Finite Group Databasebeta

← Group #10704607

Character table — Group #10704607

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222244444444444444444488888888888812121212121212121616161616161616161616162424242448484848
order122222344446662244444466121212121212121244661212121212121212444444448888242424242424242444448888
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
χ5111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111111111ii−i−iiiii−i−i−i−i-1-1-1-1ii−i−i
χ6111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111111111−i−iii−i−i−i−iiiii-1-1-1-1−i−iii
χ7111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1111−i−iii
χ8111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii1111ii−i−i
χ91111111-1-1-1-111111-1-1111111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-11-11-1
χ101111111-1-1-1-111111-1-1111111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-1-11-11-1-111-1-11111-1-1-11-11
χ111111111-1-1-1-111111-1-1111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-111111-11-111-1-111-1-1-1-111-11-11
χ121111111-1-1-1-111111-1-1111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-11-11-1-111-1-111-1-1111-11-1
χ131111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1i−i−iiii−i−i−i−iii-1-111i−i−ii
χ141111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−iii−i−i−iiiii−i−i-1-111−iii−i
χ151111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111i−i−iiii−i−i−i−iii11-1-1−iii−i
χ161111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111−iii−i−i−iiiii−i−i11-1-1i−i−ii
χ1722222222222222-2-2-2-222-2-222222222222-2-2-2-2-2-2-222-2-20000000000000000000000000000
χ1822222222222222-2-2-2-2-2-222222222-2-2-2-2-22-2-2-2-222-2-2220000000000000000000000000000
χ192222222-2-2-2-2222-2-22222-2-222-2-2-2-22222-22-2-222-2-2-2-2220000000000000000000000000000
χ202222222-2-2-2-2222-2-222-2-22222-2-2-2-2-2-2-2-22-2-2-2222222-2-20000000000000000000000000000
χ21222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ22222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ23222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-11111-2-2-1-1-1-1111111000000002i2i−2i−2i−i−i−i−iiiii00000000
χ24222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-11111-2-2-1-1-1-111111100000000−2i−2i2i2iiiii−i−i−i−i00000000
χ25222222-12222-1-1-1-2-2-2-222-2-2-1-1-1-1-1-1-1-1-1-12-2111111-1-111000000000000−i3i3−i3i3−i3i3−i3i300000000
χ26222222-12222-1-1-1-2-2-2-222-2-2-1-1-1-1-1-1-1-1-1-12-2111111-1-111000000000000i3−i3i3−i3i3−i3i3−i300000000
χ27222222-12222-1-1-1-2-2-2-2-2-222-1-1-1-1-1-11111-221111-1-111-1-10000000000003−33−3−33−3300000000
χ28222222-12222-1-1-1-2-2-2-2-2-222-1-1-1-1-1-11111-221111-1-111-1-1000000000000−33−333−33−300000000
χ29222222-1-2-2-2-2-1-1-122-2-22222-1-11111-1-1-1-1-2-2-1-111-1-11111000000002-22-2-1-111-1-11100000000
χ30222222-1-2-2-2-2-1-1-122-2-22222-1-11111-1-1-1-1-2-2-1-111-1-1111100000000-22-2211-1-111-1-100000000
χ31222222-1-2-2-2-2-1-1-122-2-2-2-2-2-2-1-11111111122-1-11111-1-1-1-1000000002i−2i−2i2i−i−iiiii−i−i00000000
χ32222222-1-2-2-2-2-1-1-122-2-2-2-2-2-2-1-11111111122-1-11111-1-1-1-100000000−2i2i2i−2iii−i−i−i−iii00000000
χ33222222-1-2-2-2-2-1-1-1-2-22222-2-2-1-11111-1-1-1-1-2211-1-11111-1-1000000000000−i3i3i3−i3−i3i3i3−i300000000
χ34222222-1-2-2-2-2-1-1-1-2-22222-2-2-1-11111-1-1-1-1-2211-1-11111-1-1000000000000i3−i3−i3i3i3−i3−i3i300000000
χ35222222-1-2-2-2-2-1-1-1-2-222-2-222-1-1111111112-211-1-1-1-1-1-1110000000000003−3−33−333−300000000
χ36222222-1-2-2-2-2-1-1-1-2-222-2-222-1-1111111112-211-1-1-1-1-1-111000000000000−333−33−3−3300000000
