Finite Group Databasebeta

← Group #10827379

Character table — Group #10827379

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order12222222344446666666444444888812121212121212122222222446688121212121212121224242424242424244444888846612122222444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1111-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-11-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1111
χ51111111111111111111111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-11111-1
χ911111111111111111111-1-11111111111-1-1-1-1111111-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-111-1-1-1-111-111-1-1-1
χ1011111111111111111111-1-11111111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-111-1-11-1-1111
χ1111111111111111111111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-111-1-1-1-1-111111
χ1211111111111111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111111-1-11111111-1-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111-1-11111-1-1-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11-1-111-1-11111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-11111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-111-1-11111-1-1-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1111111-111-1-1-1-1-1-1111-1-11
χ17222222222-2-2-2-222222222200000000-2-22222-2-22222-20000-2-2000000000000000000-2-2220000000000000-200000
χ18222222222-2-2-2-222222222200000000-2-22222-2-2-2-2-2-2-20000-2-200000000000000000022-2-20000000000000200000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222222000022000000000000000000-2-2-2-20000000000000200000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-2200002200000000000000000022220000000000000-200000
χ2122222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000022222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-100002-2-222-1-1-2-2-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-100002-2-2-2-2-1-12211111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-1-1-2-21111111111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222222222-1-11111-1-10000-222-2-211-2-2-1-1-1-11111-1-1-1-1111100000000-2-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-11111-1-10000-2-2-2-2-21122-1-1-1-111111111-1-1-1-100000000211-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-10000-2-2-22211-2-21111-1-1-1-1-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-10000-2222211221111-1-1-1-11111-1-1-1-100000000-2-1-1110000000000
χ29222-22-2-2-22000022-22-2-2-22i−2i0000−i2−i2i2i2002i2i−2i−2i0022-2-200000002−200000000−i2−i2i2i222−2−2002i−2i−i2−i2i2i20000000000002−20
χ30222-22-2-2-22000022-22-2-2-22i−2i0000−i2−i2i2i2002i2i−2i−2i00-2-22200000002−200000000−i2−i2i2i222−2−200−2i2ii2i2−i2−i2000000000000−220
χ31222-22-2-2-22000022-22-2-2-22i−2i0000i2i2−i2−i2002i2i−2i−2i0022-2-20000000−2200000000i2i2−i2−i2−2−222002i−2ii2i2−i2−i2000000000000−220
χ32222-22-2-2-22000022-22-2-2-22i−2i0000i2i2−i2−i2002i2i−2i−2i00-2-2220000000−2200000000i2i2−i2−i2−2−22200−2i2i−i2−i2i2i20000000000002−20
χ33222-22-2-2-22000022-22-2-2-2−2i2i0000−i2−i2i2i200−2i−2i2i2i0022-2-20000000−2200000000−i2−i2i2i2−2−22200−2i2i−i2−i2i2i2000000000000−220
χ34222-22-2-2-22000022-22-2-2-2−2i2i0000−i2−i2i2i200−2i−2i2i2i00-2-2220000000−2200000000−i2−i2i2i2−2−222002i−2ii2i2−i2−i20000000000002−20
