Finite Group Databasebeta

← Group #10687359

Character table — Group #10687359

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order12222234444666444466121212121212121244448888121224242424242424244444881212121224242424224444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1111111-1-1
χ91111111-1-1-1-111111-1-11111-1-1-1-1-1-11-11-1ii−i−i1-1iiii−i−i−i−i1111i−i11-1-1ii−i−i1-1-1-11-1ii−i−ii−i
χ101111111-1-1-1-111111-1-11111-1-1-1-1-1-11-11-1ii−i−i1-1iiii−i−i−i−i-1-1-1-1i−i11-1-1ii−i−i-1111-11−i−iii−ii
χ111111111-1-1-1-111111-1-11111-1-1-1-1-1-11-11-1−i−iii1-1−i−i−i−iiiii1111−ii11-1-1−i−iii1-1-1-11-1−i−iii−ii
χ121111111-1-1-1-111111-1-11111-1-1-1-1-1-11-11-1−i−iii1-1−i−i−i−iiiii-1-1-1-1−ii11-1-1−i−iii-1111-11ii−i−ii−i
χ131111111-1-1-1-111111-1-11111-1-1-1-1-1-1-11-11ii−i−i1-1iiii−i−i−i−i1111−ii-1-111−i−iii-11-1-1-11ii−i−i−ii
χ141111111-1-1-1-111111-1-11111-1-1-1-1-1-1-11-11ii−i−i1-1iiii−i−i−i−i-1-1-1-1−ii-1-111−i−iii1-1111-1−i−iiii−i
χ151111111-1-1-1-111111-1-11111-1-1-1-1-1-1-11-11−i−iii1-1−i−i−i−iiiii1111i−i-1-111ii−i−i-11-1-1-11−i−iiii−i
χ161111111-1-1-1-111111-1-11111-1-1-1-1-1-1-11-11−i−iii1-1−i−i−i−iiiii-1-1-1-1i−i-1-111ii−i−i1-1111-1ii−i−i−ii
χ1722222222222222-2-2-2-222-2-2222-2-2200000000-2-20000000022-2-20000000000002-200000000
χ1822222222222222-2-2-2-222-2-2222-2-2200000000-2-200000000-2-222000000000000-2200000000
χ192222222-2-2-2-2222-2-22222-2-2-2-2-222-200000000-220000000022-2-2000000000000-2200000000
χ202222222-2-2-2-2222-2-22222-2-2-2-2-222-200000000-2200000000-2-2220000000000002-200000000
χ21222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-2-2-1-1-1-11111000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000221111-1-1-1-1000000000000
χ25222222-1-2-2-2-2-1-1-122-2-2-1-1-1-11111112-22-22i2i−2i−2i-11−i−i−i−iiiii00002i−2i-1-111−i−iii000000000000
χ26222222-1-2-2-2-2-1-1-122-2-2-1-1-1-11111112-22-2−2i−2i2i2i-11iiii−i−i−i−i0000−2i2i-1-111ii−i−i000000000000
χ27222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1111111-22-222i2i−2i−2i-11−i−i−i−iiiii0000−2i2i11-1-1ii−i−i000000000000
χ28222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1111111-22-22−2i−2i2i2i-11iiii−i−i−i−i00002i−2i11-1-1−i−iii000000000000
χ292222-2-2222-2-22222-22-2-2-2-2-22-2-222222-2-200002-2000000000000002-22-20000000000000000
χ302222-2-2222-2-22222-22-2-2-2-2-22-2-2222-2-22200002-200000000000000-22-220000000000000000
χ312222-2-2222-2-2222-22-22-2-2222-2-2-2-2200000000-2200000000000000000000002200-2-2000000
χ322222-2-2222-2-2222-22-22-2-2222-2-2-2-2200000000-220000000000000000000000-2-20022000000
χ332222-2-22-2-2222222-2-22-2-2-2-2-222-2-2-22-2-22000022000000000000002-2-220000000000000000
χ342222-2-22-2-2222222-2-22-2-2-2-2-222-2-2-2-222-200002200000000000000-222-20000000000000000
χ352222-2-22-2-222222-222-2-2-222-22222-200000000-2-200000000000000000000002-200-22000000
χ362222-2-22-2-222222-222-2-2-222-22222-200000000-2-20000000000000000000000-22002-2000000
χ372222-2-2-122-2-2-1-1-12-22-21111-111-1-1-122-2-20000-11−i3−i3i3i3−i3−i3i3i3000000-11-11−i3i3−i3i3000000000000
χ382222-2-2-122-2-2-1-1-12-22-21111-111-1-1-122-2-20000-11i3i3−i3−i3i3i3−i3−i3000000-11-11i3−i3i3−i3000000000000
χ392222-2-2-122-2-2-1-1-12-22-21111-111-1-1-1-2-2220000-11−i3−i3i3i3−i3−i3i3i30000001-11-1i3−i3i3−i3000000000000
