Finite Group Databasebeta

← Group #10709177

Character table — Group #10709177

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222244444444444444444888888888888888888121212121212121216161616161616161624242424484896
order122234444666888822466668812121212242424244448812121212121212242424242424161616161616161644412121212121216161616884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1
χ41111111111111111111111111111111111-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ51111111111111111-1-11-1-1-1-11111111111-111-1-1-1-11111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-111-1
χ61111111111111111-1-11-1-1-1-11111111111-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-1-11
χ71111111111111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111111-111-1-11111-1-1-1-1-1-11
χ81111111111111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1
χ9222222222222-2-2-2-22222222-2-22222-2-2-2-2200-2-22220000-2-2-2-2-2-2000000000000000000000000
χ10222222222222-2-2-2-2-2-22-2-2-2-2-2-22222-2-2-2-2-20022-2-220000-2-22222000000000000000000000000
χ11222222-2-22222000022-222220022-2-20000-20000-2-2-200000000002222−2−2−2−200000000022−2−2000
χ12222222-2-22222000022-222220022-2-20000-20000-2-2-20000000000−2−2−2−22222000000000−2−222000
χ13222222-2-222220000-2-2-2-2-2-2-20022-2-200002000022-200000000002222−2−2−2−2000000000−2−222000
χ14222222-2-222220000-2-2-2-2-2-2-20022-2-200002000022-20000000000−2−2−2−2222200000000022−2−2000
χ1522222-222-2222222200-20000-2-2-2-22222220220000-22222-2-2000000000000-200-2-200000000000
χ1622222-222-2222222200-20000-2-2-2-22222220-2-20000-2-2-2-2-2-2-20000000000002002200000000000
χ1722222-222-2222-2-2-2-200-2000022-2-222-2-2-2-20000000-200002200000000000002-20022-2-20000000
χ1822222-222-2222-2-2-2-200-2000022-2-222-2-2-2-20000000-20000220000000000000-2200-2-2220000000
χ192222-12222-1-1-12222222-1-1-1-122-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-100000000222-1-1-1-1-1-10000000
χ202222-12222-1-1-12222222-1-1-1-122-1-1-1-1-1-1-1-12-2-222-1-1-11111-1-1-1-1-1-100000000-2-2-21111110000000
χ212222-12222-1-1-12222-2-22111122-1-1-1-1-1-1-1-1-222-2-211-1-1-1-1-1-1-11111000000002-2-2-1-111110000000
χ222222-12222-1-1-12222-2-22111122-1-1-1-1-1-1-1-1-2-2-2-2-211-11111-1-1111100000000-22211-1-1-1-10000000
χ232222-12222-1-1-1-2-2-2-2222-1-1-1-1-2-2-1-1-1-11111200-2-2-1-1-1−i3−i3i3i311111100000000000−i3i3−i3i3−i3i30000000
χ242222-12222-1-1-1-2-2-2-2222-1-1-1-1-2-2-1-1-1-11111200-2-2-1-1-1i3i3−i3−i311111100000000000i3−i3i3−i3i3−i30000000
χ252222-12222-1-1-1-2-2-2-2-2-221111-2-2-1-1-1-11111-2002211-1−i3−i3i3i311-1-1-1-100000000000−i3i3i3−i3i3−i30000000
χ262222-12222-1-1-1-2-2-2-2-2-221111-2-2-1-1-1-11111-2002211-1i3i3−i3−i311-1-1-1-100000000000i3−i3−i3i3−i3i30000000
χ272222-1-222-2-1-1-1222200-2−i3−i3i3i3-2-211-1-1-1-1-1-102200−i3i31-1-1-1-111−i3−i3i3i300000000-20011−i3i3i3−i30000000
χ282222-1-222-2-1-1-1222200-2−i3−i3i3i3-2-211-1-1-1-1-1-10-2-200−i3i31111111−i3−i3i3i300000000200-1-1i3−i3−i3i30000000
χ292222-1-222-2-1-1-1222200-2i3i3−i3−i3-2-211-1-1-1-1-1-102200i3−i31-1-1-1-111i3i3−i3−i300000000-20011i3−i3−i3i30000000
χ302222-1-222-2-1-1-1222200-2i3i3−i3−i3-2-211-1-1-1-1-1-10-2-200i3−i31111111i3i3−i3−i300000000200-1-1−i3i3i3−i30000000
χ312222-1-222-2-1-1-1-2-2-2-200-2−i3−i3i3i32211-1-1111100000−i3i31−i3−i3i3i3-1-1i3i3−i3−i30000000002-2i3−i3-1-1110000000
χ322222-1-222-2-1-1-1-2-2-2-200-2−i3−i3i3i32211-1-1111100000−i3i31i3i3−i3−i3-1-1i3i3−i3−i3000000000-22−i3i311-1-10000000
χ332222-1-222-2-1-1-1-2-2-2-200-2i3i3−i3−i32211-1-1111100000i3−i31−i3−i3i3i3-1-1−i3−i3i3i3000000000-22i3−i311-1-10000000
χ342222-1-222-2-1-1-1-2-2-2-200-2i3i3−i3−i32211-1-1111100000i3−i31i3i3−i3−i3-1-1−i3−i3i3i30000000002-2−i3i3-1-1110000000
χ3522-2-22200-22-2-22−22−22-202-22-22−22-20022−2−20002−200000002−22−22−2−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43000000000−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43000
χ3622-2-22200-22-2-22−22−22-202-22-22−22-20022−2−20002−200000002−22−22−2ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43000000000ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43000
χ3722-2-22200-22-2-22−22−2-220-22-222−22-20022−2−2000−2200000002−2−22−22−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43000000000ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43000
χ3822-2-22200-22-2-22−22−2-220-22-222−22-20022−2−2000−2200000002−2−22−22ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43000000000−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43000
