Finite Group Databasebeta

← Group #10692984

Character table — Group #10692984

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order122222223444466622222444444666666121212126666121212121212444444444444444488882424242424242424224444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ611111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ711111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111
χ811111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1
χ9111111-1-11-1-1-1-1111-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−iii−i−iii−i−i11-1-11-1
χ10111111-1-11-1-1-1-1111-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii−i−iii−i−iii-1-111-11
χ11111111-1-11-1-1-1-1111-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−iii−i−iii−i−i-1-111-11
χ12111111-1-11-1-1-1-1111-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−i−iii−i−iii11-1-11-1
χ13111111-1-11-1-1-1-1111-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiiii−i−iiii−i−i−i−iii11-1-1-11
χ14111111-1-11-1-1-1-1111-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiii−iii−i−i−iiiii−i−i-1-1111-1
χ15111111-1-11-1-1-1-1111-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111−i−i−i−iiiiiiiii−i−i−i−ii−i−iiii−i−i−i−iii-1-1111-1
χ16111111-1-11-1-1-1-1111-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−i−iiiii−i−i11-1-1-11
χ17222222222-2-2-2-222222222-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2-2-20000000000000000000000000000000000
χ18222222222-2-2-2-22222-2-2-2-22222-2-2222222-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000
χ1922222222-12222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-1000000
χ2022222222-12222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-211111111000000
χ2122222222-12222-1-1-12-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-11111-1-11111000000000000000022-2-2-1-1-1-11111000000
χ2222222222-12222-1-1-12-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-11111-1-111110000000000000000-2-2221111-1-1-1-1000000
χ2322222222-1-2-2-2-2-1-1-122222-2-2-2-2-2-2-1-1-1-1-1-11111-1-1-1-1111111000000000000000000003−33−33−33−3000000
χ2422222222-1-2-2-2-2-1-1-122222-2-2-2-2-2-2-1-1-1-1-1-11111-1-1-1-111111100000000000000000000−33−33−33−33000000
χ2522222222-1-2-2-2-2-1-1-12-2-2-2-22222-2-2-1-1-1-1-1-11111111111-1-1-1-1000000000000000000003−33−3−33−33000000
χ2622222222-1-2-2-2-2-1-1-12-2-2-2-22222-2-2-1-1-1-1-1-11111111111-1-1-1-100000000000000000000−33−333−33−3000000
χ27222222-2-222222222-222-2-2-2-222-2-222-2-2-2-2222222-2-2-2-2-2-2220000000000000000000000000000000000
χ28222222-2-222222222-2-2-22222-2-2-2-222-2-2-2-22222-2-222-2-222-2-20000000000000000000000000000000000
χ29222222-2-2-12222-1-1-1-222-2-2-2-222-2-2-1-11111-1-1-1-1-1-1111111-1-100000000000000000000−i3i3i3−i3−i3i3i3−i3000000
χ30222222-2-2-12222-1-1-1-222-2-2-2-222-2-2-1-11111-1-1-1-1-1-1111111-1-100000000000000000000i3−i3−i3i3i3−i3−i3i3000000
χ31222222-2-2-12222-1-1-1-2-2-22222-2-2-2-2-1-11111-1-1-1-111-1-111-1-11100000000000000000000−i3i3i3−i3i3−i3−i3i3000000
χ32222222-2-2-12222-1-1-1-2-2-22222-2-2-2-2-1-11111-1-1-1-111-1-111-1-11100000000000000000000i3−i3−i3i3−i3i3i3−i3000000
χ33222222-2-2-1-2-2-2-2-1-1-1-222-2-222-2-222-1-111111111-1-111-1-1-1-11100000000000000002i−2i2i−2i−i−iii−i−iii000000
χ34222222-2-2-1-2-2-2-2-1-1-1-222-2-222-2-222-1-111111111-1-111-1-1-1-1110000000000000000−2i2i−2i2iii−i−iii−i−i000000
χ35222222-2-2-1-2-2-2-2-1-1-1-2-2-222-2-22222-1-11111111111-1-1-1-111-1-100000000000000002i−2i−2i2i−i−iiiii−i−i000000
χ36222222-2-2-1-2-2-2-2-1-1-1-2-2-222-2-22222-1-11111111111-1-1-1-111-1-10000000000000000−2i2i2i−2iii−i−i−i−iii000000
χ372222-2-222222-2-2222-2000000002-2-2-222-2-222-2-200002-200000000000022-2-222-2-2000000000000000000
χ382222-2-222222-2-2222-2000000002-2-2-222-2-222-2-200002-2000000000000-2-222-2-222000000000000000000
χ392222-2-2222-2-222222-200000000-22-2-222-2-2-2-2220000-22000022-2-222-2-200000000000000000000000000
χ402222-2-2222-2-222222-200000000-22-2-222-2-2-2-2220000-220000-2-222-2-22200000000000000000000000000
