Finite Group Databasebeta

← Group #10694699

Character table — Group #10694699

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222222222224444444444444444444466666666888888888812121212121212121212121216161616161616161616161648484848
order1222222222344446664444444444666666121212128888888812121212121212121212888888888888444412121212121212122444
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
χ511111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1
χ9111111-1-1-1-111-1-111111-1iiii−i−i−i−i11-1-1-1-111-1-11111-1-1-1-11-1iiii−i−i−i−iiiii−i−i−i−i11-1-11-1i−i11-1-1ii−i−i1-1i−i
χ10111111-1-1-1-111-1-111111-1iiii−i−i−i−i11-1-1-1-111-1-11111-1-1-1-11-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-11−ii-1-111−i−iii-11−ii
χ11111111-1-1-1-111-1-111111-1iiii−i−i−i−i11-1-1-1-111-1-1-1-1-1-111111-1iiii−i−i−i−i−i−i−i−iiiii-1-1111-1i−i11-1-1ii−i−i-11−ii
χ12111111-1-1-1-111-1-111111-1iiii−i−i−i−i11-1-1-1-111-1-1-1-1-1-111111-1iiii−i−i−i−i−i−i−i−iiiii-1-111-11−ii-1-111−i−iii1-1i−i
χ13111111-1-1-1-111-1-111111-1−i−i−i−iiiii11-1-1-1-111-1-11111-1-1-1-11-1−i−i−i−iiiii−i−i−i−iiiii11-1-11-1−ii11-1-1−i−iii1-1−ii
χ14111111-1-1-1-111-1-111111-1−i−i−i−iiiii11-1-1-1-111-1-11111-1-1-1-11-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-11i−i-1-111ii−i−i-11i−i
χ15111111-1-1-1-111-1-111111-1−i−i−i−iiiii11-1-1-1-111-1-1-1-1-1-111111-1−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1−ii11-1-1−i−iii-11i−i
χ16111111-1-1-1-111-1-111111-1−i−i−i−iiiii11-1-1-1-111-1-1-1-1-1-111111-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-11i−i-1-111ii−i−i1-1−ii
χ1722222222222-2-2-2-2222-2-222-2-222-2-2222222-2-2-2-200000000-2-222-2-222-2-20000000000000000000000000000
χ1822222222222-2-2-2-2222-2-2-2-222-2-222222222-2-2-2-200000000-2-2-2-222-2-2220000000000000000000000000000
χ192222222222-12222-1-1-12222222222-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-10000000000002222-1-1-1-1-1-1-1-10000
χ202222222222-12222-1-1-12222222222-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-2111111110000
χ212222222222-12222-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-100000000-1-11111111100000000000022-2-2-1-1-1-111110000
χ222222222222-12222-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-100000000-1-111111111000000000000-2-2221111-1-1-1-10000
χ232222222222-1-2-2-2-2-1-1-1-2-222-2-222-2-2-1-1-1-1-1-111110000000011-1-111-1-1110000000000000000−i3i3−i3i3−i3i3−i3i30000
χ242222222222-1-2-2-2-2-1-1-1-2-222-2-222-2-2-1-1-1-1-1-111110000000011-1-111-1-1110000000000000000i3−i3i3−i3i3−i3i3−i30000
χ252222222222-1-2-2-2-2-1-1-1-2-2-2-222-2-222-1-1-1-1-1-11111000000001111-1-111-1-10000000000000000−i3i3−i3i3i3−i3i3−i30000
χ262222222222-1-2-2-2-2-1-1-1-2-2-2-222-2-222-1-1-1-1-1-11111000000001111-1-111-1-10000000000000000i3−i3i3−i3−i3i3−i3i30000
χ27222222-2-2-2-22-222-2222-222i2i−2i−2i−2i−2i2i2i22-2-2-2-2-2-22200000000-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ28222222-2-2-2-22-222-2222-22−2i−2i2i2i2i2i−2i−2i22-2-2-2-2-2-22200000000-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ29222222-2-2-2-2-12-2-22-1-1-12-22i2i2i2i−2i−2i−2i−2i-1-11111-1-11100000000-11−i−i−i−iiiii0000000000002-22i−2i-1-111−i−iii0000
