Finite Group Databasebeta

← Group #10693029

Character table — Group #10693029

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order12222234444446664444444444466121212121212121212121212121212121212888888888888888888882424242424242424444444
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
χ51111111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ61111111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ71111111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111
χ81111111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1
χ91111111-1-1-1-1-1-111111-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−iii−i−iii−i−i11-1-11-1
χ101111111-1-1-1-1-1-111111-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii−i−iii−i−iii-1-111-11
χ111111111-1-1-1-1-1-111111-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−iii−i−iii−i−i-1-111-11
χ121111111-1-1-1-1-1-111111-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−i−iii−i−iii11-1-11-1
χ131111111-1-1-1-1-1-1111-1-111-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiii−i−iiii−i−i−i−iii11-1-1-11
χ141111111-1-1-1-1-1-1111-1-111-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−iii−i−i−iiiii−i−i-1-1111-1
χ151111111-1-1-1-1-1-1111-1-111-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−ii−i−iiii−i−i−i−iii-1-1111-1
χ161111111-1-1-1-1-1-1111-1-111-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−i−iiiii−i−i11-1-1-11
χ1722222222222-2-22222222-2-2-2-2-2-2-222-2-2-2-22222-2-222-2-222-2-20000000000000000000000000000000000
χ1822222222222-2-2222-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-222-2-2220000000000000000000000000000000000
χ192222222-2-2-2-22222222-2-22-2-2-2-222222222-2-2-2-2-2-222-2-2-2-2220000000000000000000000000000000000
χ202222222-2-2-2-222222-2-2222-2-222-2-2222222-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000
χ21222222-1222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-1000000
χ22222222-1222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-211111111000000
χ23222222-1222222-1-1-1-2-2-2-2222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-11111000000
χ24222222-1222222-1-1-1-2-2-2-2222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-1000000
χ25222222-12222-2-2-1-1-12222-2-2-2-2-2-2-2-1-11111-1-1-1-111-1-111-1-11100000000000000000000−i3i3−i3i3−i3i3−i3i3000000
χ26222222-12222-2-2-1-1-12222-2-2-2-2-2-2-2-1-11111-1-1-1-111-1-111-1-11100000000000000000000i3−i3i3−i3i3−i3i3−i3000000
χ27222222-12222-2-2-1-1-1-2-2-2-2-2-2-22222-1-11111-1-1-1-11111-1-111-1-100000000000000000000−i3i3−i3i3i3−i3i3−i3000000
χ28222222-12222-2-2-1-1-1-2-2-2-2-2-2-22222-1-11111-1-1-1-11111-1-111-1-100000000000000000000i3−i3i3−i3−i3i3−i3i3000000
χ29222222-1-2-2-2-222-1-1-122-2-22-2-2-2-222-1-1-1-1-1-1111111-1-11111-1-1000000000000000000003−3−333−3−33000000
χ30222222-1-2-2-2-222-1-1-122-2-22-2-2-2-222-1-1-1-1-1-1111111-1-11111-1-100000000000000000000−333−3−333−3000000
χ31222222-1-2-2-2-222-1-1-1-2-2222-2-222-2-2-1-1-1-1-1-111111111-1-1-1-111000000000000000000003−3−33−333−3000000
χ32222222-1-2-2-2-222-1-1-1-2-2222-2-222-2-2-1-1-1-1-1-111111111-1-1-1-11100000000000000000000−333−33−3−33000000
χ33222222-1-2-2-2-2-2-2-1-1-122-2-2-22222-2-2-1-111111111-1-1-1-1-1-1111100000000000000002i−2i2i−2i−i−iii−i−iii000000
χ34222222-1-2-2-2-2-2-2-1-1-122-2-2-22222-2-2-1-111111111-1-1-1-1-1-111110000000000000000−2i2i−2i2iii−i−iii−i−i000000
χ35222222-1-2-2-2-2-2-2-1-1-1-2-222-222-2-222-1-111111111-1-11111-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i000000
χ36222222-1-2-2-2-2-2-2-1-1-1-2-222-222-2-222-1-111111111-1-11111-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii000000
χ372222-2-222-22-2222220000-22-20000-2-222-2-22-22-22-2000000000000000022-2-222-2-2000000000000000000
χ382222-2-222-22-2222220000-22-20000-2-222-2-22-22-22-20000000000000000-2-222-2-222000000000000000000
χ392222-2-222-22-2-2-222200002-220000-2-2-2-2222-22-2-22000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ402222-2-222-22-2-2-222200002-220000-2-2-2-2222-22-2-2200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ412222-2-22-22-22222220000-2-220000-2-222-2-2-22-22-220000000022-2-2-2-22200000000000000000000000000
χ422222-2-22-22-22222220000-2-220000-2-222-2-2-22-22-2200000000-2-22222-2-200000000000000000000000000