χ35222-22-2-2-22000022-22-2-2-2−2i2i0000i2i2−i2−i200−2i−2i2i2i0022-2-200000002−200000000i2i2−i2−i222−2−200−2i2ii2i2−i2−i20000000000002−20
χ36222-22-2-2-22000022-22-2-2-2−2i2i0000i2i2−i2−i200−2i−2i2i2i00-2-22200000002−200000000i2i2−i2−i222−2−2002i−2i−i2−i2i2i2000000000000−220
χ3722-22-22-2-222-22-22-2-2-222-2002i2i−2i−2i2i−2i2i−2i220000-2-2000002-20000002i2i−2i−2i00002i−2i2i−2i00000000000002-2000000000000
χ3822-22-22-2-222-22-22-2-2-222-2002i2i−2i−2i−2i2i−2i2i220000-2-200000-220000002i2i−2i−2i0000−2i2i−2i2i0000000000000-22000000000000
χ3922-22-22-2-222-22-22-2-2-222-200−2i−2i2i2i2i−2i2i−2i220000-2-200000-22000000−2i−2i2i2i00002i−2i2i−2i0000000000000-22000000000000
χ4022-22-22-2-222-22-22-2-2-222-200−2i−2i2i2i−2i2i−2i2i220000-2-2000002-2000000−2i−2i2i2i0000−2i2i−2i2i00000000000002-2000000000000
χ4122-22-22-2-2-12-22-2-1111-1-11002i2i−2i−2i2i−2i2i−2i-1-1−i3i3−i3i311000002-200−i3i300−i−iii33−3−3−ii−ii3−33−3000000000-11−i3i30000000000
χ4222-22-22-2-2-12-22-2-1111-1-11002i2i−2i−2i2i−2i2i−2i-1-1i3−i3i3−i311000002-200i3−i300−i−iii−3−333−ii−ii−33−33000000000-11i3−i30000000000
χ4322-22-22-2-2-12-22-2-1111-1-11002i2i−2i−2i−2i2i−2i2i-1-1−i3i3−i3i31100000-2200−i3i300−i−iii33−3−3i−ii−i−33−330000000001-1i3−i30000000000
χ4422-22-22-2-2-12-22-2-1111-1-11002i2i−2i−2i−2i2i−2i2i-1-1i3−i3i3−i31100000-2200i3−i300−i−iii−3−333i−ii−i3−33−30000000001-1−i3i30000000000
χ4522-22-22-2-2-12-22-2-1111-1-1100−2i−2i2i2i2i−2i2i−2i-1-1−i3i3−i3i31100000-2200−i3i300ii−i−i−3−333−ii−ii3−33−30000000001-1i3−i30000000000
χ4622-22-22-2-2-12-22-2-1111-1-1100−2i−2i2i2i2i−2i2i−2i-1-1i3−i3i3−i31100000-2200i3−i300ii−i−i33−3−3−ii−ii−33−330000000001-1−i3i30000000000
χ4722-22-22-2-2-12-22-2-1111-1-1100−2i−2i2i2i−2i2i−2i2i-1-1−i3i3−i3i311000002-200−i3i300ii−i−i−3−333i−ii−i−33−33000000000-11−i3i30000000000
χ4822-22-22-2-2-12-22-2-1111-1-1100−2i−2i2i2i−2i2i−2i2i-1-1i3−i3i3−i311000002-200i3−i300ii−i−i33−3−3i−ii−i3−33−3000000000-11i3−i30000000000
χ492-22-2-222-2222-2-2-222-22-2-2002i−2i2i−2i00002-200002-200000000000002i−2i2i−2i00000000000000002i−2i2i−2i00000002-2000000
χ502-22-2-222-2222-2-2-222-22-2-2002i−2i2i−2i00002-200002-200000000000002i−2i2i−2i0000000000000000−2i2i−2i2i0000000-22000000
χ512-22-2-222-2222-2-2-222-22-2-200−2i2i−2i2i00002-200002-20000000000000−2i2i−2i2i00000000000000002i−2i2i−2i0000000-22000000
χ522-22-2-222-2222-2-2-222-22-2-200−2i2i−2i2i00002-200002-20000000000000−2i2i−2i2i0000000000000000−2i2i−2i2i00000002-2000000
χ532-2-2-222-2222-2-22-2-2-222-22002-2-2200002-20000-222-22-20000000002-2-220000000000002-200000000000000002-2000
χ542-2-2-222-2222-2-22-2-2-222-22002-2-2200002-20000-22-22-220000000002-2-22000000000000-220000000000000000-22000
χ552-2-2-222-2222-2-22-2-2-222-2200-222-200002-20000-222-22-2000000000-222-20000000000002-20000000000000000-22000
χ562-2-2-222-2222-2-22-2-2-222-2200-222-200002-20000-22-22-22000000000-222-2000000000000-2200000000000000002-2000
χ572-2-2-222-222-222-2-2-2-222-220000000000-2200002-22-22-20002-2000000002-22-200000000-22000000000002-200000000
χ582-2-2-222-222-222-2-2-2-222-220000000000-2200002-22-22-2000-2200000000-22-2200000000-2200000000000-2200000000
χ592-2-2-222-222-222-2-2-2-222-220000000000-2200002-2-22-220002-2000000002-22-2000000002-200000000000-2200000000