χ412222-2-2-2-2222-2-2222200000000-22-2-2-2-22222-2-20000-2200002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ422222-2-2-2-2222-2-2222200000000-22-2-2-2-22222-2-20000-220000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ432222-2-2-2-22-2-2222222000000002-2-2-2-2-222-2-22200002-20000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ442222-2-2-2-22-2-2222222000000002-2-2-2-2-222-2-22200002-2000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ4522-2-22-20022i−2i2i−2i2-2-20002-22i−2i00002-200002i−2i2i−2i002-2002i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ4622-2-22-20022i−2i2i−2i2-2-20002-22i−2i00002-200002i−2i2i−2i002-2002i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ4722-2-22-20022i−2i2i−2i2-2-2000-22−2i2i00002-200002i−2i2i−2i00-2200−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ4822-2-22-20022i−2i2i−2i2-2-2000-22−2i2i00002-200002i−2i2i−2i00-2200−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ4922-2-22-2002−2i2i−2i2i2-2-20002-2−2i2i00002-20000−2i2i−2i2i002-200−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ5022-2-22-2002−2i2i−2i2i2-2-20002-2−2i2i00002-20000−2i2i−2i2i002-200−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ5122-2-22-2002−2i2i−2i2i2-2-2000-222i−2i00002-20000−2i2i−2i2i00-22002i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ5222-2-22-2002−2i2i−2i2i2-2-2000-222i−2i00002-20000−2i2i−2i2i00-22002i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ5322-2-2-220022i−2i−2i2i2-2-202-200002i−2i00-2200002i−2i−2i2i2-20000002i−2i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000000000
χ5422-2-2-220022i−2i−2i2i2-2-202-200002i−2i00-2200002i−2i−2i2i2-20000002i−2i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000000000
χ5522-2-2-220022i−2i−2i2i2-2-20-220000−2i2i00-2200002i−2i−2i2i-22000000−2i2i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000000000
χ5622-2-2-220022i−2i−2i2i2-2-20-220000−2i2i00-2200002i−2i−2i2i-22000000−2i2i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000000000
χ5722-2-2-22002−2i2i2i−2i2-2-202-20000−2i2i00-220000−2i2i2i−2i2-2000000−2i2i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000000000
χ5822-2-2-22002−2i2i2i−2i2-2-202-20000−2i2i00-220000−2i2i2i−2i2-2000000−2i2i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000000000
χ5922-2-2-22002−2i2i2i−2i2-2-20-2200002i−2i00-220000−2i2i2i−2i-220000002i−2i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000000000
χ6022-2-2-22002−2i2i2i−2i2-2-20-2200002i−2i00-220000−2i2i2i−2i-220000002i−2i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000000000
χ614444-4-444-244-4-4-2-2-2-4000000004-422-2-222-2-2220000-2200000000000000000000000000000000000000
χ624444-4-444-2-4-444-2-2-2-400000000-4422-2-22222-2-200002-200000000000000000000000000000000000000
χ634444-4-4-4-4-244-4-4-2-2-2400000000-442222-2-2-2-22200002-200000000000000000000000000000000000000
χ644444-4-4-4-4-2-4-444-2-2-24000000004-42222-2-222-2-20000-2200000000000000000000000000000000000000
χ6544-4-44-400-24i−4i4i−4i-2220004-44i−4i0000-220000−2i2i−2i2i00-2200−2i2i000000000000000000000000000000000000
χ6644-4-44-400-24i−4i4i−4i-222000-44−4i4i0000-220000−2i2i−2i2i002-2002i−2i000000000000000000000000000000000000
χ6744-4-44-400-2−4i4i−4i4i-2220004-4−4i4i0000-2200002i−2i2i−2i00-22002i−2i000000000000000000000000000000000000
χ6844-4-44-400-2−4i4i−4i4i-222000-444i−4i0000-2200002i−2i2i−2i002-200−2i2i000000000000000000000000000000000000
χ6944-4-4-4400-24i−4i−4i4i-22204-400004i−4i002-20000−2i2i2i−2i-22000000−2i2i0000000000000000000000000000000000
χ7044-4-4-4400-24i−4i−4i4i-2220-440000−4i4i002-20000−2i2i2i−2i2-20000002i−2i0000000000000000000000000000000000
χ7144-4-4-4400-2−4i4i4i−4i-22204-40000−4i4i002-200002i−2i−2i2i-220000002i−2i0000000000000000000000000000000000
χ7244-4-4-4400-2−4i4i4i−4i-2220-4400004i−4i002-200002i−2i−2i2i2-2000000−2i2i0000000000000000000000000000000000
χ734-4-44004-440000-44-400000000000004-4000000000000000000000000000000000000000000002-22-200
χ744-4-44004-440000-44-400000000000004-400000000000000000000000000000000000000000000-22-2200
χ754-4-4400-4440000-44-40000000000000-44000000000000000000000000000000000000000000002-2-2200
χ764-4-4400-4440000-44-40000000000000-4400000000000000000000000000000000000000000000-222-200
χ778-88-8000080000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ788-88-80000-4000044-4000000000000000−4i34i3000000000000000000000000000000000000000000000000
χ798-88-80000-4000044-40000000000000004i3−4i3000000000000000000000000000000000000000000000000
χ808-8-88008-8-400004-440000000000000-4400000000000000000000000000000000000000000000000000
χ818-8-8800-88-400004-4400000000000004-400000000000000000000000000000000000000000000000000

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