Finite Group Databasebeta

← Group #72343446

Character table — Group #72343446

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11222444444444444444488888888888161616161616161616161616161632323232323232323232323232323232323232323232323232323232646464646464646464646464
order1224422244444448888884488888888888888816161616161616162224444444888888888816161616161616164816163232323232323232
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-111-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-11-1-11-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-111-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11-1-11-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1111111-1-1-1-1
χ911111111-1-1-1-11-1-1-111-1-1-11-11iiii−i−i−i−i1-1ii−i−iii−i−i11-1-1111-1-1111-1-1-1-1iiii−i−i−i−i1-1i−iii−i−i1-1i−i11-1-1ii−i−i
χ1011111111-1-1-1-11-1-1-111-1-1-11-11iiii−i−i−i−i1-1ii−i−iii−i−i11-1-111-1-1-1-111-1-111iiii−i−i−i−i1-1i−i−i−iii-11−ii-1-111−i−iii
χ1111111111-1-1-1-11-1-1-111-1-1-11-11iiii−i−i−i−i1-1ii−i−iii−i−i11-1-1-1-11111-1-111-1-1−i−i−i−iiiii1-1i−iii−i−i1-1i−i-1-111−i−iii
χ1211111111-1-1-1-11-1-1-111-1-1-11-11iiii−i−i−i−i1-1ii−i−iii−i−i11-1-1-1-1-111-1-1-11111−i−i−i−iiiii1-1i−i−i−iii-11−ii11-1-1ii−i−i
χ1311111111-1-1-1-11-1-1-111-1-1-11-11−i−i−i−iiiii1-1−i−iii−i−iii11-1-1111-1-1111-1-1-1-1−i−i−i−iiiii1-1−ii−i−iii1-1−ii11-1-1−i−iii
χ1411111111-1-1-1-11-1-1-111-1-1-11-11−i−i−i−iiiii1-1−i−iii−i−iii11-1-111-1-1-1-111-1-111−i−i−i−iiiii1-1−iiii−i−i-11i−i-1-111ii−i−i
χ1511111111-1-1-1-11-1-1-111-1-1-11-11−i−i−i−iiiii1-1−i−iii−i−iii11-1-1-1-11111-1-111-1-1iiii−i−i−i−i1-1−ii−i−iii1-1−ii-1-111ii−i−i
χ1611111111-1-1-1-11-1-1-111-1-1-11-11−i−i−i−iiiii1-1−i−iii−i−iii11-1-1-1-1-111-1-1-11111iiii−i−i−i−i1-1−iiii−i−i-11i−i11-1-1−i−iii
χ1711111-1-1111-1-1111111111-1-1111-1-111-1-1-1-11-11-1111111111-111-111-11-11111-1-111-1-1-1-1-1-11111-1-1-1-11-11-11-11-1
χ1811111-1-1111-1-1111111111-1-1111-1-111-1-1-1-11-11-1111111111-1-11-1-11-11-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-11-11-11-11
χ1911111-1-1111-1-1111111111-1-1111-1-111-1-1-1-11-11-111111111-111-111-11-1111-1-111-1-111-1-1-1-11111-1-1-1-1-11-11-11-11
χ2011111-1-1111-1-1111111111-1-1111-1-111-1-1-1-11-11-111111111-11-1-11-1-11-11-1-1-1-111-1-111-1-1-1-1-1-1-1-111111-11-11-11-1
χ2111111-1-1111-1-1111111111-1-11-1-111-1-111-1-1-11-11-1-1-1-111111-111-111-11-111-1-111-1-111-1-111-1-1-1-1-1-1111-11-1-11-11
χ2211111-1-1111-1-1111111111-1-11-1-111-1-111-1-1-11-11-1-1-1-111111-1-11-1-11-11-1-1-1-1-111-1-111-1-111111111-1-1-11-111-11-1
χ2311111-1-1111-1-1111111111-1-11-1-111-1-111-1-1-11-11-1-1-1-11111-111-111-11-111111-1-111-1-1-1-111-1-1-1-1-1-111-11-111-11-1
χ2411111-1-1111-1-1111111111-1-11-1-111-1-111-1-1-11-11-1-1-1-11111-11-1-11-1-11-11-1-111-1-111-1-1-1-111111111-1-11-11-1-11-11
χ2511111-1-11-1-1111-1-1-111-1-1-1-111ii−i−i−i−iii-11i−i−iiii−i−i11-1-11-11-1111-1-11-1-1ii−i−i−i−iii-11−iiii−i−i-11−ii1-1-11i−i−ii
χ2611111-1-11-1-1111-1-1-111-1-1-1-111ii−i−i−i−iii-11i−i−iiii−i−i11-1-11-1-1-11-11-1-1111ii−i−i−i−iii-11−ii−i−iii1-1i−i-111-1−iii−i
χ2711111-1-11-1-1111-1-1-111-1-1-1-111ii−i−i−i−iii-11i−i−iiii−i−i11-1-1-1111-11-111-1-1-1−i−iiiii−i−i-11−iiii−i−i-11−ii-111-1−iii−i
χ2811111-1-11-1-1111-1-1-111-1-1-1-111ii−i−i−i−iii-11i−i−iiii−i−i11-1-1-11-11-1-1-111-111−i−iiiii−i−i-11−ii−i−iii1-1i−i1-1-11i−i−ii
