Finite Group Databasebeta

← Group #115014

Character table — Group #115014

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222222224444444444444444444444161616161616161616161616161616161616161616161616
order12222222222222444444442244448888888888888888244444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-111-1-1-1-1-11-1111-1iiiiiiii−i−i−i−i−i−i−i−i1-111-1-11-1ii−i−iii−i−i11-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-111-1-1-1-1-11-1111-1iiiiiiii−i−i−i−i−i−i−i−i1-11-11-1-11−i−iiiii−i−i-1-111−i−iii
χ1111111111-1-1-1-1-1-1-111-1-1-1-1-11-1111-1iiiiiiii−i−i−i−i−i−i−i−i-11-11-111-1ii−i−i−i−iii-1-111−i−iii
χ1211111111-1-1-1-1-1-1-111-1-1-1-1-11-1111-1iiiiiiii−i−i−i−i−i−i−i−i-11-1-111-11−i−iii−i−iii11-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-111-1-1-1-1-11-1111-1−i−i−i−i−i−i−i−iiiiiiiii1-111-1-11-1−i−iii−i−iii11-1-1−i−iii
χ1411111111-1-1-1-1-1-1-111-1-1-1-1-11-1111-1−i−i−i−i−i−i−i−iiiiiiiii1-11-11-1-11ii−i−i−i−iii-1-111ii−i−i
χ1511111111-1-1-1-1-1-1-111-1-1-1-1-11-1111-1−i−i−i−i−i−i−i−iiiiiiiii-11-11-111-1−i−iiiii−i−i-1-111ii−i−i
χ1611111111-1-1-1-1-1-1-111-1-1-1-1-11-1111-1−i−i−i−i−i−i−i−iiiiiiiii-11-1-111-11ii−i−iii−i−i11-1-1−i−iii
χ1722222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000000000000000002i−2i2i−2i00000000
χ1822222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000−2i2i−2i2i00000000
χ1922222222-2-2-2-2-2-22-2-2222222-2-2-2-2200000000000000000000000000002-2-2200000000
χ2022222222-2-2-2-2-2-22-2-2222222-2-2-2-220000000000000000000000000000-222-200000000
χ21222222-2-2222-2-22222-2-2-2-22-2-22-2-220000000000000000000220-2-20000000000000000
χ22222222-2-2222-2-22222-2-2-2-22-2-22-2-220000000000000000000-2-20220000000000000000
χ23222222-2-2222-2-22-2-2-22222-2-2-2-222-20000000000000000000000000000000000002-22-2
χ24222222-2-2222-2-22-2-2-22222-2-2-2-222-2000000000000000000000000000000000000-22-22
χ25222222-2-2-2-2-222-22-2-2-2-2-2-22-22-22220000000000000000000000000000000000002i−2i−2i2i
χ26222222-2-2-2-2-222-22-2-2-2-2-2-22-22-2222000000000000000000000000000000000000−2i2i2i−2i
χ27222222-2-2-2-2-222-2-2222222-2-222-2-2-200000000000000000002-20-220000000000000000
χ28222222-2-2-2-2-222-2-2222222-2-222-2-2-20000000000000000000-2202-20000000000000000
χ292222-2-22222-2-2-2-222222-2-22-22-22-2-200000000000000002-2-2002000000000000000000
χ302222-2-22222-2-2-2-222222-2-22-22-22-2-20000000000000000-22200-2000000000000000000
χ312222-2-22222-2-2-2-2-2-2-2-2-222-2-222-2222i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ322222-2-22222-2-2-2-2-2-2-2-2-222-2-222-222−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ332222-2-222-2-222222-2-222-2-22-2-22-22-22222-2-2-2-2-2-2-2-22222000000000000000000000000
χ342222-2-222-2-222222-2-222-2-22-2-22-22-2-2-2-2-222222222-2-2-2-2000000000000000000000000
χ352222-2-222-2-22222-222-2-222-2-2-2-22-22000000000000000022-200-2000000000000000000
χ362222-2-222-2-22222-222-2-222-2-2-2-22-220000000000000000-2-22002000000000000000000
χ372222-2-2-2-222-222-2222-2-22222-2-2-22-2000000000000000000000000000000002-22-20000
χ382222-2-2-2-222-222-2222-2-22222-2-2-22-200000000000000000000000000000000-22-220000
χ392222-2-2-2-222-222-2-2-2-222-2-2-22-222-220000000000000000000000002i−2i2i−2i000000000000
χ402222-2-2-2-222-222-2-2-2-222-2-2-22-222-22000000000000000000000000−2i2i−2i2i000000000000
χ412222-2-2-2-2-2-22-2-222-2-2-2-22222222-2-20000000000000000000000002-2-22000000000000
χ422222-2-2-2-2-2-22-2-222-2-2-2-22222222-2-2000000000000000000000000-222-2000000000000
χ432222-2-2-2-2-2-22-2-22-22222-2-2-222-2-222000000000000000000000000000000002-2-220000
χ442222-2-2-2-2-2-22-2-22-22222-2-2-222-2-22200000000000000000000000000000000-222-20000
χ4544-4-4004-40044-4-40000000000000000002222−22−222222−22−220000000000000000000000000000
χ4644-4-4004-40044-4-4000000000000000000−22−222222−22−2222220000000000000000000000000000
χ4744-4-4004-400-4-4440000000000000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000
χ4844-4-4004-400-4-444000000000000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000
χ4944-4-400-44004-44-4000000000000002222−22−22000000002222−22−22000000000000000000000000
χ5044-4-400-44004-44-400000000000000−22−22222200000000−22−222222000000000000000000000000
χ5144-4-400-4400-44-44000000000000002i22i2−2i2−2i200000000−2i2−2i22i22i2000000000000000000000000
χ5244-4-400-4400-44-4400000000000000−2i2−2i22i22i2000000002i22i2−2i2−2i2000000000000000000000000
χ534-44-44-4000000000004i−4i4i−4i00000002ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ544-44-44-4000000000004i−4i4i−4i0000000−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ554-44-44-400000000000−4i4i−4i4i00000002ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ000000000000000000000000
χ564-44-44-400000000000−4i4i−4i4i0000000−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ000000000000000000000000
χ574-44-4-44000000000004i−4i−4i4i00000002ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ584-44-4-44000000000004i−4i−4i4i0000000−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ594-44-4-4400000000000−4i4i4i−4i00000002ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ−2ζ000000000000000000000000
χ604-44-4-4400000000000−4i4i4i−4i0000000−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ2ζ000000000000000000000000
χ614-4-4400004-4000044-40000-40000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ624-4-4400004-4000044-40000-4000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ634-4-4400004-40000-4-44000040000002-2-22-222-22-2-22-222-2000000000000000000000000
χ644-4-4400004-40000-4-4400004000000-222-22-2-22-222-22-2-22000000000000000000000000
χ654-4-440000-4400004-440000-40000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ664-4-440000-4400004-440000-4000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ674-4-440000-440000-44-4000040000002-2-222-2-22-222-2-222-2000000000000000000000000
χ684-4-440000-440000-44-400004000000-222-2-222-22-2-222-2-22000000000000000000000000

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