Finite Group Databasebeta

← Group #10883564

Character table — Group #10883564

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size112222222222222222244444444444444444448888888888888888888888888888888888242424242424242448484848
order12222344446881212242424244444666888121212242424242424224466668888881212121212121212242424242424242424242424224444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-11111111111111111-11-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111-1-1-1-11111111111111111-11-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111-1-1-1-1111111111111111-11-11-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ81111111111111111111-1-1-1-1111111111111111-11-11-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ911111111111-1-111-1-1-1-11111111-1-1-1111-1-1-1-1-1-11-11-111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-11-1
χ1011111111111-1-111-1-1-1-11111111-1-1-1111-1-1-1-1-1-11-11-111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-11-11
χ1111111111111-1-111-1-1-1-11111111-1-1-1111-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-11-11
χ1211111111111-1-111-1-1-1-11111111-1-1-1111-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111-11-1
χ1311111111111-1-111-1-1-1-1-1-1-1-1111-1-1-1111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ1411111111111-1-111-1-1-1-1-1-1-1-1111-1-1-1111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ1511111111111-1-111-1-1-1-1-1-1-1-1111-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-111-1
χ1611111111111-1-111-1-1-1-1-1-1-1-1111-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-11-1-11
χ1722222-12222-122-1-1-1-1-1-12222-1-1-1222-1-1-1-1-1-1-1-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ1822222-12222-122-1-1-1-1-1-12222-1-1-1222-1-1-1-1-1-1-1-1-1-2-2-2-2111122-2-2-2-21111-1-1-1-111111111-1-1-1-1000000000000
χ1922222-12222-122-1-1-1-1-1-1-2-2-2-2-1-1-1222-1-1-1-1-1-1-1-1-12-22-2-1-111-2-222-2-2-1-1111111-1-1-1-111111111000000000000
χ2022222-12222-122-1-1-1-1-1-1-2-2-2-2-1-1-1222-1-1-1-1-1-1-1-1-1-22-2211-1-1-2-2-2-22211-1-111111111-1-1-1-11111000000000000
χ2122222-12222-1-2-2-1-111112222-1-1-1-2-2-2-1-1-11111112-22-2-1-111-2-2-2-222-1-111-1-1-1-11111-1-1-1-11111000000000000
χ2222222-12222-1-2-2-1-111112222-1-1-1-2-2-2-1-1-1111111-22-2211-1-1-2-222-2-211-1-1-1-1-1-1-1-1-1-111111111000000000000
χ2322222-12222-1-2-2-1-11111-2-2-2-2-1-1-1-2-2-2-1-1-11111112222-1-1-1-122-2-2-2-2-1-1-1-1111111111111-1-1-1-1000000000000
χ2422222-12222-1-2-2-1-11111-2-2-2-2-1-1-1-2-2-2-1-1-1111111-2-2-2-2111122222211111111-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ25222-2-222-22-222222222200002-2-22-2-22-2-222-2-2-2-2000000000000000000000000000000000000002i−2i2i−2i0000
χ26222-2-222-22-222222222200002-2-22-2-22-2-222-2-2-2-200000000000000000000000000000000000000−2i2i−2i2i0000
χ27222-2-222-22-22-2-222-2-2-2-200002-2-2-2222-2-2-2-22222000000000000000000000000000000000000002i−2i−2i2i0000
χ28222-2-222-22-22-2-222-2-2-2-200002-2-2-2222-2-2-2-2222200000000000000000000000000000000000000−2i2i2i−2i0000
χ29222-2-22-22-22200-2-200002i2i−2i−2i2-2-2000-222000000020-20022002i−2i0000-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000
χ30222-2-22-22-22200-2-200002i2i−2i−2i2-2-2000-2220000000-20200-2-200−2i2i0000222i2i−2i−2i−2i−2i2i2i00000000000000000000
