Finite Group Databasebeta

← Group #10877351

Character table — Group #10877351

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222224444444444444444444444448888888888888888888888888888888812121212121212122424242448484848
order12442223444688881212224466666668812121212121212242424248888888888242424242424242424242424242424242424242424242244888844888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ9111111111111-1-1-1-11111111111111-1-11111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-11-1
χ10111111111111-1-1-1-11111111111111-1-11111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-11
χ11111111111111-1-1-1-11111111111111-1-11111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-11-11
χ12111111111111-1-1-1-11111111111111-1-11111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111-11-1
χ13111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-111-1-1-1-11-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1111-1-11
χ14111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-111-1-1-1-11-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-111-1
χ15111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-111-1-1-1-11-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111-111-1
χ16111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-111-1-1-1-11-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1111111-1-11-1-11
χ172222222-1222-12222-1-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222-1222-12222-1-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2221111111111111111-1-1-1-1-1-10000000000000000
χ192222222-1222-12222-1-1-2-2-2-2-1-1-1111122-1-11111-1-1-1-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-1-111110000000000000000
χ202222222-1222-12222-1-1-2-2-2-2-1-1-1111122-1-11111-1-1-1-1-1-2-2-2-22222-2-211111111-1-1-1-1-1-1-1-1-1-111110000000000000000
χ212222222-1222-1-2-2-2-2-1-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-1-1-1111122-2-222-2-2-2-2-1-1-1-11111-1-1-1-111111111110000000000000000
χ222222222-1222-1-2-2-2-2-1-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-1-1-11111-2-222-2-222-2-21111-1-1-1-11111-1-1-1-11111110000000000000000
χ232222222-1222-1-2-2-2-2-1-1-2-2-2-2-1-1-11111-2-2-1-11111-1111122-2-2-2-22222-1-1-1-111111111-1-1-1-111-1-1-1-10000000000000000
χ242222222-1222-1-2-2-2-2-1-1-2-2-2-2-1-1-11111-2-2-1-11111-11111-2-22222-2-2221111-1-1-1-1-1-1-1-1111111-1-1-1-10000000000000000
χ252222-2-2222-2-222222222-22-22-2-222-2-2-2-2-2-222-2-222222000000002-20000000000000000-2-222-2-20000000000000000
χ262222-2-2222-2-22222222-22-222-2-2-2-222-2-2-2-2-2-2222222200000000-220000000000000000-2-2-2-2220000000000000000
χ272222-2-2222-2-22-2-2-2-2222-22-22-2-222-2-222-2-222-2-22-2-2-2-200000000-22000000000000000022-2-2220000000000000000
χ282222-2-2222-2-22-2-2-2-222-22-222-2-2-2-22222-2-2-2-2222-2-2-2-2000000002-200000000000000002222-2-20000000000000000
χ292222-2-22-12-2-2-12222-1-12-22-2-111-1-111-2-211-1-111-1-1-1-1-1000000002-2−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i311-1-1110000000000000000
χ302222-2-22-12-2-2-12222-1-12-22-2-111-1-111-2-211-1-111-1-1-1-1-1000000002-2i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i311-1-1110000000000000000
χ312222-2-22-12-2-2-12222-1-1-22-22-11111-1-1-2-21111-1-1-1-1-1-1-100000000-22−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i31111-1-10000000000000000
χ322222-2-22-12-2-2-12222-1-1-22-22-11111-1-1-2-21111-1-1-1-1-1-1-100000000-22i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i31111-1-10000000000000000
χ332222-2-22-12-2-2-1-2-2-2-2-1-12-22-2-111-1-1112211-1-111-1111100000000-22−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-1-111-1-10000000000000000
