Finite Group Databasebeta

← Group #192530

Character table — Group #192530

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111222244444444888888888888888888888888881111111122224444444488888888888888888888888888
order12224444224444448888224444448888888888888888882222444422444444888822444444888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111-1-1-1-111-1-11-11-1ii−i−i1-11-111-1-1i−iii−i−iii−i−i11-1-1ii−i−i1111-1-1-1-111-1-11-11-1ii−i−i1-11-111-1-1i−iii−i−iii−i−i11-1-1ii−i−i
χ101111-1-1-1-111-1-11-11-1ii−i−i1-11-1-1-111i−iii−i−i−i−iii-1-111−i−iii1111-1-1-1-111-1-11-11-1ii−i−i1-11-1-1-111i−iii−i−i−i−iii-1-111−i−iii
χ111111-1-1-1-111-1-11-11-1ii−i−i-11-1111-1-1i−i−i−iiiii−i−i-1-111−i−iii1111-1-1-1-111-1-11-11-1ii−i−i-11-1111-1-1i−i−i−iiiii−i−i-1-111−i−iii
χ121111-1-1-1-111-1-11-11-1ii−i−i-11-11-1-111i−i−i−iii−i−iii11-1-1ii−i−i1111-1-1-1-111-1-11-11-1ii−i−i-11-11-1-111i−i−i−iii−i−iii11-1-1ii−i−i
χ131111-1-1-1-111-1-11-11-1−i−iii1-11-111-1-1−ii−i−iii−i−iii11-1-1−i−iii1111-1-1-1-111-1-11-11-1−i−iii1-11-111-1-1−ii−i−iii−i−iii11-1-1−i−iii
χ141111-1-1-1-111-1-11-11-1−i−iii1-11-1-1-111−ii−i−iiiii−i−i-1-111ii−i−i1111-1-1-1-111-1-11-11-1−i−iii1-11-1-1-111−ii−i−iiiii−i−i-1-111ii−i−i
χ151111-1-1-1-111-1-11-11-1−i−iii-11-1111-1-1−iiii−i−i−i−iii-1-111ii−i−i1111-1-1-1-111-1-11-11-1−i−iii-11-1111-1-1−iiii−i−i−i−iii-1-111ii−i−i
χ161111-1-1-1-111-1-11-11-1−i−iii-11-11-1-111−iiii−i−iii−i−i11-1-1−i−iii1111-1-1-1-111-1-11-11-1−i−iii-11-11-1-111−iiii−i−iii−i−i11-1-1−i−iii
χ17222222222222-2-2-2-2222200000000-2-20000000000000000222222222222-2-2-2-2222200000000-2-20000000000000000
χ18222222222222-2-2-2-2-2-2-2-200000000220000000000000000222222222222-2-2-2-2-2-2-2-200000000220000000000000000
χ1922222222-2-2-2-22-2-2200002-2-22000000000000000000000022222222-2-2-2-22-2-2200002-2-220000000000000000000000
χ2022222222-2-2-2-22-2-220000-222-2000000000000000000000022222222-2-2-2-22-2-220000-222-20000000000000000000000
χ2122222222-2-2-2-2-222-2000000000000002-22-200000000000022222222-2-2-2-2-222-2000000000000002-22-2000000000000
χ2222222222-2-2-2-2-222-200000000000000-22-2200000000000022222222-2-2-2-2-222-200000000000000-22-22000000000000
χ232222-2-2-2-222-2-2-22-222i2i−2i−2i00000000−2i2i00000000000000002222-2-2-2-222-2-2-22-222i2i−2i−2i00000000−2i2i0000000000000000
χ242222-2-2-2-222-2-2-22-22−2i−2i2i2i000000002i−2i00000000000000002222-2-2-2-222-2-2-22-22−2i−2i2i2i000000002i−2i0000000000000000
χ252222-2-2-2-2-2-22222-2-2000022-2-200000000000000000000002222-2-2-2-2-2-22222-2-2000022-2-20000000000000000000000
χ262222-2-2-2-2-2-22222-2-20000-2-22200000000000000000000002222-2-2-2-2-2-22222-2-20000-2-2220000000000000000000000
χ272222-2-2-2-2-2-222-2-222000000000000002i−2i−2i2i0000000000002222-2-2-2-2-2-222-2-222000000000000002i−2i−2i2i000000000000
χ282222-2-2-2-2-2-222-2-22200000000000000−2i2i2i−2i0000000000002222-2-2-2-2-2-222-2-22200000000000000−2i2i2i−2i000000000000
χ292-2-2222-2-2-222-200002i−2i2i−2i0000000000000000002−22−2i2−i2i2−i22-2-2222-2-2-222-200002i−2i2i−2i0000000000000000002−22−2i2−i2i2−i2
χ302-2-2222-2-2-222-200002i−2i2i−2i000000000000000000−22−22−i2i2−i2i22-2-2222-2-2-222-200002i−2i2i−2i000000000000000000−22−22−i2i2−i2i2
χ312-2-2222-2-2-222-20000−2i2i−2i2i0000000000000000002−22−2−i2i2−i2i22-2-2222-2-2-222-20000−2i2i−2i2i0000000000000000002−22−2−i2i2−i2i2
χ322-2-2222-2-2-222-20000−2i2i−2i2i000000000000000000−22−22i2−i2i2−i22-2-2222-2-2-222-20000−2i2i−2i2i000000000000000000−22−22i2−i2i2−i2
χ332-2-22-2-222-22-2200002-2-220000000000000000002−2−222−2−222-2-22-2-222-22-2200002-2-220000000000000000002−2−222−2−22
