Finite Group Databasebeta

← Group #10691189

Character table — Group #10691189

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order12222234444666444466121212121212121288888888121224242424242424242244441212121224242424448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1
χ91111111-1-1-1-111111-1-11111-1-1-1-1-1-1ii−i−iii−i−i1-1iiii−i−i−i−i11-1-11-111-1-1ii−i−i1-1ii−i−iii−i−i1-1
χ101111111-1-1-1-111111-1-11111-1-1-1-1-1-1ii−i−iii−i−i1-1iiii−i−i−i−i-1-1111-111-1-1ii−i−i-11−i−iii−i−iii-11
χ111111111-1-1-1-111111-1-11111-1-1-1-1-1-1ii−i−i−i−iii1-1−i−i−i−iiiii11-1-1-11-1-111ii−i−i1-1ii−i−i−i−iii-11
χ121111111-1-1-1-111111-1-11111-1-1-1-1-1-1ii−i−i−i−iii1-1−i−i−i−iiiii-1-111-11-1-111ii−i−i-11−i−iiiii−i−i1-1
χ131111111-1-1-1-111111-1-11111-1-1-1-1-1-1−i−iiiii−i−i1-1iiii−i−i−i−i11-1-1-11-1-111−i−iii1-1−i−iiiii−i−i-11
χ141111111-1-1-1-111111-1-11111-1-1-1-1-1-1−i−iiiii−i−i1-1iiii−i−i−i−i-1-111-11-1-111−i−iii-11ii−i−i−i−iii1-1
χ151111111-1-1-1-111111-1-11111-1-1-1-1-1-1−i−iii−i−iii1-1−i−i−i−iiiii11-1-11-111-1-1−i−iii1-1−i−iii−i−iii1-1
χ161111111-1-1-1-111111-1-11111-1-1-1-1-1-1−i−iii−i−iii1-1−i−i−i−iiiii-1-1111-111-1-1−i−iii-11ii−i−iii−i−i-11
χ1722222222222222-2-2-2-222-2-2222-2-2200000000-2-20000000022220000000000-2-20000000000
χ1822222222222222-2-2-2-222-2-2222-2-2200000000-2-200000000-2-2-2-20000000000220000000000
χ192222222-2-2-2-2222-2-22222-2-2-2-2-222-200000000-220000000022-2-20000000000-220000000000
χ202222222-2-2-2-2222-2-22222-2-2-2-2-222-200000000-2200000000-2-22200000000002-20000000000
χ21222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-2-21111-1-1-1-1000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111000022-1-1-1-11111000000000000
χ25222222-1-2-2-2-2-1-1-122-2-2-1-1-1-11111112i2i−2i−2i2i2i−2i−2i-11−i−i−i−iiiii00002-2-1-111−i−iii000000000000
χ26222222-1-2-2-2-2-1-1-122-2-2-1-1-1-11111112i2i−2i−2i−2i−2i2i2i-11iiii−i−i−i−i0000-2211-1-1−i−iii000000000000
χ27222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1111111−2i−2i2i2i2i2i−2i−2i-11−i−i−i−iiiii0000-2211-1-1ii−i−i000000000000
χ28222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1111111−2i−2i2i2i−2i−2i2i2i-11iiii−i−i−i−i00002-2-1-111ii−i−i000000000000
χ292222-2-2222-2-22222-22-2-2-22222-222-22i−2i2i−2i0000-2-20000000000000000002i−2i2i−2i000000000000
χ302222-2-2222-2-22222-22-2-2-22222-222-2−2i2i−2i2i0000-2-2000000000000000000−2i2i−2i2i000000000000
χ312222-2-2222-2-2222-22-22-2-2-2-222-2-2-2-200000000220000000000000000000000002i−2i2i−2i000000
χ322222-2-2222-2-2222-22-22-2-2-2-222-2-2-2-20000000022000000000000000000000000−2i2i−2i2i000000
χ332222-2-22-2-2222222-2-22-2-222-2-22-2-222-2-220000-220000000000000000002-2-22000000000000
χ342222-2-22-2-2222222-2-22-2-222-2-22-2-22-222-20000-22000000000000000000-222-2000000000000
χ352222-2-22-2-222222-222-2-2-2-2-2-2-22222000000002-20000000000000000000000002-2-22000000
χ362222-2-22-2-222222-222-2-2-2-2-2-2-22222000000002-2000000000000000000000000-222-2000000
χ372222-2-2-122-2-2-1-1-12-22-211-1-1-1-11-1-112i−2i2i−2i000011−i3−i3i3i3−i3−i3i3i30000003−33−3−ii−ii000000000000
χ382222-2-2-122-2-2-1-1-12-22-211-1-1-1-11-1-112i−2i2i−2i000011i3i3−i3−i3i3i3−i3−i3000000−33−33−ii−ii000000000000
χ392222-2-2-122-2-2-1-1-12-22-211-1-1-1-11-1-11−2i2i−2i2i000011−i3−i3i3i3−i3−i3i3i3000000−33−33i−ii−i000000000000
