Finite Group Databasebeta

← Group #10868413

Character table — Group #10868413

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121244444444488121212121212121212122424242424242424444488884121212124444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1111
χ51111111111111111111111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111-1
χ911111111111111111111-1-111111111-1-1-1-111111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-11111-111-1-1-1-1-1
χ1011111111111111111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-11-1-111111
χ1111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111-1-1-1-1-111-1-1111
χ1211111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-11111111-1-1111-1-111-1-1-1
χ1311111111111111111111-1-1-1-1-1-11111-1-1-1-111111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-111-1-11
χ1411111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111-1-111111-1-111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-11111-1-1-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-111-1-1111-1-1-1-11
χ17222222222-2-2-2-2222222222000000002222-2-2-2-22222-2000000-2-2000000000000000022-2-200000000000-20000000
χ18222222222-2-2-2-2222222222000000002222-2-2-2-2-2-2-2-2-2000000-2-20000000000000000-2-2220000000000020000000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222222000000220000000000000000-2-2-2-20000000000020000000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-22000000220000000000000000222200000000000-20000000
χ2122222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100002222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-100002-2-2-2-222-1-111111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100002-2-222-2-2-1-11111111111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2222222221111-1-1-1-10000-2-2-222-2-211-1-1-1-11111-1-1-1-1111100000000-211-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-21111-1-1-1-10000-2-2-2-2-22211-1-1-1-111111111-1-1-1-1000000002-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-10000-222-2-2-2-2111111-1-1-1-1-1-1-1-11111000000002-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-21111-1-1-1-10000-2222222111111-1-1-1-11111-1-1-1-100000000-211-1-10000000000
χ292222-2-2-2-220000222-2-2-2-22-2000022−2−222-2-2000022-2-2000002−2000000000022−2−222−2−22-20022−2−20000000000002−20
χ302222-2-2-2-220000222-2-2-2-22-2000022−2−222-2-20000-2-222000002−2000000000022−2−222−2−2-2200−2−222000000000000−220
χ312222-2-2-2-220000222-2-2-2-22-20000−2−22222-2-2000022-2-200000−220000000000−2−222−2−2222-200−2−222000000000000−220
χ322222-2-2-2-220000222-2-2-2-22-20000−2−22222-2-20000-2-22200000−220000000000−2−222−2−222-220022−2−20000000000002−20
χ332222-2-2-2-220000222-2-2-2-2-22000022−2−2-2-222000022-2-200000−22000000000022−2−2−2−222-220022−2−2000000000000−220
χ342222-2-2-2-220000222-2-2-2-2-22000022−2−2-2-2220000-2-22200000−22000000000022−2−2−2−2222-200−2−2220000000000002−20
χ352222-2-2-2-220000222-2-2-2-2-220000−2−222-2-222000022-2-2000002−20000000000−2−22222−2−2-2200−2−2220000000000002−20
χ362222-2-2-2-220000222-2-2-2-2-220000−2−222-2-2220000-2-222000002−20000000000−2−22222−2−22-20022−2−2000000000000−220
