Finite Group Databasebeta

← Group #10709261

Character table — Group #10709261

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222244444444444444444888888888888888888121212121212121216161616161616161624242424484896
order1222344446668888444881212121212121212242424244448812121212121212242424242424161616161616161644412121212121216161616884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1
χ4111111111111111111111111111111111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ51111111111111111-1-111111-1-1-1-111111111-1-1-111111-1-111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-111-1
χ61111111111111111-1-111111-1-1-1-111111111-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-1-11
χ71111111111111111-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111111111-111-1-11111-1-1-1-1-1-11
χ81111111111111111-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1
χ9222222222222-2-2-2-2222-2-222222222-2-2-2-2002-2-20000222-2-2-2-2-2-2000000000000000000000000
χ10222222222222-2-2-2-2-2-22-2-222-2-2-2-222-2-2-2-200-22200002-2-2-2-22222000000000000000000000000
χ11222222-2-22222000022-200222222-2-2000000-2000000-2-2-20000002222−2−2−2−200000000022−2−2000
χ12222222-2-22222000022-200222222-2-2000000-2000000-2-2-2000000−2−2−2−22222000000000−2−222000
χ13222222-2-222220000-2-2-20022-2-2-2-2-2-20000002000000-2220000002222−2−2−2−2000000000−2−222000
χ14222222-2-222220000-2-2-20022-2-2-2-2-2-20000002000000-222000000−2−2−2−2222200000000022−2−2000
χ1522222-222-2222222200-2-2-2-2-20000222222220002222-200-2-2000000000000-200-2-200000000000
χ1622222-222-2222222200-2-2-2-2-20000222222-2-2000-2-2-2-2-200-2-20000000000002002200000000000
χ1722222-222-2222-2-2-2-200-222-2-2000022-2-2-2-2000000000-2002200000000000002-20022-2-20000000
χ1822222-222-2222-2-2-2-200-222-2-2000022-2-2-2-2000000000-200220000000000000-2200-2-2220000000
χ192222-12222-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-100000000222-1-1-1-1-1-10000000
χ202222-12222-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-2-22221111-1-1-1-1-1-1-1-1-100000000-2-2-21111110000000
χ212222-12222-1-1-12222-2-2222-1-11111-1-1-1-1-1-122-2-2-2-1-1-1-1-111-1-11111000000002-2-2-1-111110000000
χ222222-12222-1-1-12222-2-2222-1-11111-1-1-1-1-1-1-2-2-2-2-21111-111-1-1111100000000-22211-1-1-1-10000000
χ232222-12222-1-1-1-2-2-2-2222-2-2-1-1-1-1-1-1-1-11111002-2-2−i3−i3i3i3-1-1-111111100000000000−i3i3−i3i3−i3i30000000
χ242222-12222-1-1-1-2-2-2-2222-2-2-1-1-1-1-1-1-1-11111002-2-2i3i3−i3−i3-1-1-111111100000000000i3−i3i3−i3i3−i30000000
χ252222-12222-1-1-1-2-2-2-2-2-22-2-2-1-11111-1-1111100-222−i3−i3i3i3-11111-1-1-1-100000000000−i3i3i3−i3i3−i30000000
χ262222-12222-1-1-1-2-2-2-2-2-22-2-2-1-11111-1-1111100-222i3i3−i3−i3-11111-1-1-1-100000000000i3−i3−i3i3−i3i30000000
χ272222-1-222-2-1-1-1222200-2-2-211−i3−i3i3i3-1-1-1-1-1-122000-1-1-1-11−i3i311−i3−i3i3i300000000-20011−i3i3i3−i30000000
χ282222-1-222-2-1-1-1222200-2-2-211−i3−i3i3i3-1-1-1-1-1-1-2-200011111−i3i311−i3−i3i3i300000000200-1-1i3−i3−i3i30000000
χ292222-1-222-2-1-1-1222200-2-2-211i3i3−i3−i3-1-1-1-1-1-122000-1-1-1-11i3−i311i3i3−i3−i300000000-20011i3−i3−i3i30000000
χ302222-1-222-2-1-1-1222200-2-2-211i3i3−i3−i3-1-1-1-1-1-1-2-200011111i3−i311i3i3−i3−i300000000200-1-1−i3i3i3−i30000000
χ312222-1-222-2-1-1-1-2-2-2-200-22211−i3−i3i3i3-1-1111100000−i3−i3i3i31−i3i3-1-1i3i3−i3−i30000000002-2i3−i3-1-1110000000
χ322222-1-222-2-1-1-1-2-2-2-200-22211−i3−i3i3i3-1-1111100000i3i3−i3−i31−i3i3-1-1i3i3−i3−i3000000000-22−i3i311-1-10000000
χ332222-1-222-2-1-1-1-2-2-2-200-22211i3i3−i3−i3-1-1111100000−i3−i3i3i31i3−i3-1-1−i3−i3i3i3000000000-22i3−i311-1-10000000
χ342222-1-222-2-1-1-1-2-2-2-200-22211i3i3−i3−i3-1-1111100000i3i3−i3−i31i3−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
χ3722-2-22200-22-2-22−22−2-2202−22-2-22-220022−2−2000−2200000002−2−22−22−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
χ3822-2-22200-22-2-22−22−2-2202−22-2-22-220022−2−2000−2200000002−2−22−22ζ25−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
