Finite Group Databasebeta

← Group #10827739

Character table — Group #10827739

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444444444448888888888888888888888888888888888242424242424242448484848
order12442223444666121212122244444466121212121212121212122244444444666666121212121212121212121212121212121212224488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-1-111-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-1-111-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ9111111111111111111-1-1-1-111111111111111111-11-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11-11-111-1-11-11-1
χ10111111111111111111-1-1-1-111111111111111111-11-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-11-11-1-111-11-11
χ11111111111111111111-1-1-1-11111111111111111-11-11-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111-11-111-1-1-11-11
χ12111111111111111111-1-1-1-11111111111111111-11-11-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-11-11-1-1111-11-1
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111-11-1-1-1111-1-11
χ14111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111-11-1111-1-1-111-1
χ15111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111111111-1-11-11-1-1-111-111-1
χ16111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-11-1111-1-11-1-11
χ172222222-1222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ182222222-1222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-11111-1-1-1-1-1-1111111111111000000000000
χ192222222-1222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1111111112-22-2-2-222-2-2-1-1-1-111-1-11111-1-1-1-1-1-1111111000000000000
χ202222222-1222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-22-22-2-2-2-222-1-111-1-1-1-11111111111-1-1-1-1-1-1000000000000
χ212222222-1222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-12-22-2-2-2-2-22211-1-111111111-1-11111-1-1-1-111000000000000
χ222222222-1222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-22-22-2-222-2-21111-1-111111111-1-1-1-11111-1-1000000000000
χ232222222-1222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111222222-2-2-2-211-1-1-1-111-1-1-1-1-1-111111111-1-1000000000000
χ242222222-1222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111-2-2-2-222222211111111-1-1-1-111-1-1-1-1-1-1-1-111000000000000
χ252222-2-2222-2-222222222-22-222-2-2-2-2-2-22222-2-2-2-200002-200002-200002-222-2-2000000000000000000000000
χ262222-2-2222-2-222222222-22-2-2-222-2-2-2-2-2-2-2-222220000-2200002-200002-2-2-222000000000000000000000000
χ272222-2-2222-2-22222222-22-2222-2-2-2-2-2-22222-2-2-2-20000-220000-220000-22-2-222000000000000000000000000
χ282222-2-2222-2-22222222-22-22-2-222-2-2-2-2-2-2-2-2222200002-20000-220000-2222-2-2000000000000000000000000
χ292222-2-22-12-2-2-1-1-1-1-1-1-12-22-222-2-21111-1-1-1-1111100002-20000-11−i3i3−i3i3-11-1-111−i3i3−i3−i3i3i3−i3−i3i3i3−i3i3000000000000
χ302222-2-22-12-2-2-1-1-1-1-1-1-12-22-222-2-21111-1-1-1-1111100002-20000-11i3−i3i3−i3-11-1-111i3−i3i3i3−i3−i3i3i3−i3−i3i3−i3000000000000
χ312222-2-22-12-2-2-1-1-1-1-1-1-12-22-2-2-22211111111-1-1-1-10000-220000-11−i3i3i3−i3-1111-1-1−i3i3−i3−i3i3i3i3i3−i3−i3i3−i3000000000000