χ30222222-2-2-2-2-12-2-22-1-1-12-22i2i2i2i−2i−2i−2i−2i-1-11111-1-11100000000-11−i−i−i−iiiii000000000000-22−2i2i11-1-1ii−i−i0000
χ31222222-2-2-2-2-12-2-22-1-1-12-2−2i−2i−2i−2i2i2i2i2i-1-11111-1-11100000000-11iiii−i−i−i−i0000000000002-2−2i2i-1-111ii−i−i0000
χ32222222-2-2-2-2-12-2-22-1-1-12-2−2i−2i−2i−2i2i2i2i2i-1-11111-1-11100000000-11iiii−i−i−i−i000000000000-222i−2i11-1-1−i−iii0000
χ33222222-2-2-2-2-1-222-2-1-1-1-222i2i−2i−2i−2i−2i2i2i-1-1111111-1-1000000001-1−i−iiiii−i−i0000000000000000−i3i3i3−i33−3−330000
χ34222222-2-2-2-2-1-222-2-1-1-1-222i2i−2i−2i−2i−2i2i2i-1-1111111-1-1000000001-1−i−iiiii−i−i0000000000000000i3−i3−i3i3−333−30000
χ35222222-2-2-2-2-1-222-2-1-1-1-22−2i−2i2i2i2i2i−2i−2i-1-1111111-1-1000000001-1ii−i−i−i−iii0000000000000000−i3i3i3−i3−333−30000
χ36222222-2-2-2-2-1-222-2-1-1-1-22−2i−2i2i2i2i2i−2i−2i-1-1111111-1-1000000001-1ii−i−i−i−iii0000000000000000i3−i3−i3i33−3−330000
χ372222-2-222-2-222222222-2-200000000-2-2-222-2222222222222-2-20000000000000000-2-2-2-20000000000000000
χ382222-2-222-2-222222222-2-200000000-2-2-222-22222-2-2-2-2-2-2-2-2-2-2000000000000000022220000000000000000
χ392222-2-222-2-22-2-2-2-22222200000000-2-2-222-2-2-2-2-20000000022000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ402222-2-222-2-22-2-2-2-22222200000000-2-2-222-2-2-2-2-2000000002200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ412222-2-2-2-22222-2-22222-2200000000-2-22-2-2222-2-22222-2-2-2-2-220000000000000000-2-2220000000000000000
χ422222-2-2-2-22222-2-22222-2200000000-2-22-2-2222-2-2-2-2-2-22222-22000000000000000022-2-20000000000000000
χ432222-2-2-2-2222-222-22222-200000000-2-22-2-22-2-222000000002-20000000022-2-2-2-22200000000000000000000
χ442222-2-2-2-2222-222-22222-200000000-2-22-2-22-2-222000000002-200000000-2-22222-2-200000000000000000000
χ452-2-222-22-22-2200002-2-200002i−2i002i−2i2-2-22-220000−i2−i2i2i2−i2−i2i2i200002i−2i002i−2i2−22−22−22−2−i2i2−i2i20000000000000000
χ462-2-222-22-22-2200002-2-200002i−2i002i−2i2-2-22-220000i2i2−i2−i2i2i2−i2−i200002i−2i002i−2i−22−22−22−22i2−i2i2−i20000000000000000
χ472-2-222-22-22-2200002-2-20000−2i2i00−2i2i2-2-22-220000−i2−i2i2i2−i2−i2i2i20000−2i2i00−2i2i−22−22−22−22−i2i2−i2i20000000000000000
χ482-2-222-22-22-2200002-2-20000−2i2i00−2i2i2-2-22-220000i2i2−i2−i2i2i2−i2−i20000−2i2i00−2i2i2−22−22−22−2i2−i2i2−i20000000000000000
χ492-2-222-2-22-22200002-2-200002-200-222-22-22-20000−i2−i2i2i2i2i2−i2−i200002-200-22−i2i2−i2i2i2−i2i2−i2−i2i2i2−i20000000000000000
χ502-2-222-2-22-22200002-2-200002-200-222-22-22-20000i2i2−i2−i2−i2−i2i2i200002-200-22i2−i2i2−i2−i2i2−i2i2i2−i2−i2i20000000000000000
χ512-2-222-2-22-22200002-2-20000-22002-22-22-22-20000−i2−i2i2i2i2i2−i2−i20000-22002-2i2−i2i2−i2−i2i2−i2i2−i2i2i2−i20000000000000000
χ522-2-222-2-22-22200002-2-20000-22002-22-22-22-20000i2i2−i2−i2−i2−i2i2i20000-22002-2−i2i2−i2i2i2−i2i2−i2i2−i2−i2i20000000000000000
χ532-2-22-222-2-22200002-2-2002-2002-200-2222-2-20000−i2−i2i2i2−i2−i2i2i2002-2002-200−i2i2i2−i2−i2i2i2−i2i2−i2i2−i20000000000000000
χ542-2-22-222-2-22200002-2-2002-2002-200-2222-2-20000i2i2−i2−i2i2i2−i2−i2002-2002-200i2−i2−i2i2i2−i2−i2i2−i2i2−i2i20000000000000000
χ552-2-22-222-2-22200002-2-200-2200-2200-2222-2-20000−i2−i2i2i2−i2−i2i2i200-2200-2200i2−i2−i2i2i2−i2−i2i2i2−i2i2−i20000000000000000