χ3922-2-22200-22-2-2−22−222-20−222-22-22-200−2−222000−220000000−22−22−22ζ11−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
χ4022-2-22200-22-2-2−22−222-20−222-22-22-200−2−222000−220000000−22−22−22−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
χ4122-2-22200-22-2-2−22−22-220−222-2-22-2200−2−2220002−20000000−222−22−2ζ11−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
χ4222-2-22200-22-2-2−22−22-220−222-2-22-2200−2−2220002−20000000−222−22−2−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
χ432-22-2202-20-22-222-2-2000000000002-22-22-22-20002-22-20000000002−22−22−22−200000000000002−20
χ442-22-2202-20-22-222-2-2000000000002-22-22-22-20002-22-2000000000−22−22−22−220000000000000−220
χ452-22-2202-20-22-222-2-2000000000002-22-22-2-22000-22-220000000002−22−22−22−20000000000000−220
χ462-22-2202-20-22-222-2-2000000000002-22-22-2-22000-22-22000000000−22−22−22−2200000000000002−20
χ4744444-4-4-4-4444000000400-4-40000-4-40000000000000400000000000000000000000000000000
χ484444-24-4-44-2-2-2000044-400-2-2-2-2-2-222000000-4000000222000000000000000000000000000000
χ494444-24-4-44-2-2-20000-4-4-400-2-222222200000040000002-2-2000000000000000000000000000000
χ504444-2-4-4-4-4-2-2-200000040022−2i3−2i32i32i3220000000000000-22i3−2i3000000000000000000000000000000
χ514444-2-4-4-4-4-2-2-2000000400222i32i3−2i3−2i3220000000000000-2−2i32i3000000000000000000000000000000
χ5244-4-44-40044-4-422−2222−22000−2222-440000002222−22−22000000000000−22220000000000000000000000000000
χ5344-4-44-40044-4-4−2222−222200022−22-44000000−22−22222200000000000022−220000000000000000000000000000
χ5444-4-4-2400-4-22222−2222−224-4022−22-22-22-2200−2−22200022−220000000−22−22−22000000000000000000000000
χ5544-4-4-2400-4-22222−2222−22-44022−22-222-22-200−2−222000−22220000000−222−22−2000000000000000000000000
χ5644-4-4-2400-4-222−2222−22224-40−2222-22-22-220022−2−2000−222200000002−22−22−2000000000000000000000000
χ5744-4-4-2400-4-222−2222−2222-440−2222-222-22-20022−2−200022−2200000002−2−22−22000000000000000000000000
χ5844-4-4-2-4004-22222−2222−22000−22222-2−2i32i32i3−2i300−2−2220000000000002−2−i6i6i6−i6000000000000000000000000
χ5944-4-4-2-4004-22222−2222−22000−22222-22i3−2i3−2i32i300−2−2220000000000002−2i6−i6−i6i6000000000000000000000000
χ6044-4-4-2-4004-222−2222−222200022−222-2−2i32i32i3−2i30022−2−2000000000000−22i6−i6−i6i6000000000000000000000000
χ6144-4-4-2-4004-222−2222−222200022−222-22i3−2i3−2i32i30022−2−2000000000000−22−i6i6i6−i6000000000000000000000000
χ624-44-4404-40-44-4-4-444000000000004-4-44-44000000000000000000000000000000000000000000
χ634-44-440-440-44-4000000000000000-4400000000000000000000002-22-2-22-220000000000000000
χ644-44-440-440-44-4000000000000000-440000000000000000000000-22-222-22-20000000000000000
χ654-44-4-204-402-2244-4-400000000000-22-22-224-4000-22-22000000000000000000000000000000000
χ664-44-4-204-402-2244-4-400000000000-22-22-22-440002-22-2000000000000000000000000000000000
χ674-44-4-204-402-22-4-44400000000000-222-22-200000−2i32i32i3−2i3000000000000000000000000000000000
χ684-44-4-204-402-22-4-44400000000000-222-22-2000002i3−2i3−2i32i3000000000000000000000000000000000
χ694-4-4440000-4-4422−22−2222000000000000022−22−2222000000000000000000ζ11−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
χ704-4-4440000-4-4422−22−2222000000000000022−22−2222000000000000000000−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
χ714-4-4440000-4-44−222222−220000000000000−222222−22000000000000000000ζ11−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
χ724-4-4440000-4-44−222222−220000000000000−222222−22000000000000000000−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
χ738-88-8-40-8804-440000000000000004-40000000000000000000000000000000000000000000000
χ748-8-88-4000044-442−42−42420000000000000−222222−22000000000000000000000000000000000000000000
χ758-8-88-4000044-4−424242−42000000000000022−22−2222000000000000000000000000000000000000000000

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