Finite Group Databasebeta

← Group #10694700

Character table — Group #10694700

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222222222224444444444444444444466666666888888888812121212121212121212121216161616161616161616161648484848
order1222222222344446664466666688888888121212128888888812122424242424242424444444448888444412121212121212124444
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
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1
χ9111111-1-1-1-111-1-111111-111-1-1-1-1iiii−i−i−i−i11-1-11111-1-1-1-11-1iiii−i−i−i−iiiii−i−i−i−i11-1-11-1i−i11-1-1ii−i−i1-1i−i
χ10111111-1-1-1-111-1-111111-111-1-1-1-1iiii−i−i−i−i11-1-11111-1-1-1-11-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-11−ii-1-111−i−iii-11−ii
χ11111111-1-1-1-111-1-111111-111-1-1-1-1iiii−i−i−i−i11-1-1-1-1-1-111111-1iiii−i−i−i−i−i−i−i−iiiii-1-1111-1i−i11-1-1ii−i−i-11−ii
χ12111111-1-1-1-111-1-111111-111-1-1-1-1iiii−i−i−i−i11-1-1-1-1-1-111111-1iiii−i−i−i−i−i−i−i−iiiii-1-111-11−ii-1-111−i−iii1-1i−i
χ13111111-1-1-1-111-1-111111-111-1-1-1-1−i−i−i−iiiii11-1-11111-1-1-1-11-1−i−i−i−iiiii−i−i−i−iiiii11-1-11-1−ii11-1-1−i−iii1-1−ii
χ14111111-1-1-1-111-1-111111-111-1-1-1-1−i−i−i−iiiii11-1-11111-1-1-1-11-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-11i−i-1-111ii−i−i-11i−i
χ15111111-1-1-1-111-1-111111-111-1-1-1-1−i−i−i−iiiii11-1-1-1-1-1-111111-1−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1−ii11-1-1−i−iii-11i−i
χ16111111-1-1-1-111-1-111111-111-1-1-1-1−i−i−i−iiiii11-1-1-1-1-1-111111-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-11i−i-1-111ii−i−i1-1−ii
χ1722222222222-2-2-2-2222-2-222222200000000-2-2-2-200000000-2-20000000022-2-222-2-200000000000000000000
χ1822222222222-2-2-2-2222-2-222222200000000-2-2-2-200000000-2-200000000-2-222-2-22200000000000000000000
χ192222222222-12222-1-1-122-1-1-1-1-1-122222222-1-1-1-100000000-1-1-1-1-1-1-1-1-1-10000000000002222-1-1-1-1-1-1-1-10000
χ202222222222-12222-1-1-122-1-1-1-1-1-122222222-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-2111111110000
χ212222222222-12222-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-100000000-1-11111111100000000000022-2-2-1-1-1-111110000
χ222222222222-12222-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-100000000-1-111111111000000000000-2-2221111-1-1-1-10000
χ23222222-2-2-2-22-222-2222-2222-2-2-2-200000000-2-22200000000-22000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ24222222-2-2-2-22-222-2222-2222-2-2-2-200000000-2-22200000000-2200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ25222222-2-2-2-2-12-2-22-1-1-12-2-1-111112i2i2i2i−2i−2i−2i−2i-1-11100000000-11−i−i−i−iiiii0000000000002-22i−2i-1-111−i−iii0000
χ26222222-2-2-2-2-12-2-22-1-1-12-2-1-111112i2i2i2i−2i−2i−2i−2i-1-11100000000-11−i−i−i−iiiii000000000000-22−2i2i11-1-1ii−i−i0000
χ27222222-2-2-2-2-12-2-22-1-1-12-2-1-11111−2i−2i−2i−2i2i2i2i2i-1-11100000000-11iiii−i−i−i−i0000000000002-2−2i2i-1-111ii−i−i0000
χ28222222-2-2-2-2-12-2-22-1-1-12-2-1-11111−2i−2i−2i−2i2i2i2i2i-1-11100000000-11iiii−i−i−i−i000000000000-222i−2i11-1-1−i−iii0000
χ292222-2-22-2-2222-2-22222-22-2-22-2-220000000022-2-22222-2-2-2-2-220000000000000000-2-2220000000000000000
χ302222-2-22-2-2222-2-22222-22-2-22-2-220000000022-2-2-2-2-2-22222-22000000000000000022-2-20000000000000000
