χ584-44-400-44004-440000000-40000000−2i22i2−2i22i200000000−2i22i2−2i22i2000000000000000000000000
χ594-44-400-4400-44-400000004000000022−2222−2200000000−2222−2222000000000000000000000000
χ604-44-400-4400-44-4000000040000000−2222−22220000000022−2222−22000000000000000000000000
χ614-4-444-400000004004-4000-40000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ624-4-444-400000004004-4000-4000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ634-4-444-40000000-400-4400040000002-2-222-2-222-2-222-2-22000000000000000000000000
χ644-4-444-40000000-400-440004000000-222-2-222-2-222-2-222-2000000000000000000000000
χ654-4-44-440000000400-44000-40000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ664-4-44-440000000400-44000-4000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ674-4-44-440000000-4004-400040000002-2-22-222-2-222-22-2-22000000000000000000000000
χ684-4-44-440000000-4004-40004000000-222-22-2-222-2-22-222-2000000000000000000000000

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