χ322222-2-22-12-2-2-1-1-1-1-1-1-12-22-2-2-22211111111-1-1-1-10000-220000-11i3−i3−i3i3-1111-1-1i3−i3i3i3−i3−i3−i3−i3i3i3−i3i3000000000000
χ332222-2-22-12-2-2-1-1-1-1-1-1-1-22-2222-2-21111-1-1-1-111110000-2200001-1−i3i3i3−i31-111-1-1−i3i3i3i3−i3−i3−i3−i3i3i3i3−i3000000000000
χ342222-2-22-12-2-2-1-1-1-1-1-1-1-22-2222-2-21111-1-1-1-111110000-2200001-1i3−i3−i3i31-111-1-1i3−i3−i3−i3i3i3i3i3−i3−i3−i3i3000000000000
χ352222-2-22-12-2-2-1-1-1-1-1-1-1-22-22-2-22211111111-1-1-1-100002-200001-1−i3i3−i3i31-1-1-111−i3i3i3i3−i3−i3i3i3−i3−i3−i3i3000000000000
χ362222-2-22-12-2-2-1-1-1-1-1-1-1-22-22-2-22211111111-1-1-1-100002-200001-1i3−i3i3−i31-1-1-111i3−i3−i3−i3i3i3−i3−i3i3i3i3−i3000000000000
χ3722-2-22222-2-2-2222-2-2-2-22-2-22000022-2-20000000020-20002-2002-22200-220000-2-22-22-2000000000000000000
χ3822-2-22222-2-2-2222-2-2-2-22-2-22000022-2-200000000-202000-22002-2-2-200-22000022-22-22000000000000000000
χ3922-2-22222-2-2-2222-2-2-2-2-222-2000022-2-20000000020-2000-2200-2222002-20000-2-2-22-22000000000000000000
χ4022-2-22222-2-2-2222-2-2-2-2-222-2000022-2-200000000-2020002-200-22-2-2002-20000222-22-2000000000000000000
χ4122-2-2222-1-2-2-2-1-1-111112-2-220000-1-111−i3−i3i3i3−i3−i3i3i320-20002-200-11-1-1−i3i31-1−i3i3−i3i311-11-11−i3i3−i3i3i3−i3000000000000
χ4222-2-2222-1-2-2-2-1-1-111112-2-220000-1-111−i3−i3i3i3−i3−i3i3i3-202000-2200-1111i3−i31-1−i3i3−i3i3-1-11-11-1i3−i3i3−i3−i3i3000000000000
χ4322-2-2222-1-2-2-2-1-1-111112-2-220000-1-111i3i3−i3−i3i3i3−i3−i320-20002-200-11-1-1i3−i31-1i3−i3i3−i311-11-11i3−i3i3−i3−i3i3000000000000
χ4422-2-2222-1-2-2-2-1-1-111112-2-220000-1-111i3i3−i3−i3i3i3−i3−i3-202000-2200-1111−i3i31-1i3−i3i3−i3-1-11-11-1−i3i3−i3i3i3−i3000000000000
χ4522-2-2222-1-2-2-2-1-1-11111-222-20000-1-111−i3−i3i3i3−i3−i3i3i320-2000-22001-1-1-1i3−i3-11i3−i3i3−i3111-11-1−i3i3−i3i3−i3i3000000000000
χ4622-2-2222-1-2-2-2-1-1-11111-222-20000-1-111−i3−i3i3i3−i3−i3i3i3-2020002-2001-111−i3i3-11i3−i3i3−i3-1-1-11-11i3−i3i3−i3i3−i3000000000000
χ4722-2-2222-1-2-2-2-1-1-11111-222-20000-1-111i3i3−i3−i3i3i3−i3−i320-2000-22001-1-1-1−i3i3-11−i3i3−i3i3111-11-1i3−i3i3−i3i3−i3000000000000
χ4822-2-2222-1-2-2-2-1-1-11111-222-20000-1-111i3i3−i3−i3i3i3−i3−i3-2020002-2001-111i3−i3-11−i3i3−i3i3-1-1-11-11−i3i3−i3i3−i3i3000000000000
χ4922-2-22-2-2222-22-2-222-2-200002i−2i2i−2i2-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000020-2002i−2i0000
χ5022-2-22-2-2222-22-2-222-2-200002i−2i2i−2i2-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000-20200−2i2i0000
χ5122-2-22-2-2222-22-2-222-2-20000−2i2i−2i2i2-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000020-200−2i2i0000
χ5222-2-22-2-2222-22-2-222-2-20000−2i2i−2i2i2-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000-202002i−2i0000
χ5322-2-2-22-222-222-2-222-2-200002i−2i−2i2i-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000020-202i−2i000000
χ5422-2-2-22-222-222-2-222-2-200002i−2i−2i2i-22-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000-2020−2i2i000000
χ5522-2-2-22-222-222-2-222-2-20000−2i2i2i−2i-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000020-20−2i2i000000
χ5622-2-2-22-222-222-2-222-2-20000−2i2i2i−2i-22-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000-20202i−2i000000