χ31222-2-22-22-22200-2-20000−2i−2i2i2i2-2-2000-222000000020-2002200−2i2i0000-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ32222-2-22-22-22200-2-20000−2i−2i2i2i2-2-2000-2220000000-20200-2-2002i−2i000022−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ33222-2-2-1-22-22-1001133−3−32i2i−2i−2i-1110001-1-13−333−3−3020-2−i3i3-1-1002i−2i00−i3i311−i−iii−i−iii33−3−3−i3−i3i3i3000000000000
χ34222-2-2-1-22-22-1001133−3−32i2i−2i−2i-1110001-1-13−333−3−30-202i3−i31100−2i2i00i3−i3-1-1−i−iiiii−i−i−3−333−i3−i3i3i3000000000000
χ35222-2-2-1-22-22-1001133−3−3−2i−2i2i2i-1110001-1-13−333−3−3020-2i3−i3-1-100−2i2i00i3−i311ii−i−iii−i−i33−3−3i3i3−i3−i3000000000000
χ36222-2-2-1-22-22-1001133−3−3−2i−2i2i2i-1110001-1-13−333−3−30-202−i3i311002i−2i00−i3i3-1-1ii−i−i−i−iii−3−333i3i3−i3−i3000000000000
χ37222-2-2-1-22-22-10011−3−3332i2i−2i−2i-1110001-1-1−33−3−333020-2i3−i3-1-1002i−2i00i3−i311−i−iii−i−iii−3−333i3i3−i3−i3000000000000
χ38222-2-2-1-22-22-10011−3−3332i2i−2i−2i-1110001-1-1−33−3−3330-202−i3i31100−2i2i00−i3i3-1-1−i−iiiii−i−i33−3−3i3i3−i3−i3000000000000
χ39222-2-2-1-22-22-10011−3−333−2i−2i2i2i-1110001-1-1−33−3−333020-2−i3i3-1-100−2i2i00−i3i311ii−i−iii−i−i−3−333−i3−i3i3i3000000000000
χ40222-2-2-1-22-22-10011−3−333−2i−2i2i2i-1110001-1-1−33−3−3330-202i3−i311002i−2i00i3−i3-1-1ii−i−i−i−iii33−3−3−i3−i3i3i3000000000000
χ4122-22-2222-2-2200-2-200002i−2i2i−2i-22-20002-2200000020-20220000002i−2i-2-2002i−2i2i−2i00002i−2i2i−2i0000000000000000
χ4222-22-2222-2-2200-2-200002i−2i2i−2i-22-20002-22000000-2020-2-2000000−2i2i22002i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ4322-22-2222-2-2200-2-20000−2i2i−2i2i-22-20002-2200000020-2022000000−2i2i-2-200−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ4422-22-2222-2-2200-2-20000−2i2i−2i2i-22-20002-22000000-2020-2-20000002i−2i2200−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ4522-22-22-2-2222222222220000-22-2-22-2-22-2-2-22-22-200000000000000000000000000000000002-22-200000000
χ4622-22-22-2-2222222222220000-22-2-22-2-22-2-2-22-22-20000000000000000000000000000000000-22-2200000000
χ4722-22-22-2-2222-2-222-2-2-2-20000-22-22-22-22-222-22-2200000000000000000000000000000000002-2-2200000000
χ4822-22-22-2-2222-2-222-2-2-2-20000-22-22-22-22-222-22-220000000000000000000000000000000000-222-200000000
χ4922-22-2-122-2-2-1001133−3−32i−2i2i−2i1-11000-11-1−33−333−320-20-1-1−i3i300002i−2i11−i3i3−ii−ii3−33−3−ii−ii−i3i3−i3i3000000000000
χ5022-22-2-122-2-2-1001133−3−32i−2i2i−2i1-11000-11-1−33−333−3-202011i3−i30000−2i2i-1-1i3−i3−ii−ii−33−33i−ii−i−i3i3−i3i3000000000000
χ5122-22-2-122-2-2-1001133−3−3−2i2i−2i2i1-11000-11-1−33−333−320-20-1-1i3−i30000−2i2i11i3−i3i−ii−i3−33−3i−ii−ii3−i3i3−i3000000000000
χ5222-22-2-122-2-2-1001133−3−3−2i2i−2i2i1-11000-11-1−33−333−3-202011−i3i300002i−2i-1-1−i3i3i−ii−i−33−33−ii−iii3−i3i3−i3000000000000
χ5322-22-2-122-2-2-10011−3−3332i−2i2i−2i1-11000-11-13−33−3−3320-20-1-1i3−i300002i−2i11i3−i3−ii−ii−33−33−ii−iii3−i3i3−i3000000000000
χ5422-22-2-122-2-2-10011−3−3332i−2i2i−2i1-11000-11-13−33−3−33-202011−i3i30000−2i2i-1-1−i3i3−ii−ii3−33−3i−ii−ii3−i3i3−i3000000000000
χ5522-22-2-122-2-2-10011−3−333−2i2i−2i2i1-11000-11-13−33−3−3320-20-1-1−i3i30000−2i2i11−i3i3i−ii−i−33−33i−ii−i−i3i3−i3i3000000000000
χ5622-22-2-122-2-2-10011−3−333−2i2i−2i2i1-11000-11-13−33−3−33-202011i3−i300002i−2i-1-1i3−i3i−ii−i3−33−3−ii−ii−i3i3−i3i3000000000000
