Finite Group Databasebeta

← Group #10713864

Character table — Group #10713864

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222244444444444444444448888888888881616161616161616161616162424242424242424242424244848
order12222234466622224444466666612121212446612121212121212124444121212121212121244444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111-1-1-1-1111-1-111-1-1-1-111111-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i1111iiii−i−i−i−i-1-1
χ6111111111111-1-1-1-1111-1-111-1-1-1-111111-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-1−i−i−i−iiiii11
χ7111111111111-1-1-1-1111-1-111-1-1-1-111111-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii1111−i−i−i−iiiii-1-1
χ8111111111111-1-1-1-1111-1-111-1-1-1-111111-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-1iiii−i−i−i−i11
χ91111111-1-1111111111-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11-11-111-1-111-1-111-1-111-1-111-1-11-1
χ101111111-1-1111111111-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11-11-111-1-111-1-1-1-111-1-111-1-111-11
χ111111111-1-1111111111-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-11-11-1-111-1-11111-1-1-1-111-1-1111-1
χ121111111-1-1111111111-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-11-11-1-111-1-111-1-11111-1-111-1-1-11
χ131111111-1-1111-1-1-1-111-11111-1-1-1-1-1-1-1-1-11-1-111-1-11111i−i−iiii−i−i−i−iii11-1-1ii−i−i−i−iii-11
χ141111111-1-1111-1-1-1-111-11111-1-1-1-1-1-1-1-1-11-1-111-1-11111i−i−iiii−i−i−i−iii-1-111−i−iiiii−i−i1-1
χ151111111-1-1111-1-1-1-111-11111-1-1-1-1-1-1-1-1-11-1-111-1-11111−iii−i−i−iiiii−i−i11-1-1−i−iiiii−i−i-11
χ161111111-1-1111-1-1-1-111-11111-1-1-1-1-1-1-1-1-11-1-111-1-11111−iii−i−i−iiiii−i−i-1-111ii−i−i−i−iii1-1
χ1722222222222222-2-2-2-22-2-22222222222-22-2-2-2-2-2-222-2-200000000000000000000000000
χ18222222222222-2-222-2-222222-2-2-2-22222-2-222-2-2-2-2-2-22200000000000000000000000000
χ192222222-2-222222-2-2-2-2-222222222-2-2-2-22-2-2-2-2-222-2-22200000000000000000000000000
χ202222222-2-2222-2-222-2-2-2-2-222-2-2-2-2-2-2-2-22222-2-22222-2-200000000000000000000000000
χ21222222-122-1-1-1222222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ22222222-122-1-1-1222222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ23222222-122-1-1-122-2-2-2-22-2-2-1-1-1-1-1-1-1-1-1-1-22111111-1-1110000−i3i3−i3i3−i3i3−i3i300000000000000
χ24222222-122-1-1-122-2-2-2-22-2-2-1-1-1-1-1-1-1-1-1-1-22111111-1-1110000i3−i3i3−i3i3−i3i3−i300000000000000
χ25222222-122-1-1-1-2-222-2-2222-1-11111-1-1-1-1-2-2-1-1111111-1-100003−33−3−33−3300000000000000
χ26222222-122-1-1-1-2-222-2-2222-1-11111-1-1-1-1-2-2-1-1111111-1-10000−33−333−33−300000000000000
χ27222222-122-1-1-1-2-2-2-2222-2-2-1-11111-1-1-1-12-211-1-1-1-111112i2i−2i−2i−i−i−i−iiiii00000000000000
χ28222222-122-1-1-1-2-2-2-2222-2-2-1-11111-1-1-1-12-211-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i00000000000000
χ29222222-1-2-2-1-1-1222222-2-2-2-1-1-1-1-1-11111-2-2-1-1-1-11111112-22-2-1-111-1-11100000000000000
χ30222222-1-2-2-1-1-1222222-2-2-2-1-1-1-1-1-11111-2-2-1-1-1-1111111-22-2211-1-111-1-100000000000000
χ31222222-1-2-2-1-1-122-2-2-2-2-222-1-1-1-1-1-111112-21111-1-111-1-10000−i3i3i3−i3−i3i3i3−i300000000000000
χ32222222-1-2-2-1-1-122-2-2-2-2-222-1-1-1-1-1-111112-21111-1-111-1-10000i3−i3−i3i3i3−i3−i3i300000000000000
χ33222222-1-2-2-1-1-1-2-222-2-2-2-2-2-1-11111111122-1-111-1-1-1-11100003−3−33−333−300000000000000