χ5722-2-2-2-222-222222-2-2-2-222-2-20000-2-22200000000020-200002-2220022-2-200000000002-2-22-2-2000000000000
χ5822-2-2-2-222-222222-2-2-2-222-2-20000-2-222000000000-2020000-222200-2-2-2-20000000000-222-222000000000000
χ5922-2-2-2-222-222222-2-2-2-2-2-2220000-2-22200000000020-20000-22-2-20022220000000000-222-2-2-2000000000000
χ6022-2-2-2-222-222222-2-2-2-2-2-2220000-2-222000000000-20200002-2-2-200-2-22200000000002-2-2222000000000000
χ6122-2-2-2-22-1-222-1-1-1111122-2-2000011-1-1−i3−i3i3i3i3i3−i3−i3020-200002-2-1-1−i3i3-1-111−i3i3i3−i3i3−i3−i3i3i3−i3-111-111000000000000
χ6222-2-2-2-22-1-222-1-1-1111122-2-2000011-1-1−i3−i3i3i3i3i3−i3−i30-2020000-22-1-1i3−i31111−i3i3i3−i3−i3i3i3−i3−i3i31-1-11-1-1000000000000
χ6322-2-2-2-22-1-222-1-1-1111122-2-2000011-1-1i3i3−i3−i3−i3−i3i3i3020-200002-2-1-1i3−i3-1-111i3−i3−i3i3−i3i3i3−i3−i3i3-111-111000000000000
χ6422-2-2-2-22-1-222-1-1-1111122-2-2000011-1-1i3i3−i3−i3−i3−i3i3i30-2020000-22-1-1−i3i31111i3−i3−i3i3i3−i3−i3i3i3−i31-1-11-1-1000000000000
χ6522-2-2-2-22-1-222-1-1-11111-2-222000011-1-1−i3−i3i3i3i3i3−i3−i3020-20000-2211i3−i3-1-1-1-1i3−i3−i3i3−i3i3−i3i3i3−i31-1-1111000000000000
χ6622-2-2-2-22-1-222-1-1-11111-2-222000011-1-1−i3−i3i3i3i3i3−i3−i30-20200002-211−i3i311-1-1i3−i3−i3i3i3−i3i3−i3−i3i3-111-1-1-1000000000000
χ6722-2-2-2-22-1-222-1-1-11111-2-222000011-1-1i3i3−i3−i3−i3−i3i3i3020-20000-2211−i3i3-1-1-1-1−i3i3i3−i3i3−i3i3−i3−i3i31-1-1111000000000000
χ6822-2-2-2-22-1-222-1-1-11111-2-222000011-1-1i3i3−i3−i3−i3−i3i3i30-20200002-211i3−i311-1-1−i3i3i3−i3−i3i3−i3i3i3−i3-111-1-1-1000000000000
χ6944444-4-44-4-444-4-4-4-444000000004-4-44000000000000000000000000000000000000000000000000000000
χ7044444-4-4-2-4-44-22222-2-200000000-222-223−23−232323−23−23230000000000000000000000000000000000000000000000
χ7144444-4-4-2-4-44-22222-2-200000000-222-2−232323−23−232323−230000000000000000000000000000000000000000000000
χ724444-44-44-44-44-4-4-4-44400000000-444-4000000000000000000000000000000000000000000000000000000
χ734444-44-4-2-44-4-22222-2-2000000002-2-2223−23−2323−232323−230000000000000000000000000000000000000000000000
χ744444-44-4-2-44-4-22222-2-2000000002-2-22−232323−2323−23−23230000000000000000000000000000000000000000000000
χ7544-4-44-4-4-244-4-222-2-22200004i−4i4i−4i-22-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ7644-4-44-4-4-244-4-222-2-2220000−4i4i−4i4i-22-222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ7744-4-4-44-4-24-44-222-2-22200004i−4i−4i4i2-22-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ7844-4-4-44-4-24-44-222-2-2220000−4i4i4i−4i2-22-22i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ798-88i−8i0008000-800008i−8i000000000000000000000000000000000000000000000000000000000000000000
χ808-88i−8i000-40004−4i34i343−43−4i4i000000000000000000000000000000000000000000000000000000000000000000
χ818-88i−8i000-400044i3−4i3−4343−4i4i000000000000000000000000000000000000000000000000000000000000000000
χ828-8−8i8i0008000-80000−8i8i000000000000000000000000000000000000000000000000000000000000000000
χ838-8−8i8i000-40004−4i34i3−43434i−4i000000000000000000000000000000000000000000000000000000000000000000
χ848-8−8i8i000-400044i3−4i343−434i−4i000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).