Finite Group Databasebeta

← Group #10853291

Character table — Group #10853291

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
χ311111111111111111111111111-1-1-1-1111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111111111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-111-1-1-111-1-111-1-1-1
χ6111111111111111111111111-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-11-1-111-1-1111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-111-111-1-1-1-1111
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111111-1-1111-1-11111-1-1-1
χ911111111111111111111-1-1-1-1111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11-1-1-1-1-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11111-1-111-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111-1-111-1-1-111-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11-1-111111-1-11111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1111111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-11111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-111-1-1111-1-1-1-1-1-11
χ17222222222-2-2-2-222222220000220000-2-22222-2-2222200-20000-2-20000000000000000-2-222000000000-2000000000
χ18222222222-2-2-2-222222220000220000-2-22222-2-2-2-2-2-200-20000-2-2000000000000000022-2-20000000002000000000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222220020000220000000000000000-2-2-2-20000000002000000000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-200200002200000000000000002222000000000-2000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000-2-2222-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-11111-1-1000022-2-2-2-2-211-1-1-1-11111-1-1-1-1111100000000-2-1-1110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-11111-1-10000-2-2-2-2-22211-1-1-1-111111111-1-1-1-100000000211-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-10000-2-22-2-222-1-111111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-2-2-1-11111111111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-10000-2-2-222-2-2111111-1-1-1-1-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-1000022-22222111111-1-1-1-11111-1-1-1-100000000-2-1-1110000000000
χ29222-2-2-2-22200002-2-22-2-2200002-2−i2−i2i2i20022-2-20022-2-200000−i2i20000000000−i2−i2i2i2−i2−i2i2i2002-2−i2−i2i2i2000000000000−i2i20
χ30222-2-2-2-22200002-2-22-2-2200002-2−i2−i2i2i20022-2-200-2-22200000−i2i20000000000−i2−i2i2i2−i2−i2i2i200-22i2i2−i2−i2000000000000i2−i20
χ31222-2-2-2-22200002-2-22-2-2200002-2i2i2−i2−i20022-2-20022-2-200000i2−i20000000000i2i2−i2−i2i2i2−i2−i2002-2i2i2−i2−i2000000000000i2−i20
χ32222-2-2-2-22200002-2-22-2-2200002-2i2i2−i2−i20022-2-200-2-22200000i2−i20000000000i2i2−i2−i2i2i2−i2−i200-22−i2−i2i2i2000000000000−i2i20
χ33222-2-2-2-22200002-2-22-2-220000-22−i2−i2i2i200-2-2220022-2-200000i2−i20000000000−i2−i2i2i2i2i2−i2−i200-22−i2−i2i2i2000000000000i2−i20
χ34222-2-2-2-22200002-2-22-2-220000-22−i2−i2i2i200-2-22200-2-22200000i2−i20000000000−i2−i2i2i2i2i2−i2−i2002-2i2i2−i2−i2000000000000−i2i20
χ35222-2-2-2-22200002-2-22-2-220000-22i2i2−i2−i200-2-2220022-2-200000−i2i20000000000i2i2−i2−i2−i2−i2i2i200-22i2i2−i2−i2000000000000−i2i20
χ36222-2-2-2-22200002-2-22-2-220000-22i2i2−i2−i200-2-22200-2-22200000−i2i20000000000i2i2−i2−i2−i2−i2i2i2002-2−i2−i2i2i2000000000000i2−i20
