Finite Group Databasebeta

← Group #10691155

Character table — Group #10691155

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444444444448888888888888888888888888888888888242424242424242448484848
order1222223444466612121212224444446612121212121212121212246666888888881212121224242424242424242424242424242424444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111111-1-1-1-1111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-11-1-1-111ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111111-1-1-1-1111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-11-1-1-111ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111111-1-1-1-1111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-11-1-1-111−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111111-1-1-1-1111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-11-1-1-111−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-11-1-1-1-1ii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-11-1-1-1-1ii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-11-1-1-1-1−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-11-1-1-1-1−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ17222222222222222222-2-22222-2-2222222222222-2-2-2-2-2-200000000-2-2-2-20000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222-2-22200000000-2-2220000000000000000000000000000
χ192222222-2-2-2-2222-2-2-2-22222-2-2-2-2222222-2-2-2-2-2-2-2222-2-200000000-2-2220000000000000000000000000000
χ202222222-2-2-2-2222-2-2-2-222-2-222-2-222-2-2-2-22222-2-22-2222200000000-2-2-2-20000000000000000000000000000
χ21222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111000000000000
χ23222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-111111111-1-1-2-2-1-1112222-2-2-2-2-1-111-1-1-1-1-1-1-1-111111111000000000000
χ24222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-111111111-1-1-2-2-1-111-2-2-2-22222-1-11111111111-1-1-1-1-1-1-1-1000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-21111000000001111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-21111000000001111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111-1-12211-1-10000000011-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111-1-12211-1-10000000011-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000000000000
χ29222222-1-2-2-2-2-1-1-111112222-2-2-2-2-1-1-1-1-1-1111111-22-1-1110000000011-1-133−3−3−3−33333−3−3−3−333000000000000
χ30222222-1-2-2-2-2-1-1-111112222-2-2-2-2-1-1-1-1-1-1111111-22-1-1110000000011-1-1−3−33333−3−3−3−33333−3−3000000000000
χ31222222-1-2-2-2-2-1-1-1111122-2-222-2-2-1-11111-1-1-1-1112-2-1-1-1-100000000111133−3−3−3−333−3−33333−3−3000000000000
χ32222222-1-2-2-2-2-1-1-1111122-2-222-2-2-1-11111-1-1-1-1112-2-1-1-1-1000000001111−3−33333−3−333−3−3−3−333000000000000
χ33222222-1-2-2-2-2-1-1-11111-2-222-2-222-1-1-1-1-1-11111112-211-1-12i2i−2i−2i2i2i−2i−2i-1-111−i−i−i−iiiii−i−i−i−iiiii000000000000
χ34222222-1-2-2-2-2-1-1-11111-2-222-2-222-1-1-1-1-1-11111112-211-1-1−2i−2i2i2i−2i−2i2i2i-1-111iiii−i−i−i−iiiii−i−i−i−i000000000000