χ2911111-1-11-1-1111-1-1-111-1-1-1-111−i−iiiii−i−i-11−iii−i−i−iii11-1-11-11-1111-1-11-1-1−i−iiiii−i−i-11i−i−i−iii-11i−i1-1-11−iii−i
χ3011111-1-11-1-1111-1-1-111-1-1-1-111−i−iiiii−i−i-11−iii−i−i−iii11-1-11-1-1-11-11-1-1111−i−iiiii−i−i-11i−iii−i−i1-1−ii-111-1i−i−ii
χ3111111-1-11-1-1111-1-1-111-1-1-1-111−i−iiiii−i−i-11−iii−i−i−iii11-1-1-1111-11-111-1-1-1ii−i−i−i−iii-11i−i−i−iii-11i−i-111-1i−i−ii
χ3211111-1-11-1-1111-1-1-111-1-1-1-111−i−iiiii−i−i-11−iii−i−i−iii11-1-1-11-11-1-1-111-111ii−i−i−i−iii-11i−iii−i−i1-1−ii1-1-11−iii−i
χ332222200-22200-2-2-22222-2-200-22i2i00−2i−2i0000−2i02i02i−2i2i−2i2-22-20200200-20-200002i−2i002i−2i00000000000000000000
χ342222200-22200-2-2-22222-2-200-22i2i00−2i−2i0000−2i02i02i−2i2i−2i2-22-20-200-2002020000−2i2i00−2i2i00000000000000000000
χ352222200-22200-2-2-22222-2-200-22i2i00−2i−2i0000−2i02i0−2i2i−2i2i-22-22200200-20-20002i−2i002i−2i0000000000000000000000
χ362222200-22200-2-2-22222-2-200-22i2i00−2i−2i0000−2i02i0−2i2i−2i2i-22-22-200-200202000−2i2i00−2i2i0000000000000000000000
χ372222200-22200-2-2-22222-2-200-2−2i−2i002i2i00002i0−2i02i−2i2i−2i-22-22200200-20-2000−2i2i00−2i2i0000000000000000000000
χ382222200-22200-2-2-22222-2-200-2−2i−2i002i2i00002i0−2i02i−2i2i−2i-22-22-200-2002020002i−2i002i−2i0000000000000000000000
χ392222200-22200-2-2-22222-2-200-2−2i−2i002i2i00002i0−2i0−2i2i−2i2i2-22-20200200-20-20000−2i2i00−2i2i00000000000000000000
χ402222200-22200-2-2-22222-2-200-2−2i−2i002i2i00002i0−2i0−2i2i−2i2i2-22-20-200-20020200002i−2i002i−2i00000000000000000000
χ412222200-2-2-200-222-222-22200-22200220000-20-202-2-222-2-220200-200-20200002-200-2200000000000000000000
χ422222200-2-2-200-222-222-22200-22200220000-20-202-2-222-2-220-20020020-20000-22002-200000000000000000000
χ432222200-2-2-200-222-222-22200-22200220000-20-20-222-2-222-2200-200-2020002-200-220000000000000000000000
χ442222200-2-2-200-222-222-22200-22200220000-20-20-222-2-222-2-20020020-2000-22002-20000000000000000000000
χ452222200-2-2-200-222-222-22200-2-2-200-2-2000020202-2-22-222-2200-200-202000-22002-20000000000000000000000
χ462222200-2-2-200-222-222-22200-2-2-200-2-2000020202-2-22-222-2-20020020-20002-200-220000000000000000000000
χ472222200-2-2-200-222-222-22200-2-2-200-2-200002020-222-22-2-220200-200-2020000-22002-200000000000000000000
χ482222200-2-2-200-222-222-22200-2-2-200-2-200002020-222-22-2-220-20020020-200002-200-2200000000000000000000
χ4922222222222222222222222222222222222222-2-2-2-2-2-2-2-200000000000000000000-2-2-2-20000000000000000
χ50222222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-200000000000000000000-2-2220000000000000000
χ5122222222-2-2-2-22-2-2-222-2-2-22-222i2i2i2i−2i−2i−2i−2i2-22i2i−2i−2i−2i−2i2i2i-2-22200000000000000000000-22−2i2i0000000000000000
χ5222222222-2-2-2-22-2-2-222-2-2-22-22−2i−2i−2i−2i2i2i2i2i2-2−2i−2i2i2i2i2i−2i−2i-2-22200000000000000000000-222i−2i0000000000000000
χ5322222-2-2222-2-2222222222-2-2222-2-222-2-2-2-22-22-2-2-2-2-2-2-2-2-20000000000000000000022220000000000000000
χ5422222-2-2222-2-2222222222-2-22-2-222-2-222-2-2-22-222222-2-2-2-20000000000000000000022-2-20000000000000000
χ5522222-2-22-2-2222-2-2-222-2-2-2-2222i2i−2i−2i−2i−2i2i2i-222i−2i−2i2i−2i−2i2i2i-2-222000000000000000000002-22i−2i0000000000000000
χ5622222-2-22-2-2222-2-2-222-2-2-2-222−2i−2i2i2i2i2i−2i−2i-22−2i2i2i−2i2i2i−2i−2i-2-222000000000000000000002-2−2i2i0000000000000000
