Finite Group Databasebeta

← Group #10711731

Character table — Group #10711731

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888881212121212121212161616161616161616161616242424242424242424242424
order1244222344468888121222446668812121224242424668812122424242424241616161616161616448812121212242424248888888816161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ7111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111
χ8111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111
χ911-1-11-1-111-111-1-111-1-11-11-11-1-1-111-1111-1-11-11-11-11-111-1-11111-1-1-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i11-1-1
χ1011-1-11-1-111-111-1-111-1-11-11-11-1-1-111-1111-1-11-11-11-11-111-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-1
χ1111-1-11-1-111-111-1-111-1-11-11-11-1-1-111-1111-1-11-11-11-11-111-1-1-1-1-1-11111i−ii−iii−i−iii−i−i−i−iii−i−iii-1-111
χ1211-1-11-1-111-111-1-111-1-11-11-11-1-1-111-1111-1-11-11-11-11-111-1-1-1-1-1-11111−ii−ii−i−iii−i−iiiii−i−iii−i−i-1-111
χ1311-1-11-1-111-111-1-111-1-1-11-111-1-1-111-1111-1-1-11-11-111-1-1-1111111-1-1-1-1i−i−iiii−i−i−i−iiiii−i−i−i−iii-1-111
χ1411-1-11-1-111-111-1-111-1-1-11-111-1-1-111-1111-1-1-11-11-111-1-1-1111111-1-1-1-1−iii−i−i−iiiii−i−i−i−iiiii−i−i-1-111
χ1511-1-11-1-111-111-1-111-1-1-11-111-1-1-111-1111-1-1-11-11-111-1-1-111-1-1-1-11111i−i−iiii−i−i−i−iii−i−iiiii−i−i11-1-1
χ1611-1-11-1-111-111-1-111-1-1-11-111-1-1-111-1111-1-1-11-11-111-1-1-111-1-1-1-11111−iii−i−i−iiiii−i−iii−i−i−i−iii11-1-1
χ17222222222222-2-2-2-2222222222-2-2222-2-2-2-222-2-222-2-2-2-2-2-200000000000000000000000000000000
χ18222222222222-2-2-2-222-2-2-2-2222-2-2222-2-2-2-2-2-222-2-2-2-2222200000000000000000000000000000000
χ192222222-1222-12222-1-12222-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1000000000000
χ202222222-1222-12222-1-12222-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000-2-2-2-211111111000000000000
χ212222222-1222-12222-1-1-2-2-2-2-1-1-122-1-1-1-1-1-1-111-2-211-1-111110000000022-2-2-1-1-1-11111000000000000
χ222222222-1222-12222-1-1-2-2-2-2-1-1-122-1-1-1-1-1-1-111-2-211-1-1111100000000-2-2221111-1-1-1-1000000000000
χ232222222-1222-1-2-2-2-2-1-12222-1-1-1-2-2-1-1-11111-1-1-2-2-1-1111111000000000000−i3i3−i3i3−i3i3−i3i3000000000000
χ242222222-1222-1-2-2-2-2-1-12222-1-1-1-2-2-1-1-11111-1-1-2-2-1-1111111000000000000i3−i3i3−i3i3−i3i3−i3000000000000
χ252222222-1222-1-2-2-2-2-1-1-2-2-2-2-1-1-1-2-2-1-1-1111111221111-1-1-1-1000000000000−i3i3−i3i3i3−i3i3−i3000000000000
χ262222222-1222-1-2-2-2-2-1-1-2-2-2-2-1-1-1-2-2-1-1-1111111221111-1-1-1-1000000000000i3−i3i3−i3−i3i3−i3i3000000000000
χ272222-22-22-2-2222222220000-22-2-2-2-2-222222000000-2-20000000000000000000000002-22-200000000
χ282222-22-22-2-2222222220000-22-2-2-2-2-222222000000-2-2000000000000000000000000-22-2200000000
χ292222-22-22-2-222-2-2-2-2220000-22-222-2-22-2-2-2-20000002200000000000000000000000000002-22-20000
χ302222-22-22-2-222-2-2-2-2220000-22-222-2-22-2-2-2-2000000220000000000000000000000000000-22-220000
χ312222-2-2222-2-220000222-2-22-2-22002-2-200002-200-2200000022−2−222−2−2000000000000000000002−22−2
χ322222-2-2222-2-220000222-2-22-2-22002-2-200002-200-22000000−2−222−2−22200000000000000000000−22−22
