Finite Group Databasebeta

← Group #10713978

Character table — Group #10713978

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order1222223444466688886688121212122424242416161616242448484848484848481616161616161616226666882424242424882244
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ922222222222222-2-2-2-222-2-22222-2-2-2-20000-2-2000000000000000000000000000022-2-20000
χ1022222222222222-2-2-2-222-2-22222-2-2-2-20000-2-20000000000000000000000000000-2-2220000
χ11222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-122-1-1-1-100000000
χ12222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-21111-2-2111100000000
χ13222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-1-1-1-1-2-2111100000000
χ14222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-2111122-1-1-1-100000000
χ152222-2-222-22-22220000-2-2002-2-22000022−2−2002222−2−2−2−22222−2−2−2−20000000000002-2000000
χ162222-2-222-22-22220000-2-2002-2-22000022−2−2002222−2−2−2−2−2−2−2−22222000000000000-22000000
χ172222-2-222-22-22220000-2-2002-2-220000−2−22200−2−2−2−222222222−2−2−2−2000000000000-22000000
χ182222-2-222-22-22220000-2-2002-2-220000−2−22200−2−2−2−22222−2−2−2−222220000000000002-2000000
χ192222-2-22-22-222222222-2-2-2-2-222-222220000-2-200000000000000000000000000000000002-2
χ202222-2-22-22-222222222-2-2-2-2-222-222220000-2-20000000000000000000000000000000000-22
χ212222-2-22-22-22222-2-2-2-2-2-222-222-2-2-2-2-200002200000000000000002-222-2-200000000000000
χ222222-2-22-22-22222-2-2-2-2-2-222-222-2-2-2-2-20000220000000000000000-22-2-22200000000000000
χ232222-2-2-1-22-22-1-1-1-2-2-2-211221-1-1111110000-1-133−3−333−3−3000000002-2-1-1110033−3−300000000
χ242222-2-2-1-22-22-1-1-1-2-2-2-211221-1-1111110000-1-133−3−333−3−300000000-2211-1-100−3−33300000000
χ252222-2-2-1-22-22-1-1-1-2-2-2-211221-1-1111110000-1-1−3−333−3−333000000002-2-1-11100−3−33300000000
χ262222-2-2-1-22-22-1-1-1-2-2-2-211221-1-1111110000-1-1−3−333−3−33300000000-2211-1-10033−3−300000000
χ2722-2-22-2222-2-2-2-2200002-20022-2-20000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i222−2−222−2−2000000000000002i−2i0000
χ2822-2-22-2222-2-2-2-2200002-20022-2-20000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2−2−222−2−22200000000000000−2i2i0000
χ2922-2-22-2222-2-2-2-2200002-20022-2-20000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i222−2−222−2−200000000000000−2i2i0000
χ3022-2-22-2222-2-2-2-2200002-20022-2-20000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2−2−222−2−222000000000000002i−2i0000
χ3122-2-22-22-2-222-2-2222-2-22-2-22-2-22222-2-200002-2000000000000000000000000000000002-200
χ3222-2-22-22-2-222-2-2222-2-22-2-22-2-22222-2-200002-200000000000000000000000000000000-2200
χ3322-2-22-22-2-222-2-22-2-2222-22-2-2-222-2-2220000-2200000000000000000000002-22-22-200000000
χ3422-2-22-22-2-222-2-22-2-2222-22-2-2-222-2-2220000-220000000000000000000000-22-22-2200000000
χ3522-2-22-2-1-2-22211-1-2-222-112-211-1-111-1-100001-1−i3i3i3−i3i3−i3−i3i30000000000−i3i3−i3i32-2-11-1100000000
χ3622-2-22-2-1-2-22211-1-2-222-112-211-1-111-1-100001-1−i3i3i3−i3i3−i3−i3i30000000000i3−i3i3−i3-221-11-100000000
χ3722-2-22-2-1-2-22211-1-2-222-112-211-1-111-1-100001-1i3−i3−i3i3−i3i3i3−i30000000000−i3i3−i3i3-221-11-100000000
χ3822-2-22-2-1-2-22211-1-2-222-112-211-1-111-1-100001-1i3−i3−i3i3−i3i3i3−i30000000000i3−i3i3−i32-2-11-1100000000
χ3922-2-2-2222-2-22-2-2222-2-2-222-22-22-222-2-22i−2i−2i2i-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ4022-2-2-2222-2-22-2-2222-2-2-222-22-22-222-2-2−2i2i2i−2i-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ4122-2-2-2222-2-22-2-22-2-222-22-222-22-2-2-22200002-20000000022-2-2-2-22200000000000000000000
