Finite Group Databasebeta

← Group #10694775

Character table — Group #10694775

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222222222224444444444444444444466666666888888888812121212121212121212121216161616161616161616161648484848
order12222234444444466644668888888812121212121212128888888812122424242424242424888888888888448812121212242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91111111-1-1-1-1-111-11111-111iiii−i−i−i−i-1-1-111-1-1-11111-1-1-1-1-11iiii−i−i−i−i11-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1-1i−i
χ101111111-1-1-1-1-111-11111-111iiii−i−i−i−i-1-1-111-1-1-11111-1-1-1-1-11iiii−i−i−i−i11-1-1iiii−i−i−i−i-11−ii-1-111−i−iii-11−ii
χ111111111-1-1-1-1-111-11111-111iiii−i−i−i−i-1-1-111-1-1-1-1-1-1-11111-11iiii−i−i−i−i-1-111−i−i−i−iiiii1-1i−i11-1-1ii−i−i-11−ii
χ121111111-1-1-1-1-111-11111-111iiii−i−i−i−i-1-1-111-1-1-1-1-1-1-11111-11iiii−i−i−i−i-1-111−i−i−i−iiiii-11−ii-1-111−i−iii1-1i−i
χ131111111-1-1-1-1-111-11111-111−i−i−i−iiiii-1-1-111-1-1-11111-1-1-1-1-11−i−i−i−iiiii11-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1-1−ii
χ141111111-1-1-1-1-111-11111-111−i−i−i−iiiii-1-1-111-1-1-11111-1-1-1-1-11−i−i−i−iiiii11-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-11i−i
χ151111111-1-1-1-1-111-11111-111−i−i−i−iiiii-1-1-111-1-1-1-1-1-1-11111-11−i−i−i−iiiii-1-111iiii−i−i−i−i1-1−ii11-1-1−i−iii-11i−i
χ161111111-1-1-1-1-111-11111-111−i−i−i−iiiii-1-1-111-1-1-1-1-1-1-11111-11−i−i−i−iiiii-1-111iiii−i−i−i−i-11i−i-1-111ii−i−i1-1−ii
χ1722222222-2-222-2-22222-2-22200000000222-2-2-2-2200000000-2-200000000000022-2-222-2-20000000000000000
χ1822222222-2-222-2-22222-2-22200000000222-2-2-2-2200000000-2-2000000000000-2-222-2-2220000000000000000
χ192222222-222-2-2-2-2-2222-222200000000-2-2-2-2-222-2000000002-20000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ202222222-222-2-2-2-2-2222-222200000000-2-2-2-2-222-2000000002-2000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ21222222-122222222-1-1-122-1-122222222-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-10000000000002222-1-1-1-1-1-1-1-10000
χ22222222-122222222-1-1-122-1-122222222-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-2111111110000
χ23222222-122222222-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100000000-1-11111111100000000000022-2-2-1-1-1-111110000
χ24222222-122222222-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100000000-1-111111111000000000000-2-2221111-1-1-1-10000
χ25222222-1-2-2-2-2-222-2-1-1-12-2-1-12i2i2i2i−2i−2i−2i−2i111-1-1111000000001-1−i−i−i−iiiii0000000000002-22i−2i-1-111−i−iii0000
χ26222222-1-2-2-2-2-222-2-1-1-12-2-1-12i2i2i2i−2i−2i−2i−2i111-1-1111000000001-1−i−i−i−iiiii000000000000-22−2i2i11-1-1ii−i−i0000
χ27222222-1-2-2-2-2-222-2-1-1-12-2-1-1−2i−2i−2i−2i2i2i2i2i111-1-1111000000001-1iiii−i−i−i−i0000000000002-2−2i2i-1-111ii−i−i0000
χ28222222-1-2-2-2-2-222-2-1-1-12-2-1-1−2i−2i−2i−2i2i2i2i2i111-1-1111000000001-1iiii−i−i−i−i000000000000-222i−2i11-1-1−i−iii0000
χ292222-2-22222-2-2-2-222222-2-2-222-2-222-2-22-2-2-2-222200000000-2222-2-222-2-20000000000000000000000000000
χ302222-2-22222-2-2-2-222222-2-2-2-2-222-2-2222-2-2-2-222200000000-22-2-222-2-2220000000000000000000000000000