χ35222222-1-2-2-2-2-1-1-11111-2-2-2-22222-1-11111-1-1-1-111-2211112i2i−2i−2i−2i−2i2i2i-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ36222222-1-2-2-2-2-1-1-11111-2-2-2-22222-1-11111-1-1-1-111-221111−2i−2i2i2i2i2i−2i−2i-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000
χ372222-2-2222-2-2222-2-2-2-22-200002-2-2-20000000022002-20000002i−2i2i−2i2-200000000002i−2i2i−2i2i−2i2i−2i000000000000
χ382222-2-2222-2-2222-2-2-2-22-200002-2-2-20000000022002-2000000−2i2i−2i2i2-20000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ392222-2-2222-2-2222-2-2-2-2-220000-22-2-2000000002200-22002i−2i2i−2i0000-22002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ402222-2-2222-2-2222-2-2-2-2-220000-22-2-2000000002200-2200−2i2i−2i2i0000-2200−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ412222-2-22-2-22222222222-20000-22-2-200000000-2-2002-2002-2-220000-22002-22-2-22-2200000000000000000000
χ422222-2-22-2-22222222222-20000-22-2-200000000-2-2002-200-222-20000-2200-22-222-22-200000000000000000000
χ432222-2-22-2-2222222222-2200002-2-2-200000000-2-200-220000002-2-222-200000000002-22-2-22-22000000000000
χ442222-2-22-2-2222222222-2200002-2-2-200000000-2-200-22000000-222-22-20000000000-22-222-22-2000000000000
χ452222-2-2-122-2-2-1-1-111112-200002-211−i3−i3i3i3−i3−i3i3i3-1-100-11−i3i300002i−2i2i−2i-11−i3i33−3−333−3−33−ii−ii−ii−ii000000000000
χ462222-2-2-122-2-2-1-1-111112-200002-211−i3−i3i3i3−i3−i3i3i3-1-100-11−i3i30000−2i2i−2i2i-11−i3i3−333−3−333−3i−ii−ii−ii−i000000000000
χ472222-2-2-122-2-2-1-1-111112-200002-211i3i3−i3−i3i3i3−i3−i3-1-100-11i3−i300002i−2i2i−2i-11i3−i3−333−3−333−3−ii−ii−ii−ii000000000000
χ482222-2-2-122-2-2-1-1-111112-200002-211i3i3−i3−i3i3i3−i3−i3-1-100-11i3−i30000−2i2i−2i2i-11i3−i33−3−333−3−33i−ii−ii−ii−i000000000000
χ492222-2-2-122-2-2-1-1-11111-220000-2211−i3−i3i3i3−i3−i3i3i3-1-1001-1i3−i32i−2i2i−2i00001-1i3−i3−ii−ii−ii−ii3−3−333−3−33000000000000
χ502222-2-2-122-2-2-1-1-11111-220000-2211−i3−i3i3i3−i3−i3i3i3-1-1001-1i3−i3−2i2i−2i2i00001-1i3−i3i−ii−ii−ii−i−333−3−333−3000000000000
χ512222-2-2-122-2-2-1-1-11111-220000-2211i3i3−i3−i3i3i3−i3−i3-1-1001-1−i3i32i−2i2i−2i00001-1−i3i3−ii−ii−ii−ii−333−3−333−3000000000000
χ522222-2-2-122-2-2-1-1-11111-220000-2211i3i3−i3−i3i3i3−i3−i3-1-1001-1−i3i3−2i2i−2i2i00001-1−i3i3i−ii−ii−ii−i3−3−333−3−33000000000000
χ532222-2-2-1-2-222-1-1-1-1-1-1-12-20000-2211−i3−i3i3i3i3i3−i3−i31100-11i3−i32-2-2200001-1−i3i3-11-111-11-1−i3i3i3−i3i3−i3−i3i3000000000000
χ542222-2-2-1-2-222-1-1-1-1-1-1-12-20000-2211−i3−i3i3i3i3i3−i3−i31100-11i3−i3-222-200001-1−i3i31-11-1-11-11i3−i3−i3i3−i3i3i3−i3000000000000
χ552222-2-2-1-2-222-1-1-1-1-1-1-12-20000-2211i3i3−i3−i3−i3−i3i3i31100-11−i3i32-2-2200001-1i3−i3-11-111-11-1i3−i3−i3i3−i3i3i3−i3000000000000
χ562222-2-2-1-2-222-1-1-1-1-1-1-12-20000-2211i3i3−i3−i3−i3−i3i3i31100-11−i3i3-222-200001-1i3−i31-11-1-11-11−i3i3i3−i3i3−i3−i3i3000000000000
χ572222-2-2-1-2-222-1-1-1-1-1-1-1-2200002-211−i3−i3i3i3i3i3−i3−i311001-1−i3i300002-2-22-11i3−i3−i3i3i3−i3i3−i3−i3i3-11-111-11-1000000000000
χ582222-2-2-1-2-222-1-1-1-1-1-1-1-2200002-211−i3−i3i3i3i3i3−i3−i311001-1−i3i30000-222-2-11i3−i3i3−i3−i3i3−i3i3i3−i31-11-1-11-11000000000000
χ592222-2-2-1-2-222-1-1-1-1-1-1-1-2200002-211i3i3−i3−i3−i3−i3i3i311001-1i3−i300002-2-22-11−i3i3i3−i3−i3i3−i3i3i3−i3-11-111-11-1000000000000