χ34222222-1-2-2-1-1-1-2-222-2-2-2-2-2-1-11111111122-1-111-1-1-1-1110000−333−33−3−3300000000000000
χ35222222-1-2-2-1-1-1-2-2-2-222-222-1-111111111-2211-1-111-1-1-1-12i−2i−2i2i−i−iiiii−i−i00000000000000
χ36222222-1-2-2-1-1-1-2-2-2-222-222-1-111111111-2211-1-111-1-1-1-1−2i2i2i−2iii−i−i−i−iii00000000000000
χ3722-2-22-22002-2-22-22-22-20002-222-2-20000002-22-20000000000000000000000002-2002-200
χ3822-2-22-22002-2-22-22-22-20002-222-2-20000002-22-2000000000000000000000000-2200-2200
χ3922-2-22-22002-2-22-2-22-220002-222-2-2000000-22-2200000000000000000000002-2002-20000
χ4022-2-22-22002-2-22-2-22-220002-222-2-2000000-22-220000000000000000000000-2200-220000
χ4122-2-22-22002-2-2-222-2-220002-2-2-2220000002-2-2200000000000000000000002i−2i00−2i2i0000
χ4222-2-22-22002-2-2-222-2-220002-2-2-2220000002-2-220000000000000000000000−2i2i002i−2i0000
χ4322-2-22-22002-2-2-22-222-20002-2-2-222000000-222-20000000000000000000000002i−2i00−2i2i00
χ4422-2-22-22002-2-2-22-222-20002-2-2-222000000-222-2000000000000000000000000−2i2i002i−2i00
χ454444-4-4444444000000-400-4-4000044-4-400000000000000000000000000000000000000
χ464444-4-44-4-4444000000400-4-40000-4-44400000000000000000000000000000000000000
χ474444-4-4-244-2-2-2000000-40022−2i32i3−2i32i3-2-22200000000−2i32i30000000000000000000000000000
χ484444-4-4-244-2-2-2000000-400222i3−2i32i3−2i3-2-222000000002i3−2i30000000000000000000000000000
χ494444-4-4-2-4-4-2-2-200000040022−2i32i3−2i32i322-2-2000000002i3−2i30000000000000000000000000000
χ504444-4-4-2-4-4-2-2-2000000400222i3−2i32i3−2i322-2-200000000−2i32i30000000000000000000000000000
χ5144-4-44-4-200-2224-44-44-4000-22-2-222000000-22-2200000000000000000000000000000000
χ5244-4-44-4-200-2224-4-44-44000-22-2-2220000002-22-200000000000000000000000000000000
χ5344-4-44-4-200-222-444-4-44000-2222-2-2000000-222-200000000000000000000000000000000
χ5444-4-44-4-200-222-44-444-4000-2222-2-20000002-2-2200000000000000000000000000000000
χ5544-4-4-444004-4-400000004i−4i-440000000000000000004i−4i00000000000000000000000000
χ5644-4-4-444004-4-40000000−4i4i-44000000000000000000−4i4i00000000000000000000000000
χ5744-4-4-44-200-22200000004i−4i2-2−2i32i32i3−2i3000000000023−2300−2i2i00000000000000000000000000
χ5844-4-4-44-200-22200000004i−4i2-22i3−2i3−2i32i30000000000−232300−2i2i00000000000000000000000000
χ5944-4-4-44-200-2220000000−4i4i2-2−2i32i32i3−2i30000000000−2323002i−2i00000000000000000000000000
χ6044-4-4-44-200-2220000000−4i4i2-22i3−2i3−2i32i3000000000023−23002i−2i00000000000000000000000000
χ614-44-40044i−4i-44-40000000000000004i−4i000000000000000000000000002-22i−2i0000000000
χ624-44-40044i−4i-44-40000000000000004i−4i00000000000000000000000000-22−2i2i0000000000
χ634-44-4004−4i4i-44-4000000000000000−4i4i000000000000000000000000002-2−2i2i0000000000
χ644-44-4004−4i4i-44-4000000000000000−4i4i00000000000000000000000000-222i−2i0000000000
χ658-88-800-48i−8i4-44000000000000000−4i4i0000000000000000000000000000000000000000
χ668-88-800-4−8i8i4-440000000000000004i−4i0000000000000000000000000000000000000000
χ678-8-8800800-8-88000000000000000000000000000000000000000000000000000000000
χ688-8-8800-40044-400000000000000000−4i34i300000000000000000000000000000000000000
χ698-8-8800-40044-4000000000000000004i3−4i300000000000000000000000000000000000000

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