χ312222-2-222-2-2-2-2222222-22-2-2000000002-2-222-2-222222-2-2-2-22-200000000-2-222000000000000000000000000
χ322222-2-222-2-2-2-2222222-22-2-2000000002-2-222-2-22-2-2-2-222222-20000000022-2-2000000000000000000000000
χ332222-2-22-2222222-2222-2-2-2-200000000-2222222-222222222-2-200000000-2-2-2-2000000000000000000000000
χ342222-2-22-2222222-2222-2-2-2-200000000-2222222-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000
χ352222-2-22-2-2-222-2-2-222222-2-22i2i−2i−2i−2i−2i2i2i-222-2-2-2-2-200000000222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ362222-2-22-2-2-222-2-2-222222-2-2−2i−2i2i2i2i2i−2i−2i-222-2-2-2-2-20000000022−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ372222-2-2-1222-2-2-2-22-1-1-12-21122-2-222-2-2-11111-1-1-1000000001-1-1-111-1-1110000000000000000−i3i3−i3i3−i3i3−i3i30000
χ382222-2-2-1222-2-2-2-22-1-1-12-21122-2-222-2-2-11111-1-1-1000000001-1-1-111-1-1110000000000000000i3−i3i3−i3i3−i3i3−i30000
χ392222-2-2-1222-2-2-2-22-1-1-12-211-2-222-2-222-11111-1-1-1000000001-111-1-111-1-10000000000000000−i3i3−i3i3i3−i3i3−i30000
χ402222-2-2-1222-2-2-2-22-1-1-12-211-2-222-2-222-11111-1-1-1000000001-111-1-111-1-10000000000000000i3−i3i3−i3−i3i3−i3i30000
χ412222-2-2-1-2-2-222-2-2-2-1-1-122112i2i−2i−2i−2i−2i2i2i1-1-11111100000000-1-1−i−iiiii−i−i0000000000000000−i3i3i3−i33−3−330000
χ422222-2-2-1-2-2-222-2-2-2-1-1-122112i2i−2i−2i−2i−2i2i2i1-1-11111100000000-1-1−i−iiiii−i−i0000000000000000i3−i3−i3i3−333−30000
χ432222-2-2-1-2-2-222-2-2-2-1-1-12211−2i−2i2i2i2i2i−2i−2i1-1-11111100000000-1-1ii−i−i−i−iii0000000000000000−i3i3i3−i3−333−30000
χ442222-2-2-1-2-2-222-2-2-2-1-1-12211−2i−2i2i2i2i2i−2i−2i1-1-11111100000000-1-1ii−i−i−i−iii0000000000000000i3−i3−i3i33−3−330000
χ4522-2-22-222002-200-22-2-2002-22−22−22−22−222-20000-222−2−222−2−2002−22−22−22−22−22−2002-2002-20000000000000000
χ4622-2-22-222002-200-22-2-2002-22−22−22−22−222-20000-2−2−222−2−222002−22−22−22−2−22−2200-2200-220000000000000000
χ4722-2-22-222002-200-22-2-2002-2−22−22−22−2222-20000-222−2−222−2−200−22−22−22−222−22−200-2200-220000000000000000
χ4822-2-22-222002-200-22-2-2002-2−22−22−22−2222-20000-2−2−222−2−22200−22−22−22−22−22−22002-2002-20000000000000000
χ4922-2-22-22-200-220022-2-2002-2−i2i2−i2i2i2−i2i2−i2-2-220000222−2−2−2−22200−i2i2−i2i2i2−i2i2−i22−2−2200−2i2i002i−2i0000000000000000
χ5022-2-22-22-200-220022-2-2002-2−i2i2−i2i2i2−i2i2−i2-2-2200002−2−22222−2−200−i2i2−i2i2i2−i2i2−i2−222−2002i−2i00−2i2i0000000000000000
χ5122-2-22-22-200-220022-2-2002-2i2−i2i2−i2−i2i2−i2i2-2-220000222−2−2−2−22200i2−i2i2−i2−i2i2−i2i22−2−22002i−2i00−2i2i0000000000000000
χ5222-2-22-22-200-220022-2-2002-2i2−i2i2−i2−i2i2−i2i2-2-2200002−2−22222−2−200i2−i2i2−i2−i2i2−i2i2−222−200−2i2i002i−2i0000000000000000
χ5322-2-2-222200-2200-22-2-200-222−2−222−2−222-220000-222−2−2−2−222002−2−222−2−22−222−22-2002-2000000000000000000
χ5422-2-2-222200-2200-22-2-200-222−2−222−2−222-220000-2−2−22222−2−2002−2−222−2−222−2−22-2200-22000000000000000000
χ5522-2-2-222200-2200-22-2-200-22−222−2−222−22-220000-222−2−2−2−22200−222−2−222−2−222−2-2200-22000000000000000000
χ5622-2-2-222200-2200-22-2-200-22−222−2−222−22-220000-2−2−22222−2−200−222−2−222−22−2−222-2002-2000000000000000000