χ574444400-44400-4-4-4-4-4-4-444004004i4i00−4i−4i000−4i04i000000000000000000000000000000000000000000000000
χ584444400-44400-4-4-4-4-4-4-44400400−4i−4i004i4i0004i0−4i000000000000000000000000000000000000000000000000
χ594444400-4-4-400-4444-4-44-4-400400440044000-40-4000000000000000000000000000000000000000000000000
χ604444400-4-4-400-4444-4-44-4-400400-4-400-4-4000404000000000000000000000000000000000000000000000000
χ61444444444444444-4-4-4-4-4-444-400000000-4-40000000000000000000000000000000000000000000000000000
χ6244444444-4-4-4-44-4-44-4-44444-4-400000000-440000000000000000000000000000000000000000000000000000
χ6344444-4-4444-4-4444-4-4-4-4-4-4-4-4-400000000440000000000000000000000000000000000000000000000000000
χ6444444-4-44-4-4444-4-44-4-4444-44-4000000004-40000000000000000000000000000000000000000000000000000
χ6544-44-4000000004i−4i04-404i−4i0004ζ−4ζ004ζ3−4ζ3000000000000000000200-200002i−2i0000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ6644-44-4000000004i−4i04-404i−4i0004ζ−4ζ004ζ3−4ζ3000000000000000000-20020000−2i2i000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ6744-44-4000000004i−4i04-404i−4i000−4ζ4ζ00−4ζ34ζ3000000000000000000200-200002i−2i000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ6844-44-4000000004i−4i04-404i−4i000−4ζ4ζ00−4ζ34ζ3000000000000000000-20020000−2i2i0000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ6944-44-400000000−4i4i04-40−4i4i0004ζ3−4ζ3004ζ−4ζ000000000000000000200-20000−2i2i0000000000002ζ3−2ζ32ζ−2ζ000000000000
χ7044-44-400000000−4i4i04-40−4i4i0004ζ3−4ζ3004ζ−4ζ000000000000000000-200200002i−2i000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ7144-44-400000000−4i4i04-40−4i4i000−4ζ34ζ300−4ζ4ζ000000000000000000200-20000−2i2i000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ7244-44-400000000−4i4i04-40−4i4i000−4ζ34ζ300−4ζ4ζ000000000000000000-200200002i−2i0000000000002ζ3−2ζ32ζ−2ζ000000000000
χ73888-8-800-800888000000000-8000000000000000000000000000000000000000000000000000000000000000
χ74888-8-800-800-8-880000000008000000000000000000000000000000000000000000000000000000000000000
χ75888-8-88880000-800000000-80000000000000000000000000000000000000000000000000000000000000000
χ76888-8-8-8-880000-80000000080000000000000000000000000000000000000000000000000000000000000000
χ7788-88-8000000008i−8i0-880−8i8i00000000000000000000000000000000000000000000000000000000000000000
χ7888-88-800000000−8i8i0-8808i−8i00000000000000000000000000000000000000000000000000000000000000000
χ7988-8-880000000000800-800000004i2−4i2004i2−4i2000000000000000000000000000000000000000000000000000000
χ8088-8-880000000000800-80000000−4i24i200−4i24i2000000000000000000000000000000000000000000000000000000
χ8188-8-880000000000-8008000000042−4200−4242000000000000000000000000000000000000000000000000000000
χ8288-8-880000000000-80080000000−42420042−42000000000000000000000000000000000000000000000000000000
χ8316-160008-808i−8i8i−8i00000000000000000000000000000000000000000000000000000000000000000000000000
χ8416-160008-80−8i8i−8i8i00000000000000000000000000000000000000000000000000000000000000000000000000
χ8516-16000-8808i−8i−8i8i00000000000000000000000000000000000000000000000000000000000000000000000000
χ8616-16000-880−8i8i8i−8i00000000000000000000000000000000000000000000000000000000000000000000000000

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