Finite Group Databasebeta

← Group #10949032

Character table — Group #10949032

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222222444444444444888888888888888888121212121212121212121212161616161616161616162424242424244848
order12222234444666888866881212121224242424224416161616242448484848484848482244161616161616161622666666121244448844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1
χ41111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-111
χ5111111111111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-11111-1-1-1-1
χ91111-1-111-1-111111111-1-1-1-11-1-11111111-1-111-1-1-1-11111-1-1-1-11-11-11111-1-1-1-11-11111-1-1-1-111-1-11-11-1
χ101111-1-111-1-111111111-1-1-1-11-1-11111111-1-111-1-1-1-11111-1-1-1-1-11-11-1-1-1-111111-11111-1-1-1-1-1-111-11-11
χ111111-1-111-1-111111111-1-1-1-11-1-11111111-1-1-1-111-1-1-1-1-1-111111-11-1-1-1-1-11111-1111-1-111-1-111-1-11-1-11
χ121111-1-111-1-111111111-1-1-1-11-1-11111111-1-1-1-111-1-1-1-1-1-11111-11-111111-1-1-1-1-1111-1-111-1-1-1-111-111-1
χ131111-1-111-1-111111111-1-1-1-11-1-111111-1-11111-1-1-1-11111-1-1-1-11-11-11111-1-1-1-1-11-1-1-1-11111-1-1111-1-11
χ141111-1-111-1-111111111-1-1-1-11-1-111111-1-11111-1-1-1-11111-1-1-1-1-11-11-1-1-1-11111-11-1-1-1-1111111-1-1-111-1
χ151111-1-111-1-111111111-1-1-1-11-1-111111-1-111-1-111-1-1-1-1-1-111111-11-1-1-1-1-111111-1-1-111-1-111-1-1111-11-1
χ161111-1-111-1-111111111-1-1-1-11-1-111111-1-111-1-111-1-1-1-1-1-11111-11-111111-1-1-1-11-1-1-111-1-11111-1-1-11-11
χ1722222222222222-2-2-2-222-2-22222-2-2-2-200000000-2-20000000022220000000000000000000000-2-200
χ1822222222222222-2-2-2-222-2-22222-2-2-2-200000000-2-200000000-2-2-2-200000000000000000000002200
χ192222222-2-2-2-222200002200-2-2-2-2000000002−22−20022−2−222−2−22-2-2222−2−222−2−2000000000000000000
χ202222222-2-2-2-222200002200-2-2-2-2000000002−22−20022−2−222−2−2-222-2−2−222−2−222000000000000000000
χ212222222-2-2-2-222200002200-2-2-2-200000000−22−2200−2−222−2−2222-2-22−2−222−2−222000000000000000000
χ222222222-2-2-2-222200002200-2-2-2-200000000−22−2200−2−222−2−222-222-222−2−222−2−2000000000000000000
χ23222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1-1-1-1-100000000
χ24222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111000000000000-2-2-1-11111-1-100000000
χ25222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1000000000000-2-21111111100000000
χ26222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000000000002211-1-1-1-11100000000
χ272222-2-222-2-22222-2-2-2-2-2-2222-2-22-2-2-2-20000000022000000002-22-20000000000000000000000-2200
χ282222-2-222-2-22222-2-2-2-2-2-2222-2-22-2-2-2-2000000002200000000-22-2200000000000000000000002-200
χ292222-2-22-222-22220000-2-200-222-2000000002−2−220022−2−2−2−22222-2-222−2−2−2−222000000000000000000
χ302222-2-22-222-22220000-2-200-222-2000000002−2−220022−2−2−2−222-2-222−2−22222−2−2000000000000000000
χ312222-2-22-222-22220000-2-200-222-200000000−222−200−2−22222−2−222-2-2−2−22222−2−2000000000000000000
χ322222-2-22-222-22220000-2-200-222-200000000−222−200−2−22222−2−2-2-22222−2−2−2−222000000000000000000
χ332222-2-2-12-2-22-1-1-1222211-2-2-111-1-1-1-1-122-2-222-2-211-1-1-1-111110000000000002-2-1-1-1-1111100000000
χ342222-2-2-12-2-22-1-1-1222211-2-2-111-1-1-1-1-122-2-2-2-222111111-1-1-1-1000000000000-22-1-111-1-11100000000
χ352222-2-2-12-2-22-1-1-1222211-2-2-111-1-1-1-1-1-2-22222-2-211-1-1-1-11111000000000000-221111-1-1-1-100000000
χ362222-2-2-12-2-22-1-1-1222211-2-2-111-1-1-1-1-1-2-222-2-222111111-1-1-1-10000000000002-211-1-111-1-100000000
χ372-2-222-22-22-22-2-2222-2-22-22-2-22-22-2-2222-22-200002-200000000000000000000002-200002-200000000
χ382-2-222-22-22-22-2-2222-2-22-22-2-22-22-2-222-22-2200002-20000000000000000000000-220000-2200000000
χ392-2-222-22-22-22-2-22-2-2222-2-22-22-2222-2-200000000-220000000000000000000000000000002-22-20000
χ402-2-222-22-22-22-2-22-2-2222-2-22-22-2222-2-200000000-22000000000000000000000000000000-22-220000
χ412-2-222-2-1-22-2211-122-2-2-112-21-11-111-1-12-22-20000-11−i3i3−i3i3−i3i3−i3i300000000000000-11−i3i3−i3i3-1100000000
χ422-2-222-2-1-22-2211-122-2-2-112-21-11-111-1-12-22-20000-11i3−i3i3−i3i3−i3i3−i300000000000000-11i3−i3i3−i3-1100000000
χ432-2-222-2-1-22-2211-122-2-2-112-21-11-111-1-1-22-220000-11−i3i3−i3i3−i3i3−i3i3000000000000001-1i3−i3i3−i31-100000000