χ342222-2-22-12-2-2-1-2-2-2-2-1-12-22-2-111-1-1112211-1-111-1111100000000-22i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-1-111-1-10000000000000000
χ352222-2-22-12-2-2-1-2-2-2-2-1-1-22-22-11111-1-1221111-1-1-11111000000002-2−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3-1-1-1-1110000000000000000
χ362222-2-22-12-2-2-1-2-2-2-2-1-1-22-22-11111-1-1221111-1-1-11111000000002-2i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3-1-1-1-1110000000000000000
χ3722-2-22222-2-2-220000-2-22-2-2222222-2-200-2-2-2-222-200000000000000000000000000000000000022-2-200002-2000000
χ3822-2-22222-2-2-220000-2-22-2-2222222-2-200-2-2-2-222-2000000000000000000000000000000000000-2-2220000-22000000
χ3922-2-22222-2-2-220000-2-2-222-2222-2-22200-2-222-2-2-200000000000000000000000000000000000022-2-20000-22000000
χ4022-2-22222-2-2-220000-2-2-222-2222-2-22200-2-222-2-2-2000000000000000000000000000000000000-2-22200002-2000000
χ4122-2-22-2-2222-2222-2-2-2-20000-22-200002-22-20000222-2-200002i−2i2i−2i00000000002i−2i2i−2i2i−2i2i−2i2-200000000000000000000
χ4222-2-22-2-2222-2222-2-2-2-20000-22-200002-22-20000222-2-20000−2i2i−2i2i0000000000−2i2i−2i2i−2i2i−2i2i2-200000000000000000000
χ4322-2-22-2-2222-22-2-222-2-20000-22-20000-222-200002-2-22200002i−2i−2i2i00000000002i−2i2i−2i−2i2i−2i2i-2200000000000000000000
χ4422-2-22-2-2222-22-2-222-2-20000-22-20000-222-200002-2-2220000−2i2i2i−2i0000000000−2i2i−2i2i2i−2i2i−2i-2200000000000000000000
χ4522-2-22-2-2-122-2-122-2-21100001-11−i3i3−i3i32-2-11−i3i3−i3i3-1-1-11100002i−2i2i−2i003−33−33−33−3−ii−ii−ii−ii-11−i3i3−i3i30000000000000000
χ4622-2-22-2-2-122-2-122-2-21100001-11−i3i3−i3i32-2-11−i3i3−i3i3-1-1-1110000−2i2i−2i2i00−33−33−33−33i−ii−ii−ii−i-11−i3i3−i3i30000000000000000
χ4722-2-22-2-2-122-2-122-2-21100001-11i3−i3i3−i32-2-11i3−i3i3−i3-1-1-11100002i−2i2i−2i00−33−33−33−33−ii−ii−ii−ii-11i3−i3i3−i30000000000000000
χ4822-2-22-2-2-122-2-122-2-21100001-11i3−i3i3−i32-2-11i3−i3i3−i3-1-1-1110000−2i2i−2i2i003−33−33−33−3i−ii−ii−ii−i-11i3−i3i3−i30000000000000000
χ4922-2-22-2-2-122-2-1-2-2221100001-11−i3i3−i3i3-22-11−i3i3−i3i3-111-1-100002i−2i−2i2i003−33−3−33−33−ii−iii−ii−i1-1i3−i3i3−i30000000000000000
χ5022-2-22-2-2-122-2-1-2-2221100001-11−i3i3−i3i3-22-11−i3i3−i3i3-111-1-10000−2i2i2i−2i00−33−333−33−3i−ii−i−ii−ii1-1i3−i3i3−i30000000000000000
χ5122-2-22-2-2-122-2-1-2-2221100001-11i3−i3i3−i3-22-11i3−i3i3−i3-111-1-100002i−2i−2i2i00−33−333−33−3−ii−iii−ii−i1-1−i3i3−i3i30000000000000000
χ5222-2-22-2-2-122-2-1-2-2221100001-11i3−i3i3−i3-22-11i3−i3i3−i3-111-1-10000−2i2i2i−2i003−33−3−33−33i−ii−i−ii−ii1-1−i3i3−i3i30000000000000000
χ5322-2-2-22-222-22222-2-2-2-20000-2-220000-22-220000222-2-22i−2i2i−2i0000002i−2i−2i2i2i−2i−2i2i00000000-2200000000000000000000
χ5422-2-2-22-222-22222-2-2-2-20000-2-220000-22-220000222-2-2−2i2i−2i2i000000−2i2i2i−2i−2i2i2i−2i00000000-2200000000000000000000
χ5522-2-2-22-222-222-2-222-2-20000-2-2200002-2-2200002-2-2222i−2i−2i2i0000002i−2i−2i2i−2i2i2i−2i000000002-200000000000000000000
χ5622-2-2-22-222-222-2-222-2-20000-2-2200002-2-2200002-2-222−2i2i2i−2i000000−2i2i2i−2i2i−2i−2i2i000000002-200000000000000000000
χ5722-2-2-22-2-12-22-122-2-211000011-1−i3i3i3−i3-221-1−i3i3i3−i3-1-1-1112i−2i2i−2i000000−iii−i−iii−i3−3−333−3−331-1−i3i3i3−i30000000000000000
χ5822-2-2-22-2-12-22-122-2-211000011-1−i3i3i3−i3-221-1−i3i3i3−i3-1-1-111−2i2i−2i2i000000i−i−iii−i−ii−333−3−333−31-1−i3i3i3−i30000000000000000
χ5922-2-2-22-2-12-22-122-2-211000011-1i3−i3−i3i3-221-1i3−i3−i3i3-1-1-1112i−2i2i−2i000000−iii−i−iii−i−333−3−333−31-1i3−i3−i3i30000000000000000