χ312222-2-22-2-222-222-22222-2-2-22-2-2222-2-222-2-2-2-222000000002-222-2-222-2-20000000000000000000000000000
χ322222-2-22-2-222-222-22222-2-2-22-2-22-2-222-2-222-2-222000000002-2-2-222-2-2220000000000000000000000000000
χ332222-2-22-2-22-1-222-2-1-1-12-211-111-122-2-222-2-211-1-100000000-11-1-111-1-1110000000000000000−i3i3−i3i3−i3i3−i3i30000
χ342222-2-22-2-22-1-222-2-1-1-12-211-111-122-2-222-2-211-1-100000000-11-1-111-1-1110000000000000000i3−i3i3−i3i3−i3i3−i30000
χ352222-2-22-2-22-1-222-2-1-1-12-211-111-1-2-222-2-22211-1-100000000-1111-1-111-1-10000000000000000−i3i3−i3i3i3−i3i3−i30000
χ362222-2-22-2-22-1-222-2-1-1-12-211-111-1-2-222-2-22211-1-100000000-1111-1-111-1-10000000000000000i3−i3i3−i3−i3i3−i3i30000
χ372222-2-2-222-222222222-2-2-2-2-222-200000000222222222222-2-20000000000000000-2-2-2-20000000000000000
χ382222-2-2-222-222222222-2-2-2-2-222-2000000002222-2-2-2-2-2-2-2-2-2-2000000000000000022220000000000000000
χ392222-2-2-222-22-2-2-2-222222-2-2-222-22i2i−2i−2i−2i−2i2i2i-2-2-2-200000000222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ402222-2-2-222-22-2-2-2-222222-2-2-222-2−2i−2i2i2i2i2i−2i−2i-2-2-2-20000000022−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ412222-2-2-222-2-1-2-2-2-2-1-1-122111-1-112i2i−2i−2i−2i−2i2i2i111100000000-1-1−i−iiiii−i−i0000000000000000−i3i3i3−i33−3−330000
χ422222-2-2-222-2-1-2-2-2-2-1-1-122111-1-112i2i−2i−2i−2i−2i2i2i111100000000-1-1−i−iiiii−i−i0000000000000000i3−i3−i3i3−333−30000
χ432222-2-2-222-2-1-2-2-2-2-1-1-122111-1-11−2i−2i2i2i2i2i−2i−2i111100000000-1-1ii−i−i−i−iii0000000000000000−i3i3i3−i3−333−30000
χ442222-2-2-222-2-1-2-2-2-2-1-1-122111-1-11−2i−2i2i2i2i2i−2i−2i111100000000-1-1ii−i−i−i−iii0000000000000000i3−i3−i3i33−3−330000
χ4522-2-22-222-2-2200002-2-2002-222-2-22−22−22−22−2000022−2−222−2−2002−22−22−22−2002-2002-22−22−20000000000000000
χ4622-2-22-222-2-2200002-2-2002-222-2-22−22−22−22−20000−2−222−2−222002−22−22−22−200-2200-22−22−220000000000000000
χ4722-2-22-222-2-2200002-2-2002-222-2-2−22−22−22−22000022−2−222−2−200−22−22−22−2200-2200-222−22−20000000000000000
χ4822-2-22-222-2-2200002-2-2002-222-2-2−22−22−22−220000−2−222−2−22200−22−22−22−22002-2002-2−22−220000000000000000
χ4922-2-22-2-2-222200002-2-2002-2-2-222−i2i2−i2i2i2−i2i2−i2000022−2−2−2−22200−i2i2−i2i2i2−i2i2−i200−2i2i002i−2i2−2−220000000000000000
χ5022-2-22-2-2-222200002-2-2002-2-2-222−i2i2−i2i2i2−i2i2−i20000−2−22222−2−200−i2i2−i2i2i2−i2i2−i2002i−2i00−2i2i−222−20000000000000000
χ5122-2-22-2-2-222200002-2-2002-2-2-222i2−i2i2−i2−i2i2−i2i2000022−2−2−2−22200i2−i2i2−i2−i2i2−i2i2002i−2i00−2i2i2−2−220000000000000000
χ5222-2-22-2-2-222200002-2-2002-2-2-222i2−i2i2−i2−i2i2−i2i20000−2−22222−2−200i2−i2i2−i2−i2i2−i2i200−2i2i002i−2i−222−20000000000000000
χ5322-2-2-222-22-2200002-2-200-222-22-22−2−222−2−22000022−2−2−2−222002−2−222−2−222-2002-200−222−20000000000000000
χ5422-2-2-222-22-2200002-2-200-222-22-22−2−222−2−220000−2−22222−2−2002−2−222−2−22-2200-22002−2−220000000000000000
χ5522-2-2-222-22-2200002-2-200-222-22-2−222−2−222−2000022−2−2−2−22200−222−2−222−2-2200-2200−222−20000000000000000
χ5622-2-2-222-22-2200002-2-200-222-22-2−222−2−222−20000−2−22222−2−200−222−2−222−22-2002-2002−2−220000000000000000
