Finite Group Databasebeta

← Group #10694671

Character table — Group #10694671

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order12222234444444466612121212446688888888121212121212121212122424242424242424242424242424242488882424242424242424888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ91111-1-1111-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i1-11-1
χ101111-1-1111-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1i−ii−iii−i−iii−i−i−i−iii−i−iii-11-11
χ111111-1-1111-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1−ii−ii−i−iii−i−iiiii−i−iii−i−i-11-11
χ121111-1-1111-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii1-11-1
χ131111-1-1111-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111i−i−iiii−i−i−i−iiiii−i−i−i−iii1-1-11
χ141111-1-1111-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111i−i−iiii−i−i−i−iii−i−iiiii−i−i-111-1
χ151111-1-1111-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111−iii−i−i−iiiii−i−iii−i−i−i−iii-111-1
χ161111-1-1111-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111−iii−i−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ1722222222222-2-2-2-22222222-2-22222-2-222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ1822222222222-2-2-2-22222222-2-222-2-222-2-222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ192222222-2-2-2-222-2-2222-2-2-2-22-2220000000022-2-222-2-2-2-2000000000000000000000000000000002i−2i2i−2i0000
χ202222222-2-2-2-222-2-2222-2-2-2-22-2220000000022-2-222-2-2-2-200000000000000000000000000000000−2i2i−2i2i0000
χ212222222-2-2-2-2-2-222222-2-2-2-2-222200000000-2-222-2-222-2-200000000000000000000000000002i−2i2i−2i00000000
χ222222222-2-2-2-2-2-222222-2-2-2-2-222200000000-2-222-2-222-2-20000000000000000000000000000−2i2i−2i2i00000000
χ23222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ24222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ25222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-11111000000000000
χ26222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-1000000000000
χ27222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-1-122-2-222-2-211111111-1-1-1-1-1-11111-1-1-1-111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ28222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-1-122-2-222-2-211111111-1-1-1-1-1-11111-1-1-1-111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ29222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-1-1-2-222-2-22211111111-1-11111-1-1-1-11111-1-1-1-10000−i3i3−i3i3i3−i3i3−i3000000000000
χ30222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-1-1-2-222-2-22211111111-1-11111-1-1-1-11111-1-1-1-10000i3−i3i3−i3−i3i3−i3i3000000000000
χ312222-2-2222-2-22222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ322222-2-2222-2-22222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2222222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ332222-2-22-2-22222-2-22222222-22-2-200000000-2-22222-2-2-2-200000000000000000000000000002-2-2200000000
χ342222-2-22-2-22222-2-22222222-22-2-200000000-2-22222-2-2-2-20000000000000000000000000000-222-200000000
χ352222-2-22-2-222-2-22222222222-2-2-20000000022-2-2-2-222-2-2000000000000000000000000000000002-2-220000
χ362222-2-22-2-222-2-22222222222-2-2-20000000022-2-2-2-222-2-200000000000000000000000000000000-222-20000
χ372222-2-2-122-2-22222-1-1-11111-2-21122-2-2-2-2221111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-100003−3−333−3−33000000000000
χ382222-2-2-122-2-22222-1-1-11111-2-21122-2-2-2-2221111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-10000−333−3−333−3000000000000
χ392222-2-2-122-2-22222-1-1-11111-2-211-2-22222-2-21111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111100003−3−33−333−3000000000000
χ402222-2-2-122-2-22222-1-1-11111-2-211-2-22222-2-21111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111110000−333−33−3−33000000000000
χ412222-2-2-122-2-2-2-2-2-2-1-1-1111122112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111112i−2i2i−2i−i−iii−i−iii000000000000
χ422222-2-2-122-2-2-2-2-2-2-1-1-1111122112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111−2i2i−2i2iii−i−iii−i−i000000000000
χ432222-2-2-122-2-2-2-2-2-2-1-1-111112211-2-2-2-22222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-12i−2i−2i2i−i−iiiii−i−i000000000000
χ442222-2-2-122-2-2-2-2-2-2-1-1-111112211-2-2-2-22222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1−2i2i2i−2iii−i−i−i−iii000000000000
χ45444444-2-4-4-4-444-4-4-2-2-222224-4-2-200000000-2-222-2-222220000000000000000000000000000000000000000
χ46444444-2-4-4-4-4-4-444-2-2-22222-44-2-20000000022-2-222-2-2220000000000000000000000000000000000000000
χ474444-4-4-2-4-44444-4-4-2-2-2-2-2-2-2-44220000000022-2-2-2-222220000000000000000000000000000000000000000
