Finite Group Databasebeta

← Group #10714826

Character table — Group #10714826

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order12222234444666888866881212121224242424161616162424484848484848484816161616161616164444121212121212121244884488
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
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1
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
χ11222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ12222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ13222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-2-211-1-1-1-11100000000
χ14222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-222-1-11111-1-100000000
χ152222-2-222-2-222220000-2-20022-2-2000022−2−2002222−2−2−2−22222−2−2−2−20000000000002-2000000
χ162222-2-222-2-222220000-2-20022-2-2000022−2−2002222−2−2−2−2−2−2−2−22222000000000000-22000000
χ172222-2-222-2-222220000-2-20022-2-20000−2−22200−2−2−2−222222222−2−2−2−2000000000000-22000000
χ182222-2-222-2-222220000-2-20022-2-20000−2−22200−2−2−2−22222−2−2−2−222220000000000002-2000000
χ192222-2-22-222-22222222-2-2-2-2-2-22222220000-2-20000000000000000002-2-2-200002200000000
χ202222-2-22-222-22222222-2-2-2-2-2-22222220000-2-2000000000000000000-22220000-2-200000000
χ212222-2-22-222-2222-2-2-2-2-2-222-2-222-2-2-2-2000022000000000000000000000000000000002-200
χ222222-2-22-222-2222-2-2-2-2-2-222-2-222-2-2-2-200002200000000000000000000000000000000-2200
χ232222-2-2-1-222-2-1-1-1222211-2-211-1-1-1-1-1-1000011−i3−i3i3i3−i3−i3i3i300000000002-211−i3−i3i3i3-1-100000000
χ242222-2-2-1-222-2-1-1-1222211-2-211-1-1-1-1-1-1000011−i3−i3i3i3−i3−i3i3i30000000000-22-1-1i3i3−i3−i31100000000
χ252222-2-2-1-222-2-1-1-1222211-2-211-1-1-1-1-1-1000011i3i3−i3−i3i3i3−i3−i300000000002-211i3i3−i3−i3-1-100000000
χ262222-2-2-1-222-2-1-1-1222211-2-211-1-1-1-1-1-1000011i3i3−i3−i3i3i3−i3−i30000000000-22-1-1−i3−i3i3i31100000000
χ2722-2-22-2222-2-22-2-222-2-22-2-222-2-2222-2-200002-20000000022-2-222-2-200000000000000000000
χ2822-2-22-2222-2-22-2-222-2-22-2-222-2-2222-2-200002-200000000-2-222-2-22200000000000000000000
χ2922-2-22-2222-2-22-2-2-2-2222-22-22-2-22-2-2222-22-2-222-22-22-22-20000000000000000000000000000
χ3022-2-22-2222-2-22-2-2-2-2222-22-22-2-22-2-222-22-22-22-22-22-22-220000000000000000000000000000
χ3122-2-22-2-122-2-2-111-2-222-112-2-111-111-1-12-22-21-1-11-11-11-110000000000003−33−33−33−300000000
χ3222-2-22-2-122-2-2-111-2-222-112-2-111-111-1-12-22-21-1-11-11-11-11000000000000−33−33−33−3300000000
χ3322-2-22-2-122-2-2-111-2-222-112-2-111-111-1-1-22-221-11-11-11-11-10000000000003−3−33−333−300000000
χ3422-2-22-2-122-2-2-111-2-222-112-2-111-111-1-1-22-221-11-11-11-11-1000000000000−333−33−3−3300000000
χ3522-2-2-2222-22-22-2-20000-22002-22-200002−2−22002−22−2−22−2222−2−2−2−222000000000000002-20000
χ3622-2-2-2222-22-22-2-20000-22002-22-200002−2−22002−22−2−22−22−2−22222−2−200000000000000-220000
χ3722-2-2-2222-22-22-2-20000-22002-22-20000−222−200−22−222−22−222−2−2−2−22200000000000000-220000
χ3822-2-2-2222-22-22-2-20000-22002-22-20000−222−200−22−222−22−2−2−22222−2−2000000000000002-20000
χ3922-2-2-222-22-222-2-222-2-2-222-2-22-2222-2-20000-2200000000000000000000000000000000002-2
χ4022-2-2-222-22-222-2-222-2-2-222-2-22-2222-2-20000-220000000000000000000000000000000000-22
χ4122-2-2-222-22-222-2-2-2-222-22-22-22-22-2-22200002-200000000000000002i−2i00002i−2i−2i2i0000000000
χ4222-2-2-222-22-222-2-2-2-222-22-22-22-22-2-22200002-20000000000000000−2i2i0000−2i2i2i−2i0000000000
χ4322-2-2-22-1-22-22-111-2-2221-1-221-11-111-1-10000-11−i3i3i3−i3−i3i3i3−i3000000002i−2i00−33−iii−i3−300000000
χ4422-2-2-22-1-22-22-111-2-2221-1-221-11-111-1-10000-11−i3i3i3−i3−i3i3i3−i300000000−2i2i003−3i−i−ii−3300000000
χ4522-2-2-22-1-22-22-111-2-2221-1-221-11-111-1-10000-11i3−i3−i3i3i3−i3−i3i3000000002i−2i003−3−iii−i−3300000000
χ4622-2-2-22-1-22-22-111-2-2221-1-221-11-111-1-10000-11i3−i3−i3i3i3−i3−i3i300000000−2i2i00−33i−i−ii3−300000000
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
χ49444444-2-4-4-4-4-2-2-20000-2-20022220000000000i6i6−i6−i6−i6−i6i6i60000000000000000000000000000
χ50444444-2-4-4-4-4-2-2-20000-2-20022220000000000−i6−i6i6i6i6i6−i6−i60000000000000000000000000000
χ514444-4-4-24-4-44-2-2-200002200-2-22200002222−22−2200−2−2−2−222220000000000000000000000000000
χ524444-4-4-24-4-44-2-2-200002200-2-2220000−22−222222002222−2−2−2−20000000000000000000000000000
χ534444-4-4-2-444-4-2-2-2-4-4-4-4224422-2-222220000-2-2000000000000000000000000000000000000
χ5444-4-44-44-4-4444-4-400004-400-444-40000000000000000000000000000000000000000000000
χ5544-4-44-4-244-4-4-22244-4-4-22-44-222-2-2-2220000-22000000000000000000000000000000000000
χ5644-4-44-4-2-4-444-2220000-22002-2-220000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ5744-4-44-4-2-4-444-2220000-22002-2-220000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ5844-4-4-44-24-44-4-22200002-200-22-22000022−22−222200−22−222−22−20000000000000000000000000000
χ5944-4-4-44-24-44-4-22200002-200-22-220000−222222−22002−22−2−22−220000000000000000000000000000
χ6044-4-4-44-2-44-44-22244-4-42-24-42-22-2-2-22200002-2000000000000000000000000000000000000
χ614-44-40040000-4-4422−2222−220000000022−2222−2200000000000000ζ11+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
χ624-44-40040000-4-4422−2222−220000000022−2222−2200000000000000−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
χ634-44-40040000-4-44−2222−222200000000−2222−222200000000000000ζ11+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
χ644-44-40040000-4-44−2222−222200000000−2222−222200000000000000−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
χ698-88-800-4000044-442−4242−4200000000−2222−2222000000000000000000000000000000000000000000
χ708-88-800-4000044-4−4242−42420000000022−2222−22000000000000000000000000000000000000000000
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.