Finite Group Databasebeta

← Group #10691749

Character table — Group #10691749

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222244444444444444444888888888888121212121616161616161616161616162424242424242424242424242424
order1222222222344666444444466666612121212441212121212121212121244444444121212121212121222444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ6111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111
χ7111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1
χ9111111-1-1-1-11-1-11111-1ii−i−i111-1-1-1-111-1-1i−i1-1iiii−i−i−i−iii−i−i1-1i−i11-1-1ii−i−i1-11-1i−iii−i−i11-1-1
χ10111111-1-1-1-11-1-11111-1ii−i−i111-1-1-1-111-1-1i−i1-1iiii−i−i−i−iii−i−i-11−ii-1-111−i−iii1-11-1i−i−i−iii-1-111
χ11111111-1-1-1-11-1-11111-1ii−i−i111-1-1-1-111-1-1i−i1-1iiii−i−i−i−i−i−iii1-1i−i11-1-1ii−i−i-11-11−ii−i−iii-1-111
χ12111111-1-1-1-11-1-11111-1ii−i−i111-1-1-1-111-1-1i−i1-1iiii−i−i−i−i−i−iii-11−ii-1-111−i−iii-11-11−iiii−i−i11-1-1
χ13111111-1-1-1-11-1-11111-1−i−iii111-1-1-1-111-1-1−ii1-1−i−i−i−iiiiiii−i−i1-1−ii11-1-1−i−iii-11-11i−iii−i−i-1-111
χ14111111-1-1-1-11-1-11111-1−i−iii111-1-1-1-111-1-1−ii1-1−i−i−i−iiiiiii−i−i-11i−i-1-111ii−i−i-11-11i−i−i−iii11-1-1
χ15111111-1-1-1-11-1-11111-1−i−iii111-1-1-1-111-1-1−ii1-1−i−i−i−iiiii−i−iii1-1−ii11-1-1−i−iii1-11-1−ii−i−iii11-1-1
χ16111111-1-1-1-11-1-11111-1−i−iii111-1-1-1-111-1-1−ii1-1−i−i−i−iiiii−i−iii-11i−i-1-111ii−i−i1-11-1−iiii−i−i-1-111
χ1722222222222-2-2222-2-22222-2222222-2-2-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000
χ1822222222222-2-2222-2-2-2-2-2-2-2222222-2-2-2-222-2-2-2-222-2-222000000000000000000000000000000
χ192222222222-122-1-1-12222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-100000000000000
χ202222222222-122-1-1-12222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-21111111100000000000000
χ212222222222-122-1-1-122-2-2-2-22-1-1-1-1-1-1-1-1-1-1-2-2-1-111111111000022-2-2-1-1-1-1111100000000000000
χ222222222222-122-1-1-122-2-2-2-22-1-1-1-1-1-1-1-1-1-1-2-2-1-1111111110000-2-2221111-1-1-1-100000000000000
χ232222222222-1-2-2-1-1-1-2-22222-2-1-1-1-1-1-11111-2-211-1-111-1-11100000000−i3i3−i3i3−i3i3−i3i300000000000000
χ242222222222-1-2-2-1-1-1-2-22222-2-1-1-1-1-1-11111-2-211-1-111-1-11100000000i3−i3i3−i3i3−i3i3−i300000000000000
χ252222222222-1-2-2-1-1-1-2-2-2-2-2-2-2-1-1-1-1-1-11111221111-1-111-1-100000000−i3i3−i3i3i3−i3i3−i300000000000000
χ262222222222-1-2-2-1-1-1-2-2-2-2-2-2-2-1-1-1-1-1-11111221111-1-111-1-100000000i3−i3i3−i3−i3i3−i3i300000000000000
χ27222222-2-2-2-2222222-222i2i−2i−2i-222-2-2-2-2-2-222−2i2i-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ28222222-2-2-2-2222222-22−2i−2i2i2i-222-2-2-2-2-2-2222i−2i-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ29222222-2-2-2-2-122-1-1-1-222i2i−2i−2i-2-1-1111111-1-1−2i2i1-1−i−iiiii−i−i00000000−i3i3i3−i33−3−3300000000000000
χ30222222-2-2-2-2-122-1-1-1-222i2i−2i−2i-2-1-1111111-1-1−2i2i1-1−i−iiiii−i−i00000000i3−i3−i3i3−333−300000000000000
χ31222222-2-2-2-2-122-1-1-1-22−2i−2i2i2i-2-1-1111111-1-12i−2i1-1ii−i−i−i−iii00000000−i3i3i3−i3−333−300000000000000
χ32222222-2-2-2-2-122-1-1-1-22−2i−2i2i2i-2-1-1111111-1-12i−2i1-1ii−i−i−i−iii00000000i3−i3−i3i33−3−3300000000000000
χ33222222-2-2-2-2-1-2-2-1-1-12-22i2i−2i−2i2-1-11111-1-1112i−2i-11−i−i−i−iiiii00002-22i−2i-1-111−i−iii00000000000000
χ34222222-2-2-2-2-1-2-2-1-1-12-22i2i−2i−2i2-1-11111-1-1112i−2i-11−i−i−i−iiiii0000-22−2i2i11-1-1ii−i−i00000000000000
χ35222222-2-2-2-2-1-2-2-1-1-12-2−2i−2i2i2i2-1-11111-1-111−2i2i-11iiii−i−i−i−i00002-2−2i2i-1-111ii−i−i00000000000000
χ36222222-2-2-2-2-1-2-2-1-1-12-2−2i−2i2i2i2-1-11111-1-111−2i2i-11iiii−i−i−i−i0000-222i−2i11-1-1−i−iii00000000000000
χ372222-2-22-22-2222222-2-200002-2-22-2-22-2-222002-20000000000000000000000002-2-220000000000