χ6022-2-2-22-2-12-22-122-2-211000011-1i3−i3−i3i3-221-1i3−i3−i3i3-1-1-111−2i2i−2i2i000000i−i−iii−i−ii3−3−333−3−331-1i3−i3−i3i30000000000000000
χ6122-2-2-22-2-12-22-1-2-22211000011-1−i3i3i3−i32-21-1−i3i3i3−i3-111-1-12i−2i−2i2i000000−iii−ii−i−ii3−3−33−333−3-11i3−i3−i3i30000000000000000
χ6222-2-2-22-2-12-22-1-2-22211000011-1−i3i3i3−i32-21-1−i3i3i3−i3-111-1-1−2i2i2i−2i000000i−i−ii−iii−i−333−33−3−33-11i3−i3−i3i30000000000000000
χ6322-2-2-22-2-12-22-1-2-22211000011-1i3−i3−i3i32-21-1i3−i3−i3i3-111-1-12i−2i−2i2i000000−iii−ii−i−ii−333−33−3−33-11−i3i3i3−i30000000000000000
χ6422-2-2-22-2-12-22-1-2-22211000011-1i3−i3−i3i32-21-1i3−i3−i3i3-111-1-1−2i2i2i−2i000000i−i−ii−iii−i3−3−33−333−3-11−i3i3i3−i30000000000000000
χ6522-2-2-2-222-22220000-2-222-2-22-2-222220022-2-2-2-2-200000000000000000000000000000000000000002i2i−2i−2i002i−2i0000
χ6622-2-2-2-222-22220000-2-222-2-22-2-222220022-2-2-2-2-20000000000000000000000000000000000000000−2i−2i2i2i00−2i2i0000
χ6722-2-2-2-222-22220000-2-2-2-2222-2-2-2-2-2-200222222-200000000000000000000000000000000000000002i2i−2i−2i00−2i2i0000
χ6822-2-2-2-222-22220000-2-2-2-2222-2-2-2-2-2-200222222-20000000000000000000000000000000000000000−2i−2i2i2i002i−2i0000
χ6944444-4-44-4-4440000440000-44-4000000-440000-40000000000000000000000000000000000000000000000000000
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χ744444-44-4-2-44-4-20000-2-2000022-22i3−2i32i3−2i300-22−2i32i3−2i32i320000000000000000000000000000000000000000000000000000
χ7544-4-4444-2-4-4-4-20000224-4-44-2-2-2-2-222002222-2-220000000000000000000000000000000000000000000000000000
χ7644-4-4444-2-4-4-4-2000022-444-4-2-2-222-2-20022-2-22220000000000000000000000000000000000000000000000000000
χ7744-4-4-4-44-2-444-200002244-4-4-222-2-2-2-200-2-2222220000000000000000000000000000000000000000000000000000
χ7844-4-4-4-44-2-444-2000022-4-444-222222200-2-2-2-2-2-220000000000000000000000000000000000000000000000000000
χ794-44i−4i0004000-422−22−2i22i24i−4i0000000000000000000022−22−2i22i2000000000000000000000000000000002-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ804-44i−4i0004000-422−22−2i22i24i−4i0000000000000000000022−22−2i22i200000000000000000000000000000000-22−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ814-44i−4i0004000-4−22222i2−2i24i−4i00000000000000000000−22222i2−2i2000000000000000000000000000000002-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ824-44i−4i0004000-4−22222i2−2i24i−4i00000000000000000000−22222i2−2i200000000000000000000000000000000-22−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ834-4−4i4i0004000-422−222i2−2i2−4i4i0000000000000000000022−222i2−2i2000000000000000000000000000000002-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ844-4−4i4i0004000-422−222i2−2i2−4i4i0000000000000000000022−222i2−2i200000000000000000000000000000000-222i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ854-4−4i4i0004000-4−2222−2i22i2−4i4i00000000000000000000−2222−2i22i2000000000000000000000000000000002-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ864-4−4i4i0004000-4−2222−2i22i2−4i4i00000000000000000000−2222−2i22i200000000000000000000000000000000-222i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ878-88i−8i000-4000442−42−4i24i2−4i4i00000000000000000000−22222i2−2i2000000000000000000000000000000000000000000000000
χ888-88i−8i000-40004−42424i2−4i2−4i4i0000000000000000000022−22−2i22i2000000000000000000000000000000000000000000000000
χ898-8−8i8i000-4000442−424i2−4i24i−4i00000000000000000000−2222−2i22i2000000000000000000000000000000000000000000000000
χ908-8−8i8i000-40004−4242−4i24i24i−4i0000000000000000000022−222i2−2i2000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.