χ402222-2-2-122-2-2-1-1-12-22-211-1-1-1-11-1-11−2i2i−2i2i000011i3i3−i3−i3i3i3−i3−i30000003−33−3i−ii−i000000000000
χ412222-2-2-1-2-222-1-1-12-2-2211-1-111-111-12-2-2200001-133−3−3−3−333000000−333−3-111-1000000000000
χ422222-2-2-1-2-222-1-1-12-2-2211-1-111-111-12-2-2200001-1−3−33333−3−30000003−3−33-111-1000000000000
χ432222-2-2-1-2-222-1-1-12-2-2211-1-111-111-1-222-200001-133−3−3−3−3330000003−3−331-1-11000000000000
χ442222-2-2-1-2-222-1-1-12-2-2211-1-111-111-1-222-200001-1−3−33333−3−3000000−333−31-1-11000000000000
χ4522-2-22-222-22-22-2-200002-2002-2200-200002−22−2002−22−22−22−22-22-200000000000000002−22−200
χ4622-2-22-222-22-22-2-200002-2002-2200-200002−22−2002−22−22−22−2-22-220000000000000000−22−2200
χ4722-2-22-222-22-22-2-200002-2002-2200-20000−22−2200−22−22−22−222-22-20000000000000000−22−2200
χ4822-2-22-222-22-22-2-200002-2002-2200-20000−22−2200−22−22−22−22-22-2200000000000000002−22−200
χ4922-2-22-22-22-222-2-200002-200-22-20020000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i22-2-220000000000000000−i2i2i2−i200
χ5022-2-22-22-22-222-2-200002-200-22-20020000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i2-222-20000000000000000i2−i2−i2i200
χ5122-2-22-22-22-222-2-200002-200-22-20020000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i22-2-220000000000000000i2−i2−i2i200
χ5222-2-22-22-22-222-2-200002-200-22-20020000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i2-222-20000000000000000−i2i2i2−i200
χ53444444-24444-2-2-2-4-4-4-4-2-222-2-2-222-200000000220000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-4-444-2-222222-2-22000000002-20000000000000000000000000000000000
χ554444-4-4-244-4-4-2-2-2-44-442222-2-2222200000000-2-20000000000000000000000000000000000
χ564444-4-4-2-4-444-2-2-2-444-4222222-2-2-2-200000000-220000000000000000000000000000000000
χ5744-4-44-4-24-44-4-2220000-2200-22-2002000022−2222−2200−22−22−22−2200000000000000000000000000
χ5844-4-44-4-24-44-4-2220000-2200-22-20020000−2222−2222002−22−22−22−200000000000000000000000000
χ5944-4-44-4-2-44-44-2220000-22002-2200-20000−2i22i22i2−2i200i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ6044-4-44-4-2-44-44-2220000-22002-2200-200002i2−2i2−2i22i200−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ6144-4-4-4444-4-444-4-40000-44004-4-400400000000000000000000000000000000000000000000
χ6244-4-4-444-444-44-4-40000-4400-44400-400000000000000000000000000000000000000000000
χ6344-4-4-44-24-4-44-22200002-200-22200-20000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ6444-4-4-44-24-4-44-22200002-200-22200-20000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ6544-4-4-44-2-444-4-22200002-2002-2-200200000000006−6−66−666−600000000000000000000000000
χ6644-4-4-44-2-444-4-22200002-2002-2-20020000000000−666−66−6−6600000000000000000000000000
χ678-88-80080000-88-80000000000000000000000000000000000000000000000000000000000
χ688-88-800-400004-4400000043−4300000000000000000000000000000000000000000000000000
χ698-88-800-400004-44000000−434300000000000000000000000000000000000000000000000000
χ708-8-880080000-8-880000000000000000000000000000000000000000000000000000000000
χ718-8-8800-4000044-40000000000043−43000000000000000000000000000000000000000000000
χ728-8-8800-4000044-400000000000−4343000000000000000000000000000000000000000000000

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