χ4222-2-2-2222-2-22-2-22-2-222-22-222-22-2-2-22200002-200000000-2-22222-2-200000000000000000000
χ4322-2-2-22-12-2-2211-122-2-21-12-2-11-11-1-1112i−2i−2i2i1-1−ii−iii−ii−i0000000000−i3i3i3−i3003−3−3300000000
χ4422-2-2-22-12-2-2211-122-2-21-12-2-11-11-1-1112i−2i−2i2i1-1−ii−iii−ii−i0000000000i3−i3−i3i300−333−300000000
χ4522-2-2-22-12-2-2211-122-2-21-12-2-11-11-1-111−2i2i2i−2i1-1i−ii−i−ii−ii0000000000−i3i3i3−i300−333−300000000
χ4622-2-2-22-12-2-2211-122-2-21-12-2-11-11-1-111−2i2i2i−2i1-1i−ii−i−ii−ii0000000000i3−i3−i3i3003−3−3300000000
χ474444444-4-4-4-444400004400-4-4-4-40000000000000000000000000000000000000000000000
χ48444444-24444-2-2-2-4-4-4-4-2-2-4-4-2-2-2-22222000022000000000000000000000000000000000000
χ49444444-2-4-4-4-4-2-2-20000-2-2002222000000000066−6−6−6−6660000000000000000000000000000
χ50444444-2-4-4-4-4-2-2-20000-2-20022220000000000−6−66666−6−60000000000000000000000000000
χ514444-4-4-24-44-4-2-2-200002200-222-200002222−22−2200−2−2−2−222220000000000000000000000000000
χ524444-4-4-24-44-4-2-2-200002200-222-20000−22−222222002222−2−2−2−20000000000000000000000000000
χ534444-4-4-2-44-44-2-2-2444422-4-42-2-22-2-2-2-2000022000000000000000000000000000000000000
χ5444-4-44-4-244-4-422-20000-2200-2-2220000−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i20000000000000000000000000000
χ5544-4-44-4-244-4-422-20000-2200-2-22200002i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i20000000000000000000000000000
χ5644-4-44-4-2-4-44422-244-4-4-22-4422-2-2-2-2220000-22000000000000000000000000000000000000
χ5744-4-4-444-444-4-4-440000-4400-44-440000000000000000000000000000000000000000000000
χ5844-4-4-44-24-4-4422-2-4-4442-2-44-22-2222-2-20000-22000000000000000000000000000000000000
χ5944-4-4-44-2-444-422-200002-2002-22-20000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ6044-4-4-44-2-444-422-200002-2002-22-20000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ614-44-400400004-4-422−2222−220000000022−2222−2200000000000000ζ11−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+ζ4700000000000000000000
χ624-44-400400004-4-422−2222−220000000022−2222−2200000000000000−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−ζ4700000000000000000000
χ634-44-400400004-4-4−2222−222200000000−2222−222200000000000000ζ11−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+ζ4700000000000000000000
χ644-44-400400004-4-4−2222−222200000000−2222−222200000000000000−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−ζ4700000000000000000000
χ654-4-440040000-44-422−22−22220000000022−22−222200000000000000ζ11−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+ζ4700000000000000000000
χ664-4-440040000-44-422−22−22220000000022−22−222200000000000000−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−ζ4700000000000000000000
χ674-4-440040000-44-4−222222−2200000000−222222−2200000000000000ζ11−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+ζ4700000000000000000000
χ684-4-440040000-44-4−222222−2200000000−222222−2200000000000000−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−ζ4700000000000000000000
χ698-88-800-40000-44442−4242−4200000000−2222−2222000000000000000000000000000000000000000000
χ708-88-800-40000-444−4242−42420000000022−2222−22000000000000000000000000000000000000000000
χ718-8-8800-400004-4442−42−424200000000−222222−22000000000000000000000000000000000000000000
χ728-8-8800-400004-44−424242−420000000022−22−2222000000000000000000000000000000000000000000

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