χ402222-2-2-122-2-2-1-1-12-22-21111-111-1-1-1-2-2220000-11i3i3−i3−i3i3i3−i3−i30000001-11-1−i3i3−i3i3000000000000
χ412222-2-2-1-2-222-1-1-12-2-2211111-1-11112-2-220000-1-133−3−3−3−333000000-111-13−3−33000000000000
χ422222-2-2-1-2-222-1-1-12-2-2211111-1-11112-2-220000-1-1−3−33333−3−3000000-111-1−333−3000000000000
χ432222-2-2-1-2-222-1-1-12-2-2211111-1-1111-222-20000-1-133−3−3−3−3330000001-1-11−333−3000000000000
χ442222-2-2-1-2-222-1-1-12-2-2211111-1-1111-222-20000-1-1−3−33333−3−30000001-1-113−3−33000000000000
χ45444444-24444-2-2-2-4-4-4-4-2-222-2-2-222-200000000220000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-2-4-444-2-222222-2-22000000002-20000000000000000000000000000000000
χ474444-4-4-244-4-4-2-2-2-44-4422-2-2-22222-2000000002-20000000000000000000000000000000000
χ484444-4-4-2-4-444-2-2-2-444-422-2-22-2-2-2-2200000000220000000000000000000000000000000000
χ4944-4-40044-400-44-40000000040000-4000000000000000000000000000000000000002-22-200
χ5044-4-40044-400-44-40000000040000-400000000000000000000000000000000000000-22-2200
χ5144-4-4004-4400-44-400000000-400004000000000000000000000000000000000000002i−2i−2i2i00
χ5244-4-4004-4400-44-400000000-40000400000000000000000000000000000000000000−2i2i2i−2i00
χ534-44-4004004i−4i-4-440000000004i−4i00000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000
χ544-44-4004004i−4i-4-440000000004i−4i0000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000
χ554-44-400400−4i4i-4-44000000000−4i4i0000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000
χ564-44-400400−4i4i-4-44000000000−4i4i00000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000
χ574-44-400-2004i−4i22-200000023−230−2i2i−2i32i3000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ2300000000000000000000000000
χ584-44-400-2004i−4i22-200000023−230−2i2i−2i32i300000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ2300000000000000000000000000
χ594-44-400-2004i−4i22-2000000−23230−2i2i2i3−2i3000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ2300000000000000000000000000
χ604-44-400-2004i−4i22-2000000−23230−2i2i2i3−2i300000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ2300000000000000000000000000
χ614-44-400-200−4i4i22-200000023−2302i−2i2i3−2i300000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ2300000000000000000000000000
χ624-44-400-200−4i4i22-200000023−2302i−2i2i3−2i3000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ2300000000000000000000000000
χ634-44-400-200−4i4i22-2000000−232302i−2i−2i32i300000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ2300000000000000000000000000
χ644-44-400-200−4i4i22-2000000−232302i−2i−2i32i3000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ2300000000000000000000000000
χ654-4-444-4400004-4-400004-400000000000000000000000000004i−4i0000000000000000000000
χ664-4-444-4400004-4-400004-40000000000000000000000000000−4i4i0000000000000000000000
χ674-4-44-44400004-4-40000-44000000000000000000000000004i−4i000000000000000000000000
χ684-4-44-44400004-4-40000-4400000000000000000000000000−4i4i000000000000000000000000
χ6988-8-800-48-8004-4400000000-40000400000000000000000000000000000000000000000000
χ7088-8-800-4-88004-440000000040000-400000000000000000000000000000000000000000000
χ718-8-888-8-40000-4440000-440000000000000000000000000000000000000000000000000000
χ728-8-88-88-40000-44400004-40000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.