χ342-2-22-2-222-22-2200002-2-22000000000000000000−222−2−222−22-2-22-2-222-22-2200002-2-22000000000000000000−222−2−222−2
χ352-2-22-2-222-22-220000-222-20000000000000000002−2−22−222−22-2-22-2-222-22-220000-222-20000000000000000002−2−22−222−2
χ362-2-22-2-222-22-220000-222-2000000000000000000−222−22−2−222-2-22-2-222-22-220000-222-2000000000000000000−222−22−2−22
χ3744-4-44i−4i4i−4i000000000000000000000000002ζ−2ζ2ζ3−2ζ30000000044-4-44i−4i4i−4i000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ3844-4-44i−4i4i−4i00000000000000000000000000−2ζ2ζ−2ζ32ζ30000000044-4-44i−4i4i−4i00000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ3944-4-4−4i4i−4i4i000000000000000000000000002ζ3−2ζ32ζ−2ζ0000000044-4-4−4i4i−4i4i000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ4044-4-4−4i4i−4i4i00000000000000000000000000−2ζ32ζ3−2ζ2ζ0000000044-4-4−4i4i−4i4i00000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ414-44-44i−4i−4i4i00000000000000002-22i−2i0000000000000000004-44-44i−4i−4i4i00000000000000002-22i−2i000000000000000000
χ424-44-44i−4i−4i4i0000000000000000-22−2i2i0000000000000000004-44-44i−4i−4i4i0000000000000000-22−2i2i000000000000000000
χ434-44-4−4i4i4i−4i00000000000000002-2−2i2i0000000000000000004-44-4−4i4i4i−4i00000000000000002-2−2i2i000000000000000000
χ444-44-4−4i4i4i−4i0000000000000000-222i−2i0000000000000000004-44-4−4i4i4i−4i0000000000000000-222i−2i000000000000000000
χ454-4-4444-4-44-4-4400000000000000000000000000000000004-4-4444-4-44-4-440000000000000000000000000000000000
χ464-4-44-4-4444-44-400000000000000000000000000000000004-4-44-4-4444-44-40000000000000000000000000000000000
χ471111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ48111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111
χ4911111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111
χ5011111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1
χ511111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111
χ521111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-1
χ531111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ541111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ551111-1-1-1-111-1-11-11-1ii−i−i1-11-111-1-1i−iii−i−iii−i−i11-1-1ii−i−i-1-1-1-11111-1-111-11-11−i−iii-11-11-1-111−ii−i−iii−i−iii-1-111−i−iii
χ561111-1-1-1-111-1-11-11-1ii−i−i1-11-1-1-111i−iii−i−i−i−iii-1-111−i−iii-1-1-1-11111-1-111-11-11−i−iii-11-1111-1-1−ii−i−iiiii−i−i11-1-1ii−i−i
χ571111-1-1-1-111-1-11-11-1ii−i−i-11-1111-1-1i−i−i−iiiii−i−i-1-111−i−iii-1-1-1-11111-1-111-11-11−i−iii1-11-1-1-111−iiii−i−i−i−iii11-1-1ii−i−i
χ581111-1-1-1-111-1-11-11-1ii−i−i-11-11-1-111i−i−i−iii−i−iii11-1-1ii−i−i-1-1-1-11111-1-111-11-11−i−iii1-11-111-1-1−iiii−i−iii−i−i-1-111−i−iii
χ591111-1-1-1-111-1-11-11-1−i−iii1-11-111-1-1−ii−i−iii−i−iii11-1-1−i−iii-1-1-1-11111-1-111-11-11ii−i−i-11-11-1-111i−iii−i−iii−i−i-1-111ii−i−i
χ601111-1-1-1-111-1-11-11-1−i−iii1-11-1-1-111−ii−i−iiiii−i−i-1-111ii−i−i-1-1-1-11111-1-111-11-11ii−i−i-11-1111-1-1i−iii−i−i−i−iii11-1-1−i−iii
χ611111-1-1-1-111-1-11-11-1−i−iii-11-1111-1-1−iiii−i−i−i−iii-1-111ii−i−i-1-1-1-11111-1-111-11-11ii−i−i1-11-1-1-111i−i−i−iiiii−i−i11-1-1−i−iii
χ621111-1-1-1-111-1-11-11-1−i−iii-11-11-1-111−iiii−i−iii−i−i11-1-1−i−iii-1-1-1-11111-1-111-11-11ii−i−i1-11-111-1-1i−i−i−iii−i−iii-1-111ii−i−i
χ63222222222222-2-2-2-2222200000000-2-20000000000000000-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000220000000000000000
χ64222222222222-2-2-2-2-2-2-2-200000000220000000000000000-2-2-2-2-2-2-2-2-2-2-2-22222222200000000-2-20000000000000000