χ332222-2-2222-2-22000022-222-2-2-22002-2-20000-22002-200000022−2−222−2−200000000000000000000−22−22
χ342222-2-2222-2-22000022-222-2-2-22002-2-20000-22002-2000000−2−222−2−222000000000000000000002−22−2
χ3522-2-22-2-222-22222-2-2-2-22-22-22-2-22-22-22-2-2222-2-222-2-22-2-22200000000000000000000000000000000
χ3622-2-22-2-222-22222-2-2-2-2-22-222-2-22-22-22-2-222-222-2-22-2222-2-200000000000000000000000000000000
χ3722-2-22-2-2-12-22-122-2-2112-22-2-1112-2-11-111-1-1-11-22-111-111-1-10000000000003−3−333−3−33000000000000
χ3822-2-22-2-2-12-22-122-2-2112-22-2-1112-2-11-111-1-1-11-22-111-111-1-1000000000000−333−3−333−3000000000000
χ3922-2-22-2-2-12-22-122-2-211-22-22-1112-2-11-111-1-11-12-21-11-1-1-1110000000000003−3−33−333−3000000000000
χ4022-2-22-2-2-12-22-122-2-211-22-22-1112-2-11-111-1-11-12-21-11-1-1-111000000000000−333−33−3−33000000000000
χ4122-2-22-2-2-12-22-1-2-222112-22-2-111-22-11-1-1-111-112-2-11-11-1-111000000002i−2i2i−2i−i−iii−i−iii000000000000
χ4222-2-22-2-2-12-22-1-2-222112-22-2-111-22-11-1-1-111-112-2-11-11-1-11100000000−2i2i−2i2iii−i−iii−i−i000000000000
χ4322-2-22-2-2-12-22-1-2-22211-22-22-111-22-11-1-1-1111-1-221-1-1111-1-1000000002i−2i−2i2i−i−iiiii−i−i000000000000
χ4422-2-22-2-2-12-22-1-2-22211-22-22-111-22-11-1-1-1111-1-221-1-1111-1-100000000−2i2i2i−2iii−i−i−i−iii000000000000
χ4522-2-2-22-2222-220000-2-222-2-2-22-20022-200002200-2-200000022−2−2−2−222000000000000000000002−2−22
χ4622-2-2-22-2222-220000-2-222-2-2-22-20022-200002200-2-2000000−2−22222−2−200000000000000000000−222−2
χ4722-2-2-22-2222-220000-2-2-2-222-22-20022-20000-2-2002200000022−2−2−2−22200000000000000000000−222−2
χ4822-2-2-22-2222-220000-2-2-2-222-22-20022-20000-2-20022000000−2−22222−2−2000000000000000000002−2−22
χ4922-2-2-2-222-222222-2-2-2-20000-2-22-22-222-2-2220000002-200000000000000000000000000002i−2i−2i2i0000
χ5022-2-2-2-222-222222-2-2-2-20000-2-22-22-222-2-2220000002-20000000000000000000000000000−2i2i2i−2i0000
χ5122-2-2-2-222-2222-2-222-2-20000-2-222-2-22222-2-2000000-220000000000000000000000002i−2i−2i2i00000000
χ5222-2-2-2-222-2222-2-222-2-20000-2-222-2-22222-2-2000000-22000000000000000000000000−2i2i2i−2i00000000
χ5344444-4-44-44-4400004400004-4-400-44-4000000000000000000000000000000000000000000000000
χ5444444-4-4-2-44-4-20000-2-20000-222002-2200000000000023−2323−2300000000000000000000000000000000
χ5544444-4-4-2-44-4-20000-2-20000-222002-22000000000000−2323−232300000000000000000000000000000000
χ564444-44-4-2-4-44-24444-2-200002-22-4-422-2-2-2-2-200000022000000000000000000000000000000000000
χ574444-44-4-2-4-44-2-4-4-4-4-2-200002-224422-22222000000-2-2000000000000000000000000000000000000
χ584444-4-44-24-4-4-20000-2-24-4-4422-200-2220000-22002-200000000000000000000000000000000000000
χ594444-4-44-24-4-4-20000-2-2-444-422-200-22200002-200-2200000000000000000000000000000000000000
χ6044-4-44444-4-4-440000-4-4000044400-4-4-4000000000000000000000000000000000000000000000000
χ6144-4-4444-2-4-4-4-20000220000-2-2-20022200000000000023−23−232300000000000000000000000000000000
χ6244-4-4444-2-4-4-4-20000220000-2-2-200222000000000000−232323−2300000000000000000000000000000000