χ3922-2-22200-22-2-2−22−222-202-22-2−222-200−2−222000−220000000−22−22−22ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47000000000ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47000
χ4022-2-22200-22-2-2−22−222-202-22-2−222-200−2−222000−220000000−22−22−22−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47000000000−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47000
χ4122-2-22200-22-2-2−22−22-220-22-22−222-200−2−2220002−20000000−222−22−2ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47000000000−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47000
χ4222-2-22200-22-2-2−22−22-220-22-22−222-200−2−2220002−20000000−222−22−2−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47000000000ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47000
χ432-22-220-220-22-2-2-22200000000000-222-22-202i−2i000002i−2i2i−2i0000002−22−22−22−20000000000000−i2i20
χ442-22-220-220-22-2-2-22200000000000-222-22-202i−2i000002i−2i2i−2i000000−22−22−22−220000000000000i2−i20
χ452-22-220-220-22-2-2-22200000000000-222-22-20−2i2i00000−2i2i−2i2i0000002−22−22−22−20000000000000i2−i20
χ462-22-220-220-22-2-2-22200000000000-222-22-20−2i2i00000−2i2i−2i2i000000−22−22−22−220000000000000−i2i20
χ4744444-4-4-4-44440000004000000-4-4-4-40000000000040000000000000000000000000000000000
χ484444-24-4-44-2-2-2000044-4-2-2-2-200-2-2220000-400002220000000000000000000000000000000000
χ494444-24-4-44-2-2-20000-4-4-4222200-2-222000040000-2-220000000000000000000000000000000000
χ504444-2-4-4-4-4-2-2-20000004−2i3−2i32i32i30022220000000002i3−2i3-20000000000000000000000000000000000
χ514444-2-4-4-4-4-2-2-200000042i32i3−2i3−2i3002222000000000−2i32i3-20000000000000000000000000000000000
χ5244-4-44-40044-4-422−2222−220000000−2222-44002222−22−22000000000000−22220000000000000000000000000000
χ5344-4-44-40044-4-4−2222−2222000000022−22-4400−22−22222200000000000022−220000000000000000000000000000
χ5444-4-4-2400-4-22222−2222−224-40-22-2222−22-2200−2−22200022−220000000−22−22−22000000000000000000000000
χ5544-4-4-2400-4-22222−2222−22-4402-22-222−22-2200−2−222000−22220000000−222−22−2000000000000000000000000
χ5644-4-4-2400-4-222−2222−22224-40-22-22−2222-220022−2−2000−222200000002−22−22−2000000000000000000000000
χ5744-4-4-2400-4-222−2222−2222-4402-22-2−2222-220022−2−200022−2200000002−2−22−22000000000000000000000000
χ5844-4-4-2-4004-22222−2222−22000−2i32i32i3−2i3−22222-200−2−2220000000000002−2−i6i6i6−i6000000000000000000000000
χ5944-4-4-2-4004-22222−2222−220002i3−2i3−2i32i3−22222-200−2−2220000000000002−2i6−i6−i6i6000000000000000000000000
χ6044-4-4-2-4004-222−2222−2222000−2i32i32i3−2i322−222-20022−2−2000000000000−22i6−i6−i6i6000000000000000000000000
χ6144-4-4-2-4004-222−2222−22220002i3−2i3−2i32i322−222-20022−2−2000000000000−22−i6i6i6−i6000000000000000000000000
χ624-44-4404-40-44-40000000000000004-400000000000000000000002-22-2-22-220000000000000000
χ634-44-4404-40-44-40000000000000004-40000000000000000000000-22-222-22-20000000000000000
χ644-44-440-440-44-444-4-400000000000-44-44-44000000000000000000000000000000000000000000
χ654-44-4-20-4402-2244-4-4000000000002-22-22-20000000023−23−2323000000000000000000000000000000
χ664-44-4-20-4402-2244-4-4000000000002-22-22-200000000−232323−23000000000000000000000000000000
χ674-44-4-20-4402-22-4-444000000000002-2-22-2204i−4i00000−2i2i−2i2i000000000000000000000000000000
χ684-44-4-20-4402-22-4-444000000000002-2-22-220−4i4i000002i−2i2i−2i000000000000000000000000000000
χ694-4-4440000-4-4422−22−22220000000000000−222222−22000000000000000000ζ11−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+ζ470000000000000000
χ704-4-4440000-4-4422−22−22220000000000000−222222−22000000000000000000−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−ζ470000000000000000
χ714-4-4440000-4-44−222222−22000000000000022−22−2222000000000000000000ζ11−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+ζ470000000000000000
χ724-4-4440000-4-44−222222−22000000000000022−22−2222000000000000000000−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−ζ470000000000000000
χ738-88-8-408-804-44000000000000000-440000000000000000000000000000000000000000000000
χ748-8-88-4000044-442−42−4242000000000000022−22−2222000000000000000000000000000000000000000000
χ758-8-88-4000044-4−424242−420000000000000−222222−22000000000000000000000000000000000000000000

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