χ3722-2-2-2-22222-22-22-2-2-2-222002i2i−2i−2i0000000022-2-200000000000002i2i−2i−2i00000000000000002-22-2000002i−2i00000000
χ3822-2-2-2-22222-22-22-2-2-2-222002i2i−2i−2i0000000022-2-200000000000002i2i−2i−2i0000000000000000-22-2200000−2i2i00000000
χ3922-2-2-2-22222-22-22-2-2-2-22200−2i−2i2i2i0000000022-2-20000000000000−2i−2i2i2i00000000000000002-22-200000−2i2i00000000
χ4022-2-2-2-22222-22-22-2-2-2-22200−2i−2i2i2i0000000022-2-20000000000000−2i−2i2i2i0000000000000000-22-22000002i−2i00000000
χ412-22-22-2-2222-2-22-2-222-22-2002i−2i2i−2i000000002-22-22i−2i2i−2i0000000002i−2i2i−2i000000000000002i−2i0000000000002-200000
χ422-22-22-2-2222-2-22-2-222-22-2002i−2i2i−2i000000002-22-2−2i2i−2i2i0000000002i−2i2i−2i00000000000000−2i2i000000000000-2200000
χ432-22-22-2-2222-2-22-2-222-22-200−2i2i−2i2i000000002-22-22i−2i2i−2i000000000−2i2i−2i2i000000000000002i−2i000000000000-2200000
χ442-22-22-2-2222-2-22-2-222-22-200−2i2i−2i2i000000002-22-2−2i2i−2i2i000000000−2i2i−2i2i00000000000000−2i2i0000000000002-200000
χ452-22-22-2-222-222-2-2-222-22-200000000000000-22-222i−2i2i−2i02i−2i00000000002i2i−2i−2i0000000000−2i2i000000000000002-2000
χ462-22-22-2-222-222-2-2-222-22-200000000000000-22-222i−2i2i−2i0−2i2i0000000000−2i−2i2i2i0000000000−2i2i00000000000000-22000
χ472-22-22-2-222-222-2-2-222-22-200000000000000-22-22−2i2i−2i2i02i−2i00000000002i2i−2i−2i00000000002i−2i00000000000000-22000
χ482-22-22-2-222-222-2-2-222-22-200000000000000-22-22−2i2i−2i2i0−2i2i0000000000−2i−2i2i2i00000000002i−2i000000000000002-2000
χ492-2-22-22-22222-2-2-22-2-222-2002-2-222i−2i2i−2i00002-2-2200000002i−2i00002-2-2200002i−2i2i−2i0000000000000002i−2i0000000000
χ502-2-22-22-22222-2-2-22-2-222-2002-2-22−2i2i−2i2i00002-2-220000000−2i2i00002-2-220000−2i2i−2i2i000000000000000−2i2i0000000000
χ512-2-22-22-22222-2-2-22-2-222-200-222-22i−2i2i−2i00002-2-220000000−2i2i0000-222-200002i−2i2i−2i000000000000000−2i2i0000000000
χ522-2-22-22-22222-2-2-22-2-222-200-222-2−2i2i−2i2i00002-2-2200000002i−2i0000-222-20000−2i2i−2i2i0000000000000002i−2i0000000000
χ532-2-22-22-22-122-2-21-111-1-11002-2-222i−2i2i−2i3−33−3-111-100000002i−2i003−3-111-13−33−3−ii−ii−i3i3−i3i3000000000−i3i3−ii0000000000
χ542-2-22-22-22-122-2-21-111-1-11002-2-222i−2i2i−2i−33−33-111-100000002i−2i00−33-111-1−33−33−ii−iii3−i3i3−i3000000000i3−i3−ii0000000000
χ552-2-22-22-22-122-2-21-111-1-11002-2-22−2i2i−2i2i3−33−3-111-10000000−2i2i003−3-111-13−33−3i−ii−ii3−i3i3−i3000000000i3−i3i−i0000000000
χ562-2-22-22-22-122-2-21-111-1-11002-2-22−2i2i−2i2i−33−33-111-10000000−2i2i00−33-111-1−33−33i−ii−i−i3i3−i3i3000000000−i3i3i−i0000000000
χ572-2-22-22-22-122-2-21-111-1-1100-222-22i−2i2i−2i3−33−3-111-10000000−2i2i003−31-1-11−33−33−ii−ii−i3i3−i3i3000000000i3−i3i−i0000000000
χ582-2-22-22-22-122-2-21-111-1-1100-222-22i−2i2i−2i−33−33-111-10000000−2i2i00−331-1-113−33−3−ii−iii3−i3i3−i3000000000−i3i3i−i0000000000
χ592-2-22-22-22-122-2-21-111-1-1100-222-2−2i2i−2i2i3−33−3-111-100000002i−2i003−31-1-11−33−33i−ii−ii3−i3i3−i3000000000−i3i3−ii0000000000
χ602-2-22-22-22-122-2-21-111-1-1100-222-2−2i2i−2i2i−33−33-111-100000002i−2i00−331-1-113−33−3i−ii−i−i3i3−i3i3000000000i3−i3−ii0000000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-24400000000-2-2-2-222220000-400000022000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000000002222222200004000000-2-2000000000000000000000000000000000000000
