Finite Group Databasebeta

← Group #10877174

Character table — Group #10877174

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444444444448888888888888888888888888888888888242424242424242448484848
order12222234444666666622446666888812121212121212124444444488121212121212121212121212121212122424242424242424244488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ9111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1111-11-1
χ10111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-11-11
χ11111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-11-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-11-11
χ12111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-11-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-11-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-11-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1111-1-11
χ172222222-2-2-2-2222222222-2-222220000-2-2-2-2-2-2-2-2000000000000000000000000000000000000002i−2i2i−2i0000
χ182222222-2-2-2-2222222222-2-222220000-2-2-2-2-2-2-2-200000000000000000000000000000000000000−2i2i−2i2i0000
χ192222222-2-2-2-22222222-2-222-2-2-2-20000-2-2-22222-2000000000000000000000000000000000000002i−2i−2i2i0000
χ202222222-2-2-2-22222222-2-222-2-2-2-20000-2-2-22222-200000000000000000000000000000000000000−2i2i2i−2i0000
χ21222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2221111111111111111-1-1-1-1-1-1-1-1000000000000
χ23222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000000
χ24222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-22222-2-211111111-1-1-1-1-1-1-1-111111111000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-2-2-211112222-1-1-11111-122-2-222-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-11111000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-2-2-211112222-1-1-11111-1-2-222-2-222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-11111000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2-1-1-11111-122-2-2-2-22222-1-1-1-111111111-1-1-1-11111-1-1-1-1000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2-1-1-11111-1-2-22222-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-1000000000000
χ292222-2-2222-2-2-2-2-2-22222-22-222-2-222-2-22-2-222-2-22000000002-2000000000000000022-2-222-2-2000000000000
χ302222-2-2222-2-2-2-2-2-22222-22-222-2-2-2-2222-2-222-2-2200000000-220000000000000000-2-222-2-222000000000000
χ312222-2-2222-2-2-2-2-2-2222-22-22-2-22222-2-22-2-2-2-222200000000-22000000000000000022-2-2-2-222000000000000
χ322222-2-2222-2-2-2-2-2-2222-22-22-2-222-2-2222-2-2-2-2222000000002-20000000000000000-2-22222-2-2000000000000
χ332222-2-22-2-222-2-2-2-22222-2-2222-2-20000-222-2-222-200000000000000000000000000000000002-22-200000000
χ342222-2-22-2-222-2-2-2-22222-2-2222-2-20000-222-2-222-20000000000000000000000000000000000-22-2200000000
χ352222-2-22-2-222-2-2-2-2222-222-2-2-2220000-22222-2-2-200000000000000000000000000000000002-2-2200000000
χ362222-2-22-2-222-2-2-2-2222-222-2-2-2220000-22222-2-2-20000000000000000000000000000000000-222-200000000