χ3722-2-2-22200002-2-22-2002i−2i2i−2i2-200002i2i−2i−2i002-2002i−2i000000002i2i−2i−2i000000000000002-20000
χ3822-2-2-22200002-2-22-2002i−2i2i−2i2-200002i2i−2i−2i002-2002i−2i00000000−2i−2i2i2i00000000000000-220000
χ3922-2-2-22200002-2-22-200−2i2i−2i2i2-20000−2i−2i2i2i002-200−2i2i000000002i2i−2i−2i00000000000000-220000
χ4022-2-2-22200002-2-22-200−2i2i−2i2i2-20000−2i−2i2i2i002-200−2i2i00000000−2i−2i2i2i000000000000002-20000
χ4122-2-2-22200002-2-2-22002i−2i−2i2i2-200002i2i−2i−2i00-2200−2i2i00002i2i−2i−2i00000000000000002-2000000
χ4222-2-2-22200002-2-2-22002i−2i−2i2i2-200002i2i−2i−2i00-2200−2i2i0000−2i−2i2i2i0000000000000000-22000000
χ4322-2-2-22200002-2-2-2200−2i2i2i−2i2-20000−2i−2i2i2i00-22002i−2i00002i2i−2i−2i0000000000000000-22000000
χ4422-2-2-22200002-2-2-2200−2i2i2i−2i2-20000−2i−2i2i2i00-22002i−2i0000−2i−2i2i2i00000000000000002-2000000
χ454444-4-4444-4-444400000000-4-444-4-400000000000000000000000000000000000000000000
χ464444-4-44-4-44444400000000-4-4-4-44400000000000000000000000000000000000000000000
χ474444-4-4-244-4-4-2-2-20000000022-2-222−2i32i3−2i32i300000000−2i32i3000000000000000000000000000000
χ484444-4-4-244-4-4-2-2-20000000022-2-2222i3−2i32i3−2i3000000002i3−2i3000000000000000000000000000000
χ494444-4-4-2-4-444-2-2-2000000002222-2-2−2i32i3−2i32i3000000002i3−2i3000000000000000000000000000000
χ504444-4-4-2-4-444-2-2-2000000002222-2-22i3−2i32i3−2i300000000−2i32i3000000000000000000000000000000
χ5144-4-44-4400004-4-4004-40000-440000000000004-40000000000000000000000000000000000
χ5244-4-44-4400004-4-400-440000-44000000000000-440000000000000000000000000000000000
χ5344-4-44-4-20000-222004-400002-2000023−23−23230000-22000023−230000000000000000000000000000
χ5444-4-44-4-20000-222004-400002-20000−232323−230000-220000−23230000000000000000000000000000
χ5544-4-44-4-20000-22200-4400002-2000023−23−232300002-20000−23230000000000000000000000000000
χ5644-4-44-4-20000-22200-4400002-20000−232323−2300002-2000023−230000000000000000000000000000
χ5744-4-4-44-20000-2224-4004i−4i4i−4i-220000−2i−2i2i2i00-2200−2i2i00000000000000000000000000000000
χ5844-4-4-44-20000-2224-400−4i4i−4i4i-2200002i2i−2i−2i00-22002i−2i00000000000000000000000000000000
χ5944-4-4-44-20000-222-44004i−4i−4i4i-220000−2i−2i2i2i002-2002i−2i00000000000000000000000000000000
χ6044-4-4-44-20000-222-4400−4i4i4i−4i-2200002i2i−2i−2i002-200−2i2i00000000000000000000000000000000
χ614-44-4004004i−4i-44-40000000000004i−4i00000000000000002-22-22i−2i2i−2i00000000000000000000
χ624-44-4004004i−4i-44-40000000000004i−4i0000000000000000-22-22−2i2i−2i2i00000000000000000000
χ634-44-400400−4i4i-44-4000000000000−4i4i00000000000000002-22-2−2i2i−2i2i00000000000000000000
χ644-44-400400−4i4i-44-4000000000000−4i4i0000000000000000-22-222i−2i2i−2i00000000000000000000
χ654-4-440044i−4i00-4-4400000000004i−4i0000000000000000002i−2i−2i2i2-2-2200000000000000000000
χ664-4-440044i−4i00-4-4400000000004i−4i000000000000000000−2i2i2i−2i-222-200000000000000000000
χ674-4-44004−4i4i00-4-440000000000−4i4i0000000000000000002i−2i−2i2i-222-200000000000000000000
χ684-4-44004−4i4i00-4-440000000000−4i4i000000000000000000−2i2i2i−2i2-2-2200000000000000000000
χ698-88-800-4008i−8i4-44000000000000−4i4i00000000000000000000000000000000000000000000
χ708-88-800-400−8i8i4-440000000000004i−4i00000000000000000000000000000000000000000000
χ718-8-8800-48i−8i0044-40000000000−4i4i0000000000000000000000000000000000000000000000
χ728-8-8800-4−8i8i0044-400000000004i−4i0000000000000000000000000000000000000000000000

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