χ484444-4-4-2-4-444-4-444-2-2-2-2-2-2-24-42200000000-2-22222-2-2220000000000000000000000000000000000000000
χ4944-4-44-444-44-400004-4-444-4-4004-400000000000000004-40000000000000000000000000000000000000000
χ5044-4-44-44-44-4400004-4-4-4-444004-40000000000000000-440000000000000000000000000000000000000000
χ5144-4-44-4-24-44-40000-222-2-22200-220000000000000000-2200002323−23−2300002323−23−23000000000000000000000000
χ5244-4-44-4-24-44-40000-222-2-22200-220000000000000000-220000−23−2323230000−23−232323000000000000000000000000
χ5344-4-44-4-2-44-440000-22222-2-200-2200000000000000002-22323−23−2300002323−23−230000000000000000000000000000
χ5444-4-44-4-2-44-440000-22222-2-200-2200000000000000002-2−23−2323230000−23−2323230000000000000000000000000000
χ5544-4-4-4444-4-4400004-4-4-4-44400-4400000000000000004-40000000000000000000000000000000000000000
χ5644-4-4-444-444-400004-4-444-4-400-440000000000000000-440000000000000000000000000000000000000000
χ5744-4-4-44-24-4-440000-22222-2-2002-20000000000000000-2200002323−23−230000−23−232323000000000000000000000000
χ5844-4-4-44-24-4-440000-22222-2-2002-20000000000000000-220000−23−23232300002323−23−23000000000000000000000000
χ5944-4-4-44-2-444-40000-222-2-222002-200000000000000002-22323−23−230000−23−2323230000000000000000000000000000
χ6044-4-4-44-2-444-40000-222-2-222002-200000000000000002-2−23−23232300002323−23−230000000000000000000000000000
χ614-44-40040000004-4-44-40000000000−2i22i2−2i22i2000000004-4000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000000000
χ624-44-40040000004-4-44-400000000002i2−2i22i2−2i2000000004-40000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000000000
χ634-44-4004000000-44-44-40000000000−2i22i22i2−2i200000000-44000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000
χ644-44-4004000000-44-44-400000000002i2−2i2−2i22i200000000-440000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000
χ654-44-400-20000004-42-2223−2323−23000000−2i22i2−2i22i20023−230000-2200i6−i6i6−i6i2−i2i2−i2i2−i2i2−i2i6−i6i6−i6000000000000000000000000
χ664-44-400-20000004-42-2223−2323−230000002i2−2i22i2−2i20023−230000-2200−i6i6−i6i6−i2i2−i2i2−i2i2−i2i2−i6i6−i6i6000000000000000000000000
χ674-44-400-20000004-42-22−2323−2323000000−2i22i2−2i22i200−23230000-2200−i6i6−i6i6i2−i2i2−i2i2−i2i2−i2−i6i6−i6i6000000000000000000000000
χ684-44-400-20000004-42-22−2323−23230000002i2−2i22i2−2i200−23230000-2200i6−i6i6−i6−i2i2−i2i2−i2i2−i2i2i6−i6i6−i6000000000000000000000000
χ694-44-400-2000000-442-2223−2323−23000000−2i22i22i2−2i200−232300002-200−i6i6−i6i6i2−i2i2−i2−i2i2−i2i2i6−i6i6−i6000000000000000000000000
χ704-44-400-2000000-442-2223−2323−230000002i2−2i2−2i22i200−232300002-200i6−i6i6−i6−i2i2−i2i2i2−i2i2−i2−i6i6−i6i6000000000000000000000000
χ714-44-400-2000000-442-22−2323−2323000000−2i22i22i2−2i20023−2300002-200i6−i6i6−i6i2−i2i2−i2−i2i2−i2i2−i6i6−i6i6000000000000000000000000
χ724-44-400-2000000-442-22−2323−23230000002i2−2i2−2i22i20023−2300002-200−i6i6−i6i6−i2i2−i2i2i2−i2i2−i2i6−i6i6−i6000000000000000000000000
χ734-4-4400400004-400-4-4400000000−2i22i20000−2i22i200004-40000−2i22i22i2−2i200000000−2i22i22i2−2i2000000000000000000000000
χ744-4-4400400004-400-4-44000000002i2−2i200002i2−2i200004-400002i2−2i2−2i22i2000000002i2−2i2−2i22i2000000000000000000000000
χ754-4-440040000-4400-4-4400000000−2i22i200002i2−2i20000-440000−2i22i22i2−2i2000000002i2−2i2−2i22i2000000000000000000000000
χ764-4-440040000-4400-4-44000000002i2−2i20000−2i22i20000-4400002i2−2i2−2i22i200000000−2i22i22i2−2i2000000000000000000000000
χ774-4-4400-200004-40022-223−23−23230000−2i22i20000−2i22i20023−23-220000i2−i2−i2i2−i6i6i6−i6i6−i6−i6i6i2−i2−i2i2000000000000000000000000
χ784-4-4400-200004-40022-223−23−232300002i2−2i200002i2−2i20023−23-220000−i2i2i2−i2i6−i6−i6i6−i6i6i6−i6−i2i2i2−i2000000000000000000000000
χ794-4-4400-200004-40022-2−232323−230000−2i22i20000−2i22i200−2323-220000i2−i2−i2i2i6−i6−i6i6−i6i6i6−i6i2−i2−i2i2000000000000000000000000
χ804-4-4400-200004-40022-2−232323−2300002i2−2i200002i2−2i200−2323-220000−i2i2i2−i2−i6i6i6−i6i6−i6−i6i6−i2i2i2−i2000000000000000000000000
χ814-4-4400-20000-440022-223−23−23230000−2i22i200002i2−2i200−23232-20000i2−i2−i2i2i6−i6−i6i6i6−i6−i6i6−i2i2i2−i2000000000000000000000000
χ824-4-4400-20000-440022-223−23−232300002i2−2i20000−2i22i200−23232-20000−i2i2i2−i2−i6i6i6−i6−i6i6i6−i6i2−i2−i2i2000000000000000000000000
χ834-4-4400-20000-440022-2−232323−230000−2i22i200002i2−2i20023−232-20000i2−i2−i2i2−i6i6i6−i6−i6i6i6−i6−i2i2i2−i2000000000000000000000000
χ844-4-4400-20000-440022-2−232323−2300002i2−2i20000−2i22i20023−232-20000−i2i2i2−i2i6−i6−i6i6i6−i6−i6i6i2−i2−i2i2000000000000000000000000

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