χ3722-2-2-222-222-2-22-22-222-2-22i2i−2i−2i002i−2i2i−2i2-200002-200002-200000002i2i−2i−2i00002i−2i2i−2i00000000000002-2000000000000
χ3822-2-2-222-222-2-22-22-222-2-22i2i−2i−2i00−2i2i−2i2i2-200002-20000-2200000002i2i−2i−2i0000−2i2i−2i2i0000000000000-22000000000000
χ3922-2-2-222-222-2-22-22-222-2-2−2i−2i2i2i002i−2i2i−2i2-200002-20000-220000000−2i−2i2i2i00002i−2i2i−2i0000000000000-22000000000000
χ4022-2-2-222-222-2-22-22-222-2-2−2i−2i2i2i00−2i2i−2i2i2-200002-200002-20000000−2i−2i2i2i0000−2i2i−2i2i00000000000002-2000000000000
χ4122-2-2-222-2-12-2-221-11-1-1112i2i−2i−2i002i−2i2i−2i-113−33−3-1100002-2000003−3−i−iii−i3−i3i3i3−ii−ii−i3i3−i3i3000000000-113−30000000000
χ4222-2-2-222-2-12-2-221-11-1-1112i2i−2i−2i002i−2i2i−2i-11−33−33-1100002-200000−33−i−iiii3i3−i3−i3−ii−iii3−i3i3−i3000000000-11−330000000000
χ4322-2-2-222-2-12-2-221-11-1-1112i2i−2i−2i00−2i2i−2i2i-113−33−3-110000-22000003−3−i−iii−i3−i3i3i3i−ii−ii3−i3i3−i30000000001-1−330000000000
χ4422-2-2-222-2-12-2-221-11-1-1112i2i−2i−2i00−2i2i−2i2i-11−33−33-110000-2200000−33−i−iiii3i3−i3−i3i−ii−i−i3i3−i3i30000000001-13−30000000000
χ4522-2-2-222-2-12-2-221-11-1-111−2i−2i2i2i002i−2i2i−2i-113−33−3-110000-22000003−3ii−i−ii3i3−i3−i3−ii−ii−i3i3−i3i30000000001-1−330000000000
χ4622-2-2-222-2-12-2-221-11-1-111−2i−2i2i2i002i−2i2i−2i-11−33−33-110000-2200000−33ii−i−i−i3−i3i3i3−ii−iii3−i3i3−i30000000001-13−30000000000
χ4722-2-2-222-2-12-2-221-11-1-111−2i−2i2i2i00−2i2i−2i2i-113−33−3-1100002-2000003−3ii−i−ii3i3−i3−i3i−ii−ii3−i3i3−i3000000000-113−30000000000
χ4822-2-2-222-2-12-2-221-11-1-111−2i−2i2i2i00−2i2i−2i2i-11−33−33-1100002-200000−33ii−i−i−i3−i3i3i3i−ii−i−i3i3−i3i3000000000-11−330000000000
χ492-22-222-2-2222-2-222-2-2-22-22-22-2000000220000-2-22-22-20000000002-22-20000000000002-20000000000002-20000000
χ502-22-222-2-2222-2-222-2-2-22-22-22-2000000220000-2-2-22-220000000002-22-2000000000000-22000000000000-220000000
χ512-22-222-2-2222-2-222-2-2-22-2-22-22000000220000-2-22-22-2000000000-22-220000000000002-2000000000000-220000000
χ522-22-222-2-2222-2-222-2-2-22-2-22-22000000220000-2-2-22-22000000000-22-22000000000000-220000000000002-20000000
χ532-22-222-2-22-2-22222-2-2-22-20000000000-2-20000222-22-20002i−2i000000002i−2i2i−2i00000000-22000000000000002i−2i00000
χ542-22-222-2-22-2-22222-2-2-22-20000000000-2-20000222-22-2000−2i2i00000000−2i2i−2i2i00000000-2200000000000000−2i2i00000
χ552-22-222-2-22-2-22222-2-2-22-20000000000-2-2000022-22-220002i−2i000000002i−2i2i−2i000000002-200000000000000−2i2i00000
χ562-22-222-2-22-2-22222-2-2-22-20000000000-2-2000022-22-22000−2i2i00000000−2i2i−2i2i000000002-2000000000000002i−2i00000
χ572-2-22-22-2222-22-2-222-2-2-222i−2i−2i2i0000002-20000-2200000000000002i−2i−2i2i00000000000000002i−2i2i−2i00000000002-2000
χ582-2-22-22-2222-22-2-222-2-2-222i−2i−2i2i0000002-20000-2200000000000002i−2i−2i2i0000000000000000−2i2i−2i2i0000000000-22000
χ592-2-22-22-2222-22-2-222-2-2-22−2i2i2i−2i0000002-20000-220000000000000−2i2i2i−2i00000000000000002i−2i2i−2i0000000000-22000
χ602-2-22-22-2222-22-2-222-2-2-22−2i2i2i−2i0000002-20000-220000000000000−2i2i2i−2i0000000000000000−2i2i−2i2i00000000002-2000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2000044000022-2-2-2-222000000-4000022000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-400002222222200000040000-2-2000000000000000000000000000000000000000