χ5722-2-2-22-22-22200002-2-200-22-22-22−i2i2i2−i2i2−i2−i2i2000022−2−222−2−200−i2i2i2−i2i2−i2−i2i2−2i2i002i−2i00−22−220000000000000000
χ5822-2-2-22-22-22200002-2-200-22-22-22−i2i2i2−i2i2−i2−i2i20000−2−222−2−22200−i2i2i2−i2i2−i2−i2i22i−2i00−2i2i002−22−20000000000000000
χ5922-2-2-22-22-22200002-2-200-22-22-22i2−i2−i2i2−i2i2i2−i2000022−2−222−2−200i2−i2−i2i2−i2i2i2−i22i−2i00−2i2i00−22−220000000000000000
χ6022-2-2-22-22-22200002-2-200-22-22-22i2−i2−i2i2−i2i2i2−i20000−2−222−2−22200i2−i2−i2i2−i2i2i2−i2−2i2i002i−2i002−22−20000000000000000
χ614444444444-2-4-4-4-4-2-2-2-4-4-2-2-2-2-2-20000000022220000000022000000000000000000000000000000000000
χ62444444-4-4-4-4-2-444-4-2-2-2-44-2-222220000000022-2-2000000002-2000000000000000000000000000000000000
χ634444-4-44-4-44-24-4-44-2-2-2-4422-222-200000000-2-222000000002-2000000000000000000000000000000000000
χ644444-4-4-444-4-24444-2-2-2-4-4222-2-2200000000-2-2-2-20000000022000000000000000000000000000000000000
χ6544-4-44-444-4-4-20000-22200-22-2-22222−2222−2222−2222−2200000000000000−22−22−22−220000000000000000000000000000
χ6644-4-44-444-4-4-20000-22200-22-2-222−2222−2222−2222−2222000000000000002−22−22−22−20000000000000000000000000000
χ6744-4-44-4-4-444-20000-22200-2222-2-2−2i22i2−2i22i22i2−2i22i2−2i200000000000000i2−i2i2−i2−i2i2−i2i20000000000000000000000000000
χ6844-4-44-4-4-444-20000-22200-2222-2-22i2−2i22i2−2i2−2i22i2−2i22i200000000000000−i2i2−i2i2i2−i2i2−i20000000000000000000000000000
χ6944-4-4-444-44-4-20000-222002-2-22-2222−22−222222−22−222200000000000000−222−2−222−20000000000000000000000000000
χ7044-4-4-444-44-4-20000-222002-2-22-22−222222−22−222222−22000000000000002−2−222−2−220000000000000000000000000000
χ7144-4-4-44-44-44-20000-222002-22-22-2−2i22i22i2−2i22i2−2i2−2i22i200000000000000i2−i2−i2i2−i2i2i2−i20000000000000000000000000000
χ7244-4-4-44-44-44-20000-222002-22-22-22i2−2i2−2i22i2−2i22i22i2−2i200000000000000−i2i2i2−i2i2−i2−i2i20000000000000000000000000000
χ734-44-4000000404i−4i0-44-40000000000000000004i−4i22−2222−22−2i22i2−2i22i200000000000000000000000000000000000000
χ744-44-4000000404i−4i0-44-40000000000000000004i−4i−2222−22222i2−2i22i2−2i200000000000000000000000000000000000000
χ754-44-400000040−4i4i0-44-4000000000000000000−4i4i22−2222−222i2−2i22i2−2i200000000000000000000000000000000000000
χ764-44-400000040−4i4i0-44-4000000000000000000−4i4i−2222−2222−2i22i2−2i22i200000000000000000000000000000000000000
χ774-4-440000004400-4-4-4400000000000000004-40000004i−4i−4i4i00000000000000000000000000000000000000
χ784-4-440000004400-4-4-4400000000000000004-4000000−4i4i4i−4i00000000000000000000000000000000000000
χ794-4-440000004-4004-4-440000000000000000-44004-4-44000000000000000000000000000000000000000000
χ804-4-440000004-4004-4-440000000000000000-4400-444-4000000000000000000000000000000000000000000
χ818-88-8000000-408i−8i04-44000000000000000000−4i4i0000000000000000000000000000000000000000000000
χ828-88-8000000-40−8i8i04-440000000000000000004i−4i0000000000000000000000000000000000000000000000
χ838-8-88000000-4800-844-40000000000000000-44000000000000000000000000000000000000000000000000
χ848-8-88000000-4-800844-400000000000000004-4000000000000000000000000000000000000000000000000

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