χ372222-2-2-122-2-21111-1-1-12-22-2-1-11122-2-2-111-1-111-1000000002-2−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-1-111-1-111000000000000
χ382222-2-2-122-2-21111-1-1-12-22-2-1-11122-2-2-111-1-111-1000000002-2i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-1-111-1-111000000000000
χ392222-2-2-122-2-21111-1-1-12-22-2-1-111-2-222-111-1-111-100000000-22−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i311-1-111-1-1000000000000
χ402222-2-2-122-2-21111-1-1-12-22-2-1-111-2-222-111-1-111-100000000-22i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i311-1-111-1-1000000000000
χ412222-2-2-122-2-21111-1-1-1-22-2211-1-122-2-2-11111-1-1-100000000-22−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-1-11111-1-1000000000000
χ422222-2-2-122-2-21111-1-1-1-22-2211-1-122-2-2-11111-1-1-100000000-22i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-1-11111-1-1000000000000
χ432222-2-2-122-2-21111-1-1-1-22-2211-1-1-2-222-11111-1-1-1000000002-2−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i311-1-1-1-111000000000000
χ442222-2-2-122-2-21111-1-1-1-22-2211-1-1-2-222-11111-1-1-1000000002-2i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i311-1-1-1-111000000000000
χ4522-2-22-22-222-222-2-22-2-2000000002-22-2-22-200002002i−2i002i−2i0000002i−2i2i−2i00002i−2i2i−2i2-22-20000000000000000
χ4622-2-22-22-222-222-2-22-2-2000000002-22-2-22-20000200−2i2i00−2i2i000000−2i2i−2i2i0000−2i2i−2i2i2-22-20000000000000000
χ4722-2-22-22-222-222-2-22-2-200000000-22-22-22-200002002i−2i00−2i2i0000002i−2i2i−2i0000−2i2i−2i2i-22-220000000000000000
χ4822-2-22-22-222-222-2-22-2-200000000-22-22-22-20000200−2i2i002i−2i000000−2i2i−2i2i00002i−2i2i−2i-22-220000000000000000
χ4922-2-22-2-1-222-2-1-111-1110000−i3i3−i3i32-22-21-11−i3i3−i3i3-1002i−2i002i−2i003−33−3−ii−ii3−33−3−ii−ii-11-11−i3i3−i3i3000000000000
χ5022-2-22-2-1-222-2-1-111-1110000−i3i3−i3i32-22-21-11−i3i3−i3i3-100−2i2i00−2i2i00−33−33i−ii−i−33−33i−ii−i-11-11−i3i3−i3i3000000000000
χ5122-2-22-2-1-222-2-1-111-1110000−i3i3−i3i3-22-221-11−i3i3−i3i3-1002i−2i00−2i2i003−33−3−ii−ii−33−33i−ii−i1-11-1i3−i3i3−i3000000000000
χ5222-2-22-2-1-222-2-1-111-1110000−i3i3−i3i3-22-221-11−i3i3−i3i3-100−2i2i002i−2i00−33−33i−ii−i3−33−3−ii−ii1-11-1i3−i3i3−i3000000000000
χ5322-2-22-2-1-222-2-1-111-1110000i3−i3i3−i32-22-21-11i3−i3i3−i3-1002i−2i002i−2i00−33−33−ii−ii−33−33−ii−ii-11-11i3−i3i3−i3000000000000
χ5422-2-22-2-1-222-2-1-111-1110000i3−i3i3−i32-22-21-11i3−i3i3−i3-100−2i2i00−2i2i003−33−3i−ii−i3−33−3i−ii−i-11-11i3−i3i3−i3000000000000
χ5522-2-22-2-1-222-2-1-111-1110000i3−i3i3−i3-22-221-11i3−i3i3−i3-1002i−2i00−2i2i00−33−33−ii−ii3−33−3i−ii−i1-11-1−i3i3−i3i3000000000000
χ5622-2-22-2-1-222-2-1-111-1110000i3−i3i3−i3-22-221-11i3−i3i3−i3-100−2i2i002i−2i003−33−3i−ii−i−33−33−ii−ii1-11-1−i3i3−i3i3000000000000
χ5722-2-2-222-22-22-2-2222-2-2000000002-2-22-2-22000022i−2i002i−2i00002i−2i−2i2i00002i−2i−2i2i00002-2-220000000000000000
χ5822-2-2-222-22-22-2-2222-2-2000000002-2-22-2-2200002−2i2i00−2i2i0000−2i2i2i−2i0000−2i2i2i−2i00002-2-220000000000000000
χ5922-2-2-222-22-22-2-2222-2-200000000-222-2-2-22000022i−2i00−2i2i00002i−2i−2i2i0000−2i2i2i−2i0000-222-20000000000000000