χ562-2-22-222-2-22200002-2-200-2200-2200-2222-2-20000i2i2−i2−i2i2i2−i2−i200-2200-2200−i2i2i2−i2−i2i2i2−i2−i2i2−i2i20000000000000000
χ572-2-22-22-222-2200002-2-2002i−2i00−2i2i00-22-2-2220000−i2−i2i2i2i2i2−i2−i2002i−2i00−2i2i002−2−22−222−2i2−i2−i2i20000000000000000
χ582-2-22-22-222-2200002-2-2002i−2i00−2i2i00-22-2-2220000i2i2−i2−i2−i2−i2i2i2002i−2i00−2i2i00−222−22−2−22−i2i2i2−i20000000000000000
χ592-2-22-22-222-2200002-2-200−2i2i002i−2i00-22-2-2220000−i2−i2i2i2i2i2−i2−i200−2i2i002i−2i00−222−22−2−22i2−i2−i2i20000000000000000
χ602-2-22-22-222-2200002-2-200−2i2i002i−2i00-22-2-2220000i2i2−i2−i2−i2−i2i2i200−2i2i002i−2i002−2−22−222−2−i2i2i2−i20000000000000000
χ614444-4-444-4-4-24444-2-2-2-4-400000000222-2-22-2-2-2-20000000022000000000000000000000000000000000000
χ624444-4-444-4-4-2-4-4-4-4-2-2-24400000000222-2-22222200000000-2-2000000000000000000000000000000000000
χ634444-4-4-4-444-24-4-44-2-2-2-440000000022-222-2-2-222000000002-2000000000000000000000000000000000000
χ644444-4-4-4-444-2-444-4-2-2-24-40000000022-222-222-2-200000000-22000000000000000000000000000000000000
χ6544-4-4000000404i−4i0-44-40000000000000000004i−4i22−2222−22−2i22i2−2i22i200000000000000000000000000000000000000
χ6644-4-4000000404i−4i0-44-40000000000000000004i−4i−2222−22222i2−2i22i2−2i200000000000000000000000000000000000000
χ6744-4-400000040−4i4i0-44-4000000000000000000−4i4i22−2222−222i2−2i22i2−2i200000000000000000000000000000000000000
χ6844-4-400000040−4i4i0-44-4000000000000000000−4i4i−2222−2222−2i22i2−2i22i200000000000000000000000000000000000000
χ694-44-40000004400-4-4-4400000000000000004-4004i−4i−4i4i000000000000000000000000000000000000000000
χ704-44-40000004400-4-4-4400000000000000004-400−4i4i4i−4i000000000000000000000000000000000000000000
χ714-44-40000004-4004-4-440000000000000000-440000004-4-4400000000000000000000000000000000000000
χ724-44-40000004-4004-4-440000000000000000-44000000-444-400000000000000000000000000000000000000
χ734-4-444-44-44-4-20000-22200004i−4i004i−4i-222-22-20000000000000000−2i2i00−2i2i0000000000000000000000000000
χ744-4-444-44-44-4-20000-2220000−4i4i00−4i4i-222-22-200000000000000002i−2i002i−2i0000000000000000000000000000
χ754-4-444-4-44-44-20000-22200004-400-44-22-22-220000000000000000-22002-20000000000000000000000000000
χ764-4-444-4-44-44-20000-2220000-44004-4-22-22-2200000000000000002-200-220000000000000000000000000000
χ774-4-44-444-4-44-20000-222004-4004-4002-2-2-22200000000000000-2200-22000000000000000000000000000000
χ784-4-44-444-4-44-20000-22200-4400-44002-2-2-222000000000000002-2002-2000000000000000000000000000000
χ794-4-44-44-444-4-20000-222004i−4i00−4i4i002-222-2-200000000000000−2i2i002i−2i000000000000000000000000000000
χ804-4-44-44-444-4-20000-22200−4i4i004i−4i002-222-2-2000000000000002i−2i00−2i2i000000000000000000000000000000
χ8188-8-8000000-408i−8i04-44000000000000000000−4i4i0000000000000000000000000000000000000000000000
χ8288-8-8000000-40−8i8i04-440000000000000000004i−4i0000000000000000000000000000000000000000000000
χ838-88-8000000-4800-844-40000000000000000-44000000000000000000000000000000000000000000000000
χ848-88-8000000-4-800844-400000000000000004-4000000000000000000000000000000000000000000000000

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