χ602-2-2-222-222-222-2-2-2-222-220000000000-2200002-2-22-22000-2200000000-22-22000000002-2000000000002-200000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2440000000022-2-2-2-2220000-400002200000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-40000000022222222000040000-2-200000000000000000000000000000000000000000
χ63444-44-4-4-4-20000-2-22-22224i−4i0000−2i2−2i22i22i200−2i−2i2i2i000000000000022−2200000000i2i2−i2−i2−2−22200000000000000000000000
χ64444-44-4-4-4-20000-2-22-22224i−4i00002i22i2−2i2−2i200−2i−2i2i2i0000000000000−222200000000−i2−i2i2i222−2−200000000000000000000000
χ65444-44-4-4-4-20000-2-22-2222−4i4i0000−2i2−2i22i22i2002i2i−2i−2i0000000000000−222200000000i2i2−i2−i222−2−200000000000000000000000
χ66444-44-4-4-4-20000-2-22-2222−4i4i00002i22i2−2i2−2i2002i2i−2i−2i000000000000022−2200000000−i2−i2i2i2−2−22200000000000000000000000
χ6744-44-44-4-44-44-444-4-4-444-40000000000-4-40000440000000000000000000000000000000000000000000000000000
χ6844-44-44-4-4-2-44-44-2222-2-22000000000022−2i32i3−2i32i3-2-20000000002i3−2i300000000000000000000000000000000000000000
χ6944-44-44-4-4-2-44-44-2222-2-220000000000222i3−2i32i3−2i3-2-2000000000−2i32i300000000000000000000000000000000000000000
χ7044-4-4-4-444400004-44-4-4-4400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ7144-4-4-4-444400004-44-4-4-44000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ7244-4-4-4-444-20000-22-2222-200000022−22−22220023−23−232300000000000000000000000−222−26−6−6600000000000000000000000
χ7344-4-4-4-444-20000-22-2222-200000022−22−222200−232323−2300000000000000000000000−222−2−666−600000000000000000000000
χ7444-4-4-4-444-20000-22-2222-2000000−222222−220023−23−2323000000000000000000000002−2−22−666−600000000000000000000000
χ7544-4-4-4-444-20000-22-2222-2000000−222222−2200−232323−23000000000000000000000002−2−226−6−6600000000000000000000000
χ764-444-4-4-4440000-44-4-4-44400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ774-444-4-4-4440000-44-4-4-444000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ784-44-4-444-44-4-444-444-44-4-40000000000-440000-440000000000000000000000000000000000000000000000000000
χ794-44-4-444-4-244-4-42-2-22-222004i−4i4i−4i0000-220000-220000000000000−2i2i−2i2i00000000000000000000000000000000000
χ804-44-4-444-4-244-4-42-2-22-22200−4i4i−4i4i0000-220000-2200000000000002i−2i2i−2i00000000000000000000000000000000000
χ814-44-4-444-4-2-4-4442-2-22-22200000000002-200002-20000000000000000023−23−23230000000000000000000000000000000
χ824-44-4-444-4-2-4-4442-2-22-22200000000002-200002-200000000000000000−232323−230000000000000000000000000000000
χ834-4-444-44-440000-4-444-44-40000000000000000004-4-44000000000000000000000000000000000000000000000000
χ844-4-444-44-440000-4-444-44-4000000000000000000-444-4000000000000000000000000000000000000000000000000
χ854-4-4-444-44-24-4-44222-2-22-2004-4-440000-2200002-20000000000000-222-200000000000000000000000000000000000
χ864-4-4-444-44-24-4-44222-2-22-200-444-40000-2200002-200000000000002-2-2200000000000000000000000000000000000
χ874-4-4-444-44-2-444-4222-2-22-200000000002-20000-2200000004-400000000-22-220000000000000000000000000000000
χ884-4-4-444-44-2-444-4222-2-22-200000000002-20000-220000000-44000000002-22-20000000000000000000000000000000
χ898-888-8-8-88-400004-4444-4-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-888-88-8-4000044-4-44-440000000000000000000000000000000000000000000000000000000000000000000000

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