χ6022-2-2-222-22-22-2-2222-2-200000000-222-2-2-2200002−2i2i002i−2i0000−2i2i2i−2i00002i−2i−2i2i0000-222-20000000000000000
χ6122-2-2-22-1-22-2211-1-1-1110000−i3i3i3−i32-2-2211-1−i3i3i3−i3-12i−2i002i−2i0000−iii−i3−3−33−iii−i3−3−33-111-1−i3i3i3−i3000000000000
χ6222-2-2-22-1-22-2211-1-1-1110000−i3i3i3−i32-2-2211-1−i3i3i3−i3-1−2i2i00−2i2i0000i−i−ii−333−3i−i−ii−333−3-111-1−i3i3i3−i3000000000000
χ6322-2-2-22-1-22-2211-1-1-1110000−i3i3i3−i3-222-211-1−i3i3i3−i3-12i−2i00−2i2i0000−iii−i3−3−33i−i−ii−333−31-1-11i3−i3−i3i3000000000000
χ6422-2-2-22-1-22-2211-1-1-1110000−i3i3i3−i3-222-211-1−i3i3i3−i3-1−2i2i002i−2i0000i−i−ii−333−3−iii−i3−3−331-1-11i3−i3−i3i3000000000000
χ6522-2-2-22-1-22-2211-1-1-1110000i3−i3−i3i32-2-2211-1i3−i3−i3i3-12i−2i002i−2i0000−iii−i−333−3−iii−i−333−3-111-1i3−i3−i3i3000000000000
χ6622-2-2-22-1-22-2211-1-1-1110000i3−i3−i3i32-2-2211-1i3−i3−i3i3-1−2i2i00−2i2i0000i−i−ii3−3−33i−i−ii3−3−33-111-1i3−i3−i3i3000000000000
χ6722-2-2-22-1-22-2211-1-1-1110000i3−i3−i3i3-222-211-1i3−i3−i3i3-12i−2i00−2i2i0000−iii−i−333−3i−i−ii3−3−331-1-11−i3i3i3−i3000000000000
χ6822-2-2-22-1-22-2211-1-1-1110000i3−i3−i3i3-222-211-1i3−i3−i3i3-1−2i2i002i−2i0000i−i−ii3−3−33−iii−i−333−31-1-11−i3i3i3−i3000000000000
χ69444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4-2-2-2-20000222222220000000000000000000000000000000000000000000000
χ70444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44422220000222-2-2-2-220000000000000000000000000000000000000000000000
χ714444-4-4-2-4-4442222-2-2-24-4-44-2-22200002-2-222-2-220000000000000000000000000000000000000000000000
χ724444-4-4-2-4-4442222-2-2-2-444-422-2-200002-2-2-2-22220000000000000000000000000000000000000000000000
χ7344-4-44-444-4-4444-4-44-4-40000000000004-440000-40000000000000000000000000000000000000000000000
χ7444-4-44-4-24-4-44-2-222-2220000−2i32i3−2i32i30000-22-22i3−2i32i3−2i320000000000000000000000000000000000000000000000
χ7544-4-44-4-24-4-44-2-222-22200002i3−2i32i3−2i30000-22-2−2i32i3−2i32i320000000000000000000000000000000000000000000000
χ7644-4-4-4444-44-4-4-4444-4-400000000000044-40000-40000000000000000000000000000000000000000000000
χ7744-4-4-44-24-44-422-2-2-2220000−2i32i32i3−2i30000-2-222i3−2i3−2i32i320000000000000000000000000000000000000000000000
χ7844-4-4-44-24-44-422-2-2-22200002i3−2i3−2i32i30000-2-22−2i32i32i3−2i320000000000000000000000000000000000000000000000
χ798-88-800800000000-88-8000000000000000000000000000000000000000000000000000000000000000000
χ808-88-800-40000−4i34i3−4i34i34-44000000000000000000000000000000000000000000000000000000000000000000
χ818-88-800-400004i3−4i34i3−4i34-44000000000000000000000000000000000000000000000000000000000000000000
χ828-8-8800800000000-8-88000000000000000000000000000000000000000000000000000000000000000000
χ838-8-8800-40000−4i34i34i3−4i344-4000000000000000000000000000000000000000000000000000000000000000000
χ848-8-8800-400004i3−4i3−4i34i344-4000000000000000000000000000000000000000000000000000000000000000000

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