χ63444-4-4-4-44-20000-222-222-200004-4−2i2−2i22i22i200-2-22200000000000−2i22i20000000000i2i2−i2−i2i2i2−i2−i200000000000000000000000
χ64444-4-4-4-44-20000-222-222-200004-42i22i2−2i2−2i200-2-222000000000002i2−2i20000000000−i2−i2i2i2−i2−i2i2i200000000000000000000000
χ65444-4-4-4-44-20000-222-222-20000-44−2i2−2i22i22i20022-2-2000000000002i2−2i20000000000i2i2−i2−i2−i2−i2i2i200000000000000000000000
χ66444-4-4-4-44-20000-222-222-20000-442i22i2−2i2−2i20022-2-200000000000−2i22i20000000000−i2−i2i2i2i2i2−i2−i200000000000000000000000
χ6744-444-4-4-440000-4-444-44-400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ6844-444-4-4-440000-4-444-44-4000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ6944-444-4-4-4-2000022-2-22-2200000022−22−22220023−23−232300000000000000000000000−222−2−666−600000000000000000000000
χ7044-444-4-4-4-2000022-2-22-2200000022−22−222200−232323−2300000000000000000000000−222−26−6−6600000000000000000000000
χ7144-444-4-4-4-2000022-2-22-22000000−222222−220023−23−2323000000000000000000000002−2−226−6−6600000000000000000000000
χ7244-444-4-4-4-2000022-2-22-22000000−222222−2200−232323−23000000000000000000000002−2−22−666−600000000000000000000000
χ7344-4-4-444-44-444-4-44-444-4-40000000000-440000-440000000000000000000000000000000000000000000000000000
χ7444-4-4-444-4-2-444-42-22-2-22200000000002-223−2323−232-200000000000−2323000000000000000000000000000000000000000
χ7544-4-4-444-4-2-444-42-22-2-22200000000002-2−2323−23232-20000000000023−23000000000000000000000000000000000000000
χ764-444-4-44-4400004-44-44-4-40000000000000000004-4-44000000000000000000000000000000000000000000000000
χ774-444-4-44-4400004-44-44-4-4000000000000000000-444-4000000000000000000000000000000000000000000000000
χ784-44-444-4-4-244-4-4-2-2222-224-44-4000000-2-20000220000000000000-22-2200000000000000000000000000000000000
χ794-44-444-4-4-244-4-4-2-2222-22-44-44000000-2-200002200000000000002-22-200000000000000000000000000000000000
χ804-44-444-4-4-2-4-444-2-2222-220000000000220000-2-200000004i−4i00000000−2i2i−2i2i0000000000000000000000000000000
χ814-44-444-4-4-2-4-444-2-2222-220000000000220000-2-20000000−4i4i000000002i−2i2i−2i0000000000000000000000000000000
χ824-4-44-44-444-44-44-444-4-4-440000000000-4400004-40000000000000000000000000000000000000000000000000000
χ834-4-44-44-44-24-44-42-2-2222-24i−4i−4i4i000000-2200002-20000000000000−2i2i2i−2i00000000000000000000000000000000000
χ844-4-44-44-44-24-44-42-2-2222-2−4i4i4i−4i000000-2200002-200000000000002i−2i−2i2i00000000000000000000000000000000000
χ854-4-44-44-44-2-44-442-2-2222-200000000002-20000-220000000000000000023−23−23230000000000000000000000000000000
χ864-4-44-44-44-2-44-442-2-2222-200000000002-20000-2200000000000000000−232323−230000000000000000000000000000000
χ874-4-4-44-44440000-4-4-4-444400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ884-4-4-44-44440000-4-4-4-4444000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ898-888-8-88-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-88-888-400004444-4-4-40000000000000000000000000000000000000000000000000000000000000000000000

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