χ382222-2-22-22-2222222-2-200002-2-22-2-22-2-222002-2000000000000000000000000-222-20000000000
χ392222-2-22-22-22-2-2222220000-2-2-22-2-2222-2-200-22000000002i2i−2i−2i0000000000000000−2i2i00000000
χ402222-2-22-22-22-2-2222220000-2-2-22-2-2222-2-200-2200000000−2i−2i2i2i00000000000000002i−2i00000000
χ412222-2-2-22-222222222-20000-2-2-2-222-2222200-2-20000000022220000000000000000-2-200000000
χ422222-2-2-22-222222222-20000-2-2-2-222-2222200-2-200000000-2-2-2-200000000000000002200000000
χ432222-2-2-22-222-2-2222-2200002-2-2-222-2-2-2-2-2002200000000000000000000000022-2-20000000000
χ442222-2-2-22-222-2-2222-2200002-2-2-222-2-2-2-2-20022000000000000000000000000-2-2220000000000
χ452-2-222-22-2-222002-2-2002-22-202-222-2-2000000002-2002-2000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ462-2-222-22-2-222002-2-2002-22-202-222-2-2000000002-2002-2000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ472-2-222-22-2-222002-2-200-22-2202-222-2-200000000-2200-22000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ482-2-222-22-2-222002-2-200-22-2202-222-2-200000000-2200-22000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ492-2-222-2-222-22002-2-2002i−2i−2i2i02-2-2-222000000002i−2i00−2i2i0000000000000000000000002−2−22−i2i2i2−i2
χ502-2-222-2-222-22002-2-2002i−2i−2i2i02-2-2-222000000002i−2i00−2i2i000000000000000000000000−222−2i2−i2−i2i2
χ512-2-222-2-222-22002-2-200−2i2i2i−2i02-2-2-22200000000−2i2i002i−2i0000000000000000000000002−2−22i2−i2−i2i2
χ522-2-222-2-222-22002-2-200−2i2i2i−2i02-2-2-22200000000−2i2i002i−2i000000000000000000000000−222−2−i2i2i2−i2
χ534444-4-44-44-4-244-2-2-2-4-40000422-222-222-2-200-2200000000000000000000000000000000000000
χ544444-4-44-44-4-2-4-4-2-2-2440000-422-222-2-2-222002-200000000000000000000000000000000000000
χ554444-4-4-44-44-244-2-2-24-40000-4222-2-22-2-2-2-2002200000000000000000000000000000000000000
χ564444-4-4-44-44-2-4-4-2-2-2-4400004222-2-22222200-2-200000000000000000000000000000000000000
χ5744-4-400000044i−4i-44-40000000000000004i−4i0000000000002+2i−2−2i2−2i−2+2i00000000000000000000000000
χ5844-4-400000044i−4i-44-40000000000000004i−4i000000000000−2−2i2+2i−2+2i2−2i00000000000000000000000000
χ5944-4-40000004−4i4i-44-4000000000000000−4i4i0000000000002−2i−2+2i2+2i−2−2i00000000000000000000000000
χ6044-4-40000004−4i4i-44-4000000000000000−4i4i000000000000−2+2i2−2i−2−2i2+2i00000000000000000000000000
χ614-4-444-44-4-44-200-222004-44-40-22-2-22200000000-2200-2200000000000000000000000000000000
χ624-4-444-44-4-44-200-22200-44-440-22-2-222000000002-2002-200000000000000000000000000000000
χ634-4-444-4-444-4-200-222004i−4i−4i4i0-2222-2-200000000−2i2i002i−2i00000000000000000000000000000000
χ644-4-444-4-444-4-200-22200−4i4i4i−4i0-2222-2-2000000002i−2i00−2i2i00000000000000000000000000000000
χ654-4-44-4444-4-44004-4-40000000-444-44-40000000000000000000000000000000000000000000000
χ664-4-44-4444-4-4-200-22200000002-2-22-220000000000−2i32i300−2i32i3000000000000000000000000000000
χ674-4-44-4444-4-4-200-22200000002-2-22-2200000000002i3−2i3002i3−2i3000000000000000000000000000000
χ684-4-44-44-4-4444004-4-40000000-44-44-440000000000000000000000000000000000000000000000
χ694-4-44-44-4-444-200-22200000002-22-22-2000000000023−2300−2323000000000000000000000000000000
χ704-4-44-44-4-444-200-22200000002-22-22-20000000000−23230023−23000000000000000000000000000000
χ7188-8-8000000-48i−8i4-44000000000000000−4i4i000000000000000000000000000000000000000000
χ7288-8-8000000-4−8i8i4-440000000000000004i−4i000000000000000000000000000000000000000000
χ738-88-8000000800-8-8800000000000000000000000000000000000000000000000000000000000
χ748-88-8000000-40044-40000000000000−4i34i300000000000000000000000000000000000000000000
χ758-88-8000000-40044-400000000000004i3−4i300000000000000000000000000000000000000000000

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