χ5722-2-222-222-22222222222-2-22-2-22-2-22-2-22-2-2-22-22000000002-2000000002-2-22000000002-2-22000000000000
χ5822-2-222-222-2222222222-222-2-2-22-2-22-2-22-2-2-22-2200000000-2200000000-222-200000000-222-2000000000000
χ5922-2-222-222-22-2-222-2-2-2-22-2-22-2-2222-2-2-22222-22-200000000-22000000002-2-2200000000-222-2000000000000
χ6022-2-222-222-22-2-222-2-2-2-2-222-2-2-2222-2-2-22222-22-2000000002-200000000-222-2000000002-2-22000000000000
χ6122-2-22-1-222-2-122-1-1-1-1-1-12-2-2211-1-2-2211-1111-11-10000−i3i3−i3i32-20000i3−i3i3−i3-111-1−i3i3i3−i3−i3i3i3−i3-111-1000000000000
χ6222-2-22-1-222-2-122-1-1-1-1-1-12-2-2211-1-2-2211-1111-11-10000i3−i3i3−i32-20000−i3i3−i3i3-111-1i3−i3−i3i3i3−i3−i3i3-111-1000000000000
χ6322-2-22-1-222-2-122-1-1-1-1-1-1-222-211-1-2-2211-1111-11-10000−i3i3i3−i3-220000i3−i3−i3i31-1-11−i3i3i3−i3i3−i3−i3i31-1-11000000000000
χ6422-2-22-1-222-2-122-1-1-1-1-1-1-222-211-1-2-2211-1111-11-10000i3−i3−i3i3-220000−i3i3i3−i31-1-11i3−i3−i3i3−i3i3i3−i31-1-11000000000000
χ6522-2-22-1-222-2-1-2-2-1-111112-2-2211-122-211-1-1-1-11-110000−i3i3i3−i3-220000i3−i3−i3i3-111-1i3−i3−i3i3−i3i3i3−i31-1-11000000000000
χ6622-2-22-1-222-2-1-2-2-1-111112-2-2211-122-211-1-1-1-11-110000i3−i3−i3i3-220000−i3i3i3−i3-111-1−i3i3i3−i3i3−i3−i3i31-1-11000000000000
χ6722-2-22-1-222-2-1-2-2-1-11111-222-211-122-211-1-1-1-11-110000−i3i3−i3i32-20000i3−i3i3−i31-1-11i3−i3−i3i3i3−i3−i3i3-111-1000000000000
χ6822-2-22-1-222-2-1-2-2-1-11111-222-211-122-211-1-1-1-11-110000i3−i3i3−i32-20000−i3i3−i3i31-1-11−i3i3i3−i3−i3i3i3−i3-111-1000000000000
χ69444444-4-4-4-4400-4-400000000444000-4-4-40000000000000000000000000000000000000000000000000000
χ7044444-2-4-4-4-4-200222323−23−230000-2-2-200022223−23−23−2323230000000000000000000000000000000000000000000000
χ7144444-2-4-4-4-4-20022−23−2323230000-2-2-2000222−23232323−23−230000000000000000000000000000000000000000000000
χ72444-4-4-24-44-4-244-2-2-2-2-2-20000-2224-4-4-222-2-222220000000000000000000000000000000000000000000000
χ73444-4-4-24-44-4-2-4-4-2-222220000-222-444-22222-2-2-2-20000000000000000000000000000000000000000000000
χ7444-44-4-2-4-444-244-2-2-2-2-2-200002-22-44-42-2222-22-220000000000000000000000000000000000000000000000
χ7544-44-4-2-4-444-2-4-4-2-2222200002-224-442-22-2-22-22-20000000000000000000000000000000000000000000000
χ7644-4-4444-4-44400-4-400000000-4-4400044-40000000000000000000000000000000000000000000000000000
χ7744-4-44-24-4-44-200222323−23−23000022-2000-2-22−232323−23−23230000000000000000000000000000000000000000000000
χ7844-4-44-24-4-44-20022−23−232323000022-2000-2-2223−23−232323−230000000000000000000000000000000000000000000000
χ798-800080000-8−4i24i200−4i24i2−4i24i200000000000000000000000000000000000000000000000000000000000000000
χ808-800080000-84i2−4i2004i2−4i24i2−4i200000000000000000000000000000000000000000000000000000000000000000
χ818-8000-400004−4i24i243−434ζ5+4ζ7−4ζ5−4ζ74ζ13+4ζ23−4ζ13−4ζ2300000000000000000000000000000000000000000000000000000000000000000
χ828-8000-400004−4i24i2−43434ζ13+4ζ23−4ζ13−4ζ234ζ5+4ζ7−4ζ5−4ζ700000000000000000000000000000000000000000000000000000000000000000
χ838-8000-4000044i2−4i243−43−4ζ5−4ζ74ζ5+4ζ7−4ζ13−4ζ234ζ13+4ζ2300000000000000000000000000000000000000000000000000000000000000000
χ848-8000-4000044i2−4i2−4343−4ζ13−4ζ234ζ13+4ζ23−4ζ5−4ζ74ζ5+4ζ700000000000000000000000000000000000000000000000000000000000000000

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