χ442-2-222-2-1-22-2211-122-2-2-112-21-11-111-1-1-22-220000-11i3−i3i3−i3i3−i3i3−i3000000000000001-1−i3i3−i3i31-100000000
χ452-2-22-222-2-222-2-2222-2-2-22-22-2-222-2-2222-2-220000-2200000000000000000000002-20000-2200000000
χ462-2-22-222-2-222-2-2222-2-2-22-22-2-222-2-222-222-20000-220000000000000000000000-2200002-200000000
χ472-2-22-222-2-222-2-22-2-222-222-2-2-22222-2-2000000002-20000000000000000000000000000002-2-220000
χ482-2-22-222-2-222-2-22-2-222-222-2-2-22222-2-2000000002-2000000000000000000000000000000-222-20000
χ492-2-22-22-1-2-22211-122-2-21-1-2211-1-111-1-12-2-2200001-1−i3i3−i3i3i3−i3i3−i300000000000000-11−i3i3i3−i31-100000000
χ502-2-22-22-1-2-22211-122-2-21-1-2211-1-111-1-12-2-2200001-1i3−i3i3−i3−i3i3−i3i300000000000000-11i3−i3−i3i31-100000000
χ512-2-22-22-1-2-22211-122-2-21-1-2211-1-111-1-1-222-200001-1−i3i3−i3i3i3−i3i3−i3000000000000001-1i3−i3−i3i3-1100000000
χ522-2-22-22-1-2-22211-122-2-21-1-2211-1-111-1-1-222-200001-1i3−i3i3−i3−i3i3−i3i3000000000000001-1−i3i3i3−i3-1100000000
χ53444444-24444-2-2-2-4-4-4-4-2-2-4-4-2-2-2-22222000000002200000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-20000-2-20022220000000022−2222−2200−2−222−2−222000000000000000000000000000000
χ55444444-2-4-4-4-4-2-2-20000-2-200222200000000−2222−22220022−2−222−2−2000000000000000000000000000000
χ564444-4-4-24-4-44-2-2-2-4-4-4-42244-222-2222200000000-2-200000000000000000000000000000000000000
χ574444-4-4-2-444-4-2-2-2000022002-2-220000000022−22−222200−2−22222−2−2000000000000000000000000000000
χ584444-4-4-2-444-4-2-2-2000022002-2-2200000000−222222−220022−2−2−2−222000000000000000000000000000000
χ5944-4-400400004-4-422−2222−220000000022−2222−2200000000000000000000000000−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ43000000000000000000
χ6044-4-400400004-4-422−2222−220000000022−2222−22000000000000000000000000002ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43000000000000000000
χ6144-4-400400004-4-4−2222−222200000000−2222−2222000000000000000000000000002ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47000000000000000000
χ6244-4-400400004-4-4−2222−222200000000−2222−222200000000000000000000000000−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47000000000000000000
χ634-44-40040000-44-422−22−222200000000−222222−2200000000000000000000002ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ43−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ470000000000000000000000
χ644-44-40040000-44-422−22−222200000000−222222−220000000000000000000000−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ432ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ470000000000000000000000
χ654-44-40040000-44-4−222222−220000000022−22−22220000000000000000000000−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ430000000000000000000000
χ664-44-40040000-44-4−222222−220000000022−22−222200000000000000000000002ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ472ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ430000000000000000000000
χ674-4-444-444-44-4-4-4400004-4004-44-40000000000000000000000000000000000000000000000000000
χ684-4-444-4-24-44-422-20000-2200-22-2200000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000000000
χ694-4-444-4-24-44-422-20000-2200-22-2200000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000000000
χ704-4-444-4-2-44-4422-2-4-444-22-442-22-2-2-222000000002-200000000000000000000000000000000000000
χ714-4-44-44444-4-4-4-440000-440044-4-40000000000000000000000000000000000000000000000000000
χ724-4-44-44-244-4-422-200002-200-2-22200000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000000000
χ734-4-44-44-244-4-422-200002-200-2-22200000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000000000
χ744-4-44-44-2-4-44422-2-4-4442-24-422-2-2-2-22200000000-2200000000000000000000000000000000000000
χ7588-8-800-40000-44442−4242−4200000000−2222−2222000000000000000000000000000000000000000000000000
χ7688-8-800-40000-444−4242−42420000000022−2222−22000000000000000000000000000000000000000000000000
χ778-88-800-400004-4442−42−42420000000022−22−2222000000000000000000000000000000000000000000000000
χ788-88-800-400004-44−424242−4200000000−222222−22000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.