χ432222-2-22-22-22-2-2222000022-20000-2-2-2-222-22-222-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ442222-2-22-22-22-2-2222000022-20000-2-2-2-222-22-222-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ4522-2-22-2222-2-200-22-22-22-200000002-2000022-2-2002-2002-2002−22−22−22−22−22−22−22−2000000000000000000
χ4622-2-22-2222-2-200-22-22-22-200000002-2000022-2-2002-2002-200−22−22−22−22−22−22−22−22000000000000000000
χ4722-2-22-2222-2-200-22-2-22-2200000002-2000022-2-200-2200-22002−22−22−22−2−22−22−22−22000000000000000000
χ4822-2-22-2222-2-200-22-2-22-2200000002-2000022-2-200-2200-2200−22−22−22−222−22−22−22−2000000000000000000
χ4922-2-22-22-2-22200-22-22-2-2200000002-20000-2-222002-200-2200−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ5022-2-22-22-2-22200-22-22-2-2200000002-20000-2-222002-200-2200i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ5122-2-22-22-2-22200-22-2-222-200000002-20000-2-22200-22002-200−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ5222-2-22-22-2-22200-22-2-222-200000002-20000-2-22200-22002-200i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ5322-2-2-2222-2-2200-22-200000002i−2i2i−2i-2200002-2-2200002i−2i002i−2i−i2i2i2−i2−i2i2i2−i22−2−222−2−22000000000000000000
χ5422-2-2-2222-2-2200-22-200000002i−2i2i−2i-2200002-2-2200002i−2i002i−2ii2−i2−i2i2i2−i2−i2i2−222−2−222−2000000000000000000
χ5522-2-2-2222-2-2200-22-20000000−2i2i−2i2i-2200002-2-220000−2i2i00−2i2i−i2i2i2−i2−i2i2i2−i2−222−2−222−2000000000000000000
χ5622-2-2-2222-2-2200-22-20000000−2i2i−2i2i-2200002-2-220000−2i2i00−2i2ii2−i2−i2i2i2−i2−i2i22−2−222−2−22000000000000000000
χ5722-2-2-222-222-200-22-200000002i−2i−2i2i-220000-222-200002i−2i00−2i2i2−2−22−222−2i2−i2−i2i2−i2i2i2−i2000000000000000000
χ5822-2-2-222-222-200-22-200000002i−2i−2i2i-220000-222-200002i−2i00−2i2i−222−22−2−22−i2i2i2−i2i2−i2−i2i2000000000000000000
χ5922-2-2-222-222-200-22-20000000−2i2i2i−2i-220000-222-20000−2i2i002i−2i2−2−22−222−2−i2i2i2−i2i2−i2−i2i2000000000000000000
χ6022-2-2-222-222-200-22-20000000−2i2i2i−2i-220000-222-20000−2i2i002i−2i−222−22−2−22i2−i2−i2i2−i2i2i2−i2000000000000000000
χ614444-4-4-24-44-444-2-2-20000-44-4000022-2-222-22-22-22000000000000000000000000000000000000000000
χ624444-4-4-24-44-4-4-4-2-2-200004-4400002222-2-2-22-222-2000000000000000000000000000000000000000000
χ634444-4-4-2-44-4444-2-2-20000-4-44000022-2-2222-22-22-2000000000000000000000000000000000000000000
χ644444-4-4-2-44-44-4-4-2-2-2000044-400002222-2-22-22-2-22000000000000000000000000000000000000000000
χ6544-4-44-4-244-4-4002-224-44-40000000-220000-2-22200-2200-22000000000000000000000000000000000000
χ6644-4-44-4-244-4-4002-22-44-440000000-220000-2-222002-2002-2000000000000000000000000000000000000
χ6744-4-44-4-2-4-444002-224-4-440000000-22000022-2-200-22002-2000000000000000000000000000000000000
χ6844-4-44-4-2-4-444002-22-444-40000000-22000022-2-2002-200-22000000000000000000000000000000000000
χ6944-4-4-44-24-4-44002-2200000004i−4i4i−4i2-20000-222-20000−2i2i00−2i2i0000000000000000000000000000000000
χ7044-4-4-44-24-4-44002-220000000−4i4i−4i4i2-20000-222-200002i−2i002i−2i0000000000000000000000000000000000
χ7144-4-4-44-2-444-4002-2200000004i−4i−4i4i2-200002-2-220000−2i2i002i−2i0000000000000000000000000000000000
χ7244-4-4-44-2-444-4002-220000000−4i4i4i−4i2-200002-2-2200002i−2i00−2i2i0000000000000000000000000000000000
χ734-4-4400400004i−4i-4-4400000000000004i−4i000000000000000000000000000000000000000000002i−2i2-200
χ744-4-4400400004i−4i-4-4400000000000004i−4i00000000000000000000000000000000000000000000−2i2i-2200
χ754-4-440040000−4i4i-4-440000000000000−4i4i000000000000000000000000000000000000000000002i−2i-2200
χ764-4-440040000−4i4i-4-440000000000000−4i4i00000000000000000000000000000000000000000000−2i2i2-200
χ778-88-80080000008-8-800000000000000000000000000000000000000000000000000000000000000000
χ788-88-800-4000000-444000000000000000−4i34i3000000000000000000000000000000000000000000000000
χ798-88-800-4000000-4440000000000000004i3−4i3000000000000000000000000000000000000000000000000
χ808-8-8800-400008i−8i44-40000000000000−4i4i00000000000000000000000000000000000000000000000000
χ818-8-8800-40000−8i8i44-400000000000004i−4i00000000000000000000000000000000000000000000000000

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