χ5722-2-2-222-2002-20022-2-200-22−i2i2i2−i2i2−i2−i2i2-22-20000222−2−222−2−200−i2i2i2−i2i2−i2−i2i2−22−22−2i2i002i−2i000000000000000000
χ5822-2-2-222-2002-20022-2-200-22−i2i2i2−i2i2−i2−i2i2-22-200002−2−222−2−22200−i2i2i2−i2i2−i2−i2i22−22−22i−2i00−2i2i000000000000000000
χ5922-2-2-222-2002-20022-2-200-22i2−i2−i2i2−i2i2i2−i2-22-20000222−2−222−2−200i2−i2−i2i2−i2i2i2−i2−22−222i−2i00−2i2i000000000000000000
χ6022-2-2-222-2002-20022-2-200-22i2−i2−i2i2−i2i2i2−i2-22-200002−2−222−2−22200i2−i2−i2i2−i2i2i2−i22−22−2−2i2i002i−2i000000000000000000
χ61444444-24-4-444-4-44-2-2-2-4-4-2-200000000-2-2-22222-20000000022000000000000000000000000000000000000
χ62444444-2-444-4-4-4-4-4-2-2-2-44-2-20000000022222-2-2200000000-22000000000000000000000000000000000000
χ634444-4-4-24-4-4-4-4444-2-2-2-442200000000-222-2-222-200000000-22000000000000000000000000000000000000
χ644444-4-4-2-4444444-4-2-2-2-4-422000000002-2-2-2-2-2-220000000022000000000000000000000000000000000000
χ6544-4-44-4-24004-400-4-22200-2222−2222−2222−2222−22-2-22000020000000000−22−22−22−220000000000000000000000000000
χ6644-4-44-4-24004-400-4-22200-22−2222−2222−2222−2222-2-220000200000000002−22−22−22−20000000000000000000000000000
χ6744-4-44-4-2-400-44004-22200-22−2i22i2−2i22i22i2−2i22i2−2i222-20000-20000000000i2−i2i2−i2−i2i2−i2i20000000000000000000000000000
χ6844-4-44-4-2-400-44004-22200-222i2−2i22i2−2i2−2i22i2−2i22i222-20000-20000000000−i2i2−i2i2i2−i2i2−i20000000000000000000000000000
χ6944-4-4-44-2400-4400-4-222002-222−22−222222−22−2222-22-2000020000000000−222−2−222−20000000000000000000000000000
χ7044-4-4-44-2400-4400-4-222002-2−222222−22−222222−22-22-20000200000000002−2−222−2−220000000000000000000000000000
χ7144-4-4-44-2-4004-4004-222002-2−2i22i22i2−2i22i2−2i2−2i22i22-220000-20000000000i2−i2−i2i2−i2i2i2−i20000000000000000000000000000
χ7244-4-4-44-2-4004-4004-222002-22i2−2i2−2i22i2−2i22i22i2−2i22-220000-20000000000−i2i2i2−i2i2−i2−i2i20000000000000000000000000000
χ734-44-4004000004-40-4-440000000000000004-400000004i−4i4i−4i00000000000000000000000000000000000000
χ744-44-4004000004-40-4-440000000000000004-40000000−4i4i−4i4i00000000000000000000000000000000000000
χ754-44-400400000-440-4-44000000000000000-440004i−4i4i−4i000000000000000000000000000000000000000000
χ764-44-400400000-440-4-44000000000000000-44000−4i4i−4i4i000000000000000000000000000000000000000000
χ774-4-4400404-400000-44-4000000000000000004-40−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ784-4-4400404-400000-44-4000000000000000004-402i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ794-4-440040-4400000-44-400000000000000000-440−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ804-4-440040-4400000-44-400000000000000000-4402i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ818-88-800-4000008-8044-4000000000000000-440000000000000000000000000000000000000000000000000
χ828-88-800-400000-88044-40000000000000004-40000000000000000000000000000000000000000000000000
χ838-8-8800-408-8000004-4400000000000000000-4400000000000000000000000000000000000000000000000
χ848-8-8800-40-88000004-44000000000000000004-400000000000000000000000000000000000000000000000

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