χ634444-4-4-4-4-20000-2-2-222224-400002222−22−22-2-222000000000000022−220000000000−2−222−2−22200000000000000000000000
χ644444-4-4-4-4-20000-2-2-222224-40000−22−222222-2-2220000000000000−2222000000000022−2−222−2−200000000000000000000000
χ654444-4-4-4-4-20000-2-2-22222-4400002222−22−2222-2-20000000000000−22220000000000−2−22222−2−200000000000000000000000
χ664444-4-4-4-4-20000-2-2-22222-440000−22−22222222-2-2000000000000022−22000000000022−2−2−2−22200000000000000000000000
χ6744-4-444-4-4400004-4-444-4-400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ6844-4-444-4-4400004-4-444-4-4000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ6944-4-4-4-4444-44-444-4-4-4-44400000000000000-4-4440000000000000000000000000000000000000000000000000000
χ7044-4-4-4-444-24-44-4-22222-2-2004i4i−4i−4i00000000-2-2220000000000000−2i−2i2i2i00000000000000000000000000000000000
χ7144-4-4-4-444-24-44-4-22222-2-200−4i−4i4i4i00000000-2-22200000000000002i2i−2i−2i00000000000000000000000000000000000
χ7244-4-4-4-444-2-44-44-22222-2-20000000000000022-2-200000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ7344-4-4-4-444-2-44-44-22222-2-20000000000000022-2-2000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ744-44-44-4-44-24-4-4422-2-22-22004i−4i4i−4i00000000-22-220000000000000−2i2i−2i2i00000000000000000000000000000000000
χ754-44-44-4-44-24-4-4422-2-22-2200−4i4i−4i4i00000000-22-2200000000000002i−2i2i−2i00000000000000000000000000000000000
χ764-44-44-4-44-2-444-422-2-22-22000000000000002-22-2000004i−4i0000000000−2i−2i2i2i0000000000000000000000000000000
χ774-44-44-4-44-2-444-422-2-22-22000000000000002-22-200000−4i4i00000000002i2i−2i−2i0000000000000000000000000000000
χ784-44-4-444-440000-4-44-44-440000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ794-44-4-444-440000-4-44-44-44000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ804-4-444-44-440000-44-44-4-44000000−2i22i22i2−2i200000000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ814-4-444-44-440000-44-44-4-440000002i2−2i2−2i22i2000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ824-4-444-44-4-200002-22-222-2000000−2i22i22i2−2i223−23−23230000000000000000000000000i2−i2−i2i2i6−i6−i6i600000000000000000000000
χ834-4-444-44-4-200002-22-222-2000000−2i22i22i2−2i2−232323−230000000000000000000000000i2−i2−i2i2−i6i6i6−i600000000000000000000000
χ844-4-444-44-4-200002-22-222-20000002i2−2i2−2i22i223−23−23230000000000000000000000000−i2i2i2−i2−i6i6i6−i600000000000000000000000
χ854-4-444-44-4-200002-22-222-20000002i2−2i2−2i22i2−232323−230000000000000000000000000−i2i2i2−i2i6−i6−i6i600000000000000000000000
χ864-4-44-44-444-4-444-44-4-444-400000000000000-444-40000000000000000000000000000000000000000000000000000
χ874-4-44-44-44-2-4-4442-222-2-22000000000023−2323−232-2-2200000000000−2323000000000000000000000000000000000000000
χ884-4-44-44-44-2-4-4442-222-2-220000000000−2323−23232-2-220000000000023−23000000000000000000000000000000000000000
χ8988-8-888-8-8-40000-444-4-4440000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-888-8-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).