χ6522222222-2-2-2-22-2-2200002-2-220000000000000000000000-2-2-2-2-2-2-2-22222-222-20000-222-20000000000000000000000
χ6622222222-2-2-2-22-2-220000-222-20000000000000000000000-2-2-2-2-2-2-2-22222-222-200002-2-220000000000000000000000
χ6722222222-2-2-2-2-222-2000000000000002-22-2000000000000-2-2-2-2-2-2-2-222222-2-2200000000000000-22-22000000000000
χ6822222222-2-2-2-2-222-200000000000000-22-22000000000000-2-2-2-2-2-2-2-222222-2-22000000000000002-22-2000000000000
χ692222-2-2-2-222-2-2-22-222i2i−2i−2i00000000−2i2i0000000000000000-2-2-2-22222-2-2222-22-2−2i−2i2i2i000000002i−2i0000000000000000
χ702222-2-2-2-222-2-2-22-22−2i−2i2i2i000000002i−2i0000000000000000-2-2-2-22222-2-2222-22-22i2i−2i−2i00000000−2i2i0000000000000000
χ712222-2-2-2-2-2-22222-2-2000022-2-20000000000000000000000-2-2-2-2222222-2-2-2-2220000-2-2220000000000000000000000
χ722222-2-2-2-2-2-22222-2-20000-2-2220000000000000000000000-2-2-2-2222222-2-2-2-222000022-2-20000000000000000000000
χ732222-2-2-2-2-2-222-2-222000000000000002i−2i−2i2i000000000000-2-2-2-2222222-2-222-2-200000000000000−2i2i2i−2i000000000000
χ742222-2-2-2-2-2-222-2-22200000000000000−2i2i2i−2i000000000000-2-2-2-2222222-2-222-2-2000000000000002i−2i−2i2i000000000000
χ752-2-2222-2-2-222-200002i−2i2i−2i0000000000000000002−22−2i2−i2i2−i2-222-2-2-2222-2-220000−2i2i−2i2i000000000000000000−22−22−i2i2−i2i2
χ762-2-2222-2-2-222-200002i−2i2i−2i000000000000000000−22−22−i2i2−i2i2-222-2-2-2222-2-220000−2i2i−2i2i0000000000000000002−22−2i2−i2i2−i2
χ772-2-2222-2-2-222-20000−2i2i−2i2i0000000000000000002−22−2−i2i2−i2i2-222-2-2-2222-2-2200002i−2i2i−2i000000000000000000−22−22i2−i2i2−i2
χ782-2-2222-2-2-222-20000−2i2i−2i2i000000000000000000−22−22i2−i2i2−i2-222-2-2-2222-2-2200002i−2i2i−2i0000000000000000002−22−2−i2i2−i2i2
χ792-2-22-2-222-22-2200002-2-220000000000000000002−2−222−2−22-222-222-2-22-22-20000-222-2000000000000000000−222−2−222−2
χ802-2-22-2-222-22-2200002-2-22000000000000000000−222−2−222−2-222-222-2-22-22-20000-222-20000000000000000002−2−222−2−22
χ812-2-22-2-222-22-220000-222-20000000000000000002−2−22−222−2-222-222-2-22-22-200002-2-22000000000000000000−222−22−2−22
χ822-2-22-2-222-22-220000-222-2000000000000000000−222−22−2−22-222-222-2-22-22-200002-2-220000000000000000002−2−22−222−2
χ8344-4-44i−4i4i−4i000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000-4-444−4i4i−4i4i00000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ8444-4-44i−4i4i−4i00000000000000000000000000−2ζ2ζ−2ζ32ζ300000000-4-444−4i4i−4i4i000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ8544-4-4−4i4i−4i4i000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000-4-4444i−4i4i−4i00000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ8644-4-4−4i4i−4i4i00000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000-4-4444i−4i4i−4i000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ874-44-44i−4i−4i4i00000000000000002-22i−2i000000000000000000-44-44−4i4i4i−4i0000000000000000-22−2i2i000000000000000000
χ884-44-44i−4i−4i4i0000000000000000-22−2i2i000000000000000000-44-44−4i4i4i−4i00000000000000002-22i−2i000000000000000000
χ894-44-4−4i4i4i−4i00000000000000002-2−2i2i000000000000000000-44-444i−4i−4i4i0000000000000000-222i−2i000000000000000000
χ904-44-4−4i4i4i−4i0000000000000000-222i−2i000000000000000000-44-444i−4i−4i4i00000000000000002-2−2i2i000000000000000000
χ914-4-4444-4-44-4-440000000000000000000000000000000000-444-4-4-444-444-40000000000000000000000000000000000
χ924-4-44-4-4444-44-40000000000000000000000000000000000-444-444-4-4-44-440000000000000000000000000000000000

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