χ602222-2-2-1-2-222-1-1-1-1-1-1-1-2200002-211i3i3−i3−i3−i3−i3i3i311001-1i3−i30000-222-2-11−i3i3−i3i3i3−i3i3−i3−i3i31-11-1-11-11000000000000
χ612-22-22-222i−2i2i−2i2-2-22i2i−2i−2i002i−2i2-2002-22i−2i2i−2i2-22-22i−2i00000000000000000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ622-22-22-222i−2i2i−2i2-2-22i2i−2i−2i002i−2i2-2002-22i−2i2i−2i2-22-22i−2i0000000000000000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ632-22-22-222i−2i2i−2i2-2-22i2i−2i−2i00−2i2i-22002-2−2i2i−2i2i-22-222i−2i00000000000000000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i0000
χ642-22-22-222i−2i2i−2i2-2-22i2i−2i−2i00−2i2i-22002-2−2i2i−2i2i-22-222i−2i0000000000000000000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i0000
χ652-22-22-22−2i2i−2i2i2-2-2−2i−2i2i2i002i−2i-22002-22i−2i2i−2i-22-22−2i2i00000000000000000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i0000
χ662-22-22-22−2i2i−2i2i2-2-2−2i−2i2i2i002i−2i-22002-22i−2i2i−2i-22-22−2i2i0000000000000000000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i0000
χ672-22-22-22−2i2i−2i2i2-2-2−2i−2i2i2i00−2i2i2-2002-2−2i2i−2i2i2-22-2−2i2i00000000000000000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ682-22-22-22−2i2i−2i2i2-2-2−2i−2i2i2i00−2i2i2-2002-2−2i2i−2i2i2-22-2−2i2i0000000000000000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ694-44-44-4-24i−4i4i−4i-222−2i−2i2i2i004i−4i4-400-22−2i2i−2i2i-22-22−2i2i0000000000000000000000000000000000000000000000
χ704-44-44-4-24i−4i4i−4i-222−2i−2i2i2i00−4i4i-4400-222i−2i2i−2i2-22-2−2i2i0000000000000000000000000000000000000000000000
χ714-44-44-4-2−4i4i−4i4i-2222i2i−2i−2i004i−4i-4400-22−2i2i−2i2i2-22-22i−2i0000000000000000000000000000000000000000000000
χ724-44-44-4-2−4i4i−4i4i-2222i2i−2i−2i00−4i4i4-400-222i−2i2i−2i-22-222i−2i0000000000000000000000000000000000000000000000
χ734-44-4-4444i−4i−4i4i4-4-4−4i−4i4i4i00000000-44000000004i−4i0000000000000000000000000000000000000000000000
χ744-44-4-444−4i4i4i−4i4-4-44i4i−4i−4i00000000-4400000000−4i4i0000000000000000000000000000000000000000000000
χ754-44-4-44-24i−4i−4i4i-2222i2i−2i−2i000000002-223−23−2323−2i32i32i3−2i3−2i2i0000000000000000000000000000000000000000000000
χ764-44-4-44-24i−4i−4i4i-2222i2i−2i−2i000000002-2−232323−232i3−2i3−2i32i3−2i2i0000000000000000000000000000000000000000000000
χ774-44-4-44-2−4i4i4i−4i-222−2i−2i2i2i000000002-223−23−23232i3−2i3−2i32i32i−2i0000000000000000000000000000000000000000000000
χ784-44-4-44-2−4i4i4i−4i-222−2i−2i2i2i000000002-2−232323−23−2i32i32i3−2i32i−2i0000000000000000000000000000000000000000000000
χ7988-8-80080000-88-80000000000000000000000000000000000000000000000000000000000000000000000
χ8088-8-800-400004-4443−4343−43000000000000000000000000000000000000000000000000000000000000000000
χ8188-8-800-400004-44−4343−4343000000000000000000000000000000000000000000000000000000000000000000
χ828-8-880080000-8-880000000000000000000000000000000000000000000000000000000000000000000000
χ838-8-8800-4000044-4−4i34i34i3−4i3000000000000000000000000000000000000000000000000000000000000000000
χ848-8-8800-4000044-44i3−4i3−4i34i3000000000000000000000000000000000000000000000000000000000000000000

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