χ6344-4-4-44-4-244-4-200002244-4-42-2200-2-220000-2-2002200000000000000000000000000000000000000
χ6444-4-4-44-4-244-4-2000022-4-4442-2200-2-2200002200-2-200000000000000000000000000000000000000
χ6544-4-4-4-44-2-444-244-4-422000022-2-442-2-222-2-2000000-22000000000000000000000000000000000000
χ6644-4-4-4-44-2-444-2-4-44422000022-24-42-2-2-2-2220000002-2000000000000000000000000000000000000
χ674-44i−4i0004000-4−2i22i222−224i−4i00000000000022−22−2i22i2000000000000ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47ζ11+ζ13−ζ25+ζ29−ζ31−ζ41+ζ43−ζ47−ζ11−ζ13+ζ25−ζ29+ζ31+ζ41−ζ43+ζ47ζ11+ζ13+ζ25+ζ29+ζ31+ζ41+ζ43+ζ47−ζ11−ζ13−ζ25−ζ29−ζ31−ζ41−ζ43−ζ47000000000000000000000000
χ684-44i−4i0004000-4−2i22i222−224i−4i00000000000022−22−2i22i2000000000000−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47−ζ11−ζ13+ζ25−ζ29+ζ31+ζ41−ζ43+ζ47ζ11+ζ13−ζ25+ζ29−ζ31−ζ41+ζ43−ζ47−ζ11−ζ13−ζ25−ζ29−ζ31−ζ41−ζ43−ζ47ζ11+ζ13+ζ25+ζ29+ζ31+ζ41+ζ43+ζ47000000000000000000000000
χ694-44i−4i0004000-42i2−2i2−22224i−4i000000000000−22222i2−2i2000000000000ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47−ζ11−ζ13−ζ25−ζ29−ζ31−ζ41−ζ43−ζ47ζ11+ζ13+ζ25+ζ29+ζ31+ζ41+ζ43+ζ47ζ11+ζ13−ζ25+ζ29−ζ31−ζ41+ζ43−ζ47−ζ11−ζ13+ζ25−ζ29+ζ31+ζ41−ζ43+ζ47000000000000000000000000
χ704-44i−4i0004000-42i2−2i2−22224i−4i000000000000−22222i2−2i2000000000000−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47ζ11+ζ13+ζ25+ζ29+ζ31+ζ41+ζ43+ζ47−ζ11−ζ13−ζ25−ζ29−ζ31−ζ41−ζ43−ζ47−ζ11−ζ13+ζ25−ζ29+ζ31+ζ41−ζ43+ζ47ζ11+ζ13−ζ25+ζ29−ζ31−ζ41+ζ43−ζ47000000000000000000000000
χ714-4−4i4i0004000-4−2i22i2−2222−4i4i000000000000−2222−2i22i2000000000000ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47ζ11+ζ13+ζ25+ζ29+ζ31+ζ41+ζ43+ζ47−ζ11−ζ13−ζ25−ζ29−ζ31−ζ41−ζ43−ζ47−ζ11−ζ13+ζ25−ζ29+ζ31+ζ41−ζ43+ζ47ζ11+ζ13−ζ25+ζ29−ζ31−ζ41+ζ43−ζ47000000000000000000000000
χ724-4−4i4i0004000-4−2i22i2−2222−4i4i000000000000−2222−2i22i2000000000000−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47−ζ11−ζ13−ζ25−ζ29−ζ31−ζ41−ζ43−ζ47ζ11+ζ13+ζ25+ζ29+ζ31+ζ41+ζ43+ζ47ζ11+ζ13−ζ25+ζ29−ζ31−ζ41+ζ43−ζ47−ζ11−ζ13+ζ25−ζ29+ζ31+ζ41−ζ43+ζ47000000000000000000000000
χ734-4−4i4i0004000-42i2−2i222−22−4i4i00000000000022−222i2−2i2000000000000ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47−ζ11−ζ13+ζ25−ζ29+ζ31+ζ41−ζ43+ζ47ζ11+ζ13−ζ25+ζ29−ζ31−ζ41+ζ43−ζ47−ζ11−ζ13−ζ25−ζ29−ζ31−ζ41−ζ43−ζ47ζ11+ζ13+ζ25+ζ29+ζ31+ζ41+ζ43+ζ47000000000000000000000000
χ744-4−4i4i0004000-42i2−2i222−22−4i4i00000000000022−222i2−2i2000000000000−ζ11+ζ13+ζ25+ζ29−ζ31+ζ41−ζ43−ζ47ζ11−ζ13−ζ25−ζ29+ζ31−ζ41+ζ43+ζ47−ζ11+ζ13−ζ25+ζ29+ζ31−ζ41−ζ43+ζ47ζ11−ζ13+ζ25−ζ29−ζ31+ζ41+ζ43−ζ47ζ11+ζ13−ζ25+ζ29−ζ31−ζ41+ζ43−ζ47−ζ11−ζ13+ζ25−ζ29+ζ31+ζ41−ζ43+ζ47ζ11+ζ13+ζ25+ζ29+ζ31+ζ41+ζ43+ζ47−ζ11−ζ13−ζ25−ζ29−ζ31−ζ41−ζ43−ζ47000000000000000000000000
χ758-88i−8i000-40004−4i24i242−42−4i4i000000000000−22222i2−2i200000000000000000000000000000000000000000000
χ768-88i−8i000-400044i2−4i2−4242−4i4i00000000000022−22−2i22i200000000000000000000000000000000000000000000
χ778-8−8i8i000-40004−4i24i2−42424i−4i00000000000022−222i2−2i200000000000000000000000000000000000000000000
χ788-8−8i8i000-400044i2−4i242−424i−4i000000000000−2222−2i22i200000000000000000000000000000000000000000000

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