Finite Group Databasebeta

← Group #13166263

Character table — Group #13166263

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size112224444444444444444991818183636363622444888888888888888818183636367272727233666121212121212121212121212121212122727545454108108108108
order12488336612121212242424242424242444288888836122424336612121212242424242424242412126242424242424224886666121212122424242424242424442888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-1
χ3111111111111111111111-1-1-1-1-1ii−i−i111111111111111111111-1-1-1-1-1ii−i−i111111111111111111111-1-1-1-1-1ii−i−i
χ4111111111111111111111-1-1-1-1-1−i−iii111111111111111111111-1-1-1-1-1−i−iii111111111111111111111-1-1-1-1-1−i−iii
χ5111-1-111111111-1-1-1-1-1-1-1-1111-1-11-11-1111-1-111111111-1-1-1-1-1-1-1-1111-1-11-11-1111-1-111111111-1-1-1-1-1-1-1-1111-1-11-11-1
χ6111-1-111111111-1-1-1-1-1-1-1-1111-1-1-11-11111-1-111111111-1-1-1-1-1-1-1-1111-1-1-11-11111-1-111111111-1-1-1-1-1-1-1-1111-1-1-11-11
χ7111-1-111111111-1-1-1-1-1-1-1-1-1-1-111i−i−ii111-1-111111111-1-1-1-1-1-1-1-1-1-1-111i−i−ii111-1-111111111-1-1-1-1-1-1-1-1-1-1-111i−i−ii
χ8111-1-111111111-1-1-1-1-1-1-1-1-1-1-111−iii−i111-1-111111111-1-1-1-1-1-1-1-1-1-1-111−iii−i111-1-111111111-1-1-1-1-1-1-1-1-1-1-111−iii−i
χ922-2002222-2-2-2-20000000022-200000022-2002222-2-2-2-20000000022-200000022-2002222-2-2-2-20000000022-2000000
χ1022-2002222-2-2-2-200000000-2-2200000022-2002222-2-2-2-200000000-2-2200000022-2002222-2-2-2-200000000-2-22000000
χ112-202−222-2-200002222−2−2−2−22i−2i0i2−i200002-202−222-2-200002222−2−2−2−22i−2i0i2−i200002-202−222-2-200002222−2−2−2−22i−2i0i2−i20000
χ122-202−222-2-200002222−2−2−2−2−2i2i0−i2i200002-202−222-2-200002222−2−2−2−2−2i2i0−i2i200002-202−222-2-200002222−2−2−2−2−2i2i0−i2i20000
χ132-20−2222-2-20000−2−2−2−222222i−2i0−i2i200002-20−2222-2-20000−2−2−2−222222i−2i0−i2i200002-20−2222-2-20000−2−2−2−222222i−2i0−i2i20000
χ142-20−2222-2-20000−2−2−2−22222−2i2i0i2−i200002-20−2222-2-20000−2−2−2−22222−2i2i0i2−i200002-20−2222-2-20000−2−2−2−22222−2i2i0i2−i20000
χ15444441-21-211-2-211-2-211-2-2000000000444441-21-211-2-211-2-211-2-2000000000444441-21-211-2-211-2-211-2-2000000000
χ1644444-21-21-2-211-2-211-2-21100000000044444-21-21-2-211-2-211-2-21100000000044444-21-21-2-211-2-211-2-211000000000
χ17444-4-41-21-211-2-2-1-122-1-122000000000444-4-41-21-211-2-2-1-122-1-122000000000444-4-41-21-211-2-2-1-122-1-122000000000
χ18444-4-4-21-21-2-21122-1-122-1-1000000000444-4-4-21-21-2-21122-1-122-1-1000000000444-4-4-21-21-2-21122-1-122-1-1000000000
χ1944-4001-21-2-1-1223i−3i003i−3i0000000000044-4001-21-2-1-1223i−3i003i−3i0000000000044-4001-21-2-1-1223i−3i003i−3i00000000000
χ2044-4001-21-2-1-122−3i3i00−3i3i0000000000044-4001-21-2-1-122−3i3i00−3i3i0000000000044-4001-21-2-1-122−3i3i00−3i3i00000000000
χ2144-400-21-2122-1-1003i−3i003i−3i00000000044-400-21-2122-1-1003i−3i003i−3i00000000044-400-21-2122-1-1003i−3i003i−3i000000000
χ2244-400-21-2122-1-100−3i3i00−3i3i00000000044-400-21-2122-1-100−3i3i00−3i3i00000000044-400-21-2122-1-100−3i3i00−3i3i000000000
χ234-4022−221-2-123i−3i002ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ3220000000004-4022−221-2-123i−3i002ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ3220000000004-4022−221-2-123i−3i002ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ322000000000
χ244-4022−221-2-12−3i3i00−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ3220000000004-4022−221-2-12−3i3i00−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ3220000000004-4022−221-2-12−3i3i00−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ322000000000
χ254-4022−22-212-1003i−3i−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ30000000004-4022−22-212-1003i−3i−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ30000000004-4022−22-212-1003i−3i−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3000000000
χ264-4022−22-212-100−3i3i−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ30000000004-4022−22-212-100−3i3i−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ30000000004-4022−22-212-100−3i3i−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ3000000000
χ274-40−22221-2-123i−3i00−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−20000000004-40−22221-2-123i−3i00−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−20000000004-40−22221-2-123i−3i00−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−2000000000
χ284-40−22221-2-12−3i3i00ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−20000000004-40−22221-2-12−3i3i00ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−20000000004-40−22221-2-12−3i3i00ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−2000000000
χ294-40−2222-212-1003i−3i22−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ30000000004-40−2222-212-1003i−3i22−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ30000000004-40−2222-212-1003i−3i22−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ3000000000
χ304-40−2222-212-100−3i3i22ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ30000000004-40−2222-212-100−3i3i22ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ30000000004-40−2222-212-100−3i3i22ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ3000000000
χ31111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3211111111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ33111111111111111111111-1-1-1-1-1ii−i−i111111111111111111111-1-1-1-1-1ii−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111−i−iii
χ34111111111111111111111-1-1-1-1-1−i−iii111111111111111111111-1-1-1-1-1−i−iii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111ii−i−i
χ35111-1-111111111-1-1-1-1-1-1-1-1111-1-11-11-1111-1-111111111-1-1-1-1-1-1-1-1111-1-11-11-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-111-11-11
χ36111-1-111111111-1-1-1-1-1-1-1-1111-1-1-11-11111-1-111111111-1-1-1-1-1-1-1-1111-1-1-11-11-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1111-11-1
χ37111-1-111111111-1-1-1-1-1-1-1-1-1-1-111i−i−ii111-1-111111111-1-1-1-1-1-1-1-1-1-1-111i−i−ii-1-1-111-1-1-1-1-1-1-1-111111111111-1-1−iii−i
χ38111-1-111111111-1-1-1-1-1-1-1-1-1-1-111−iii−i111-1-111111111-1-1-1-1-1-1-1-1-1-1-111−iii−i-1-1-111-1-1-1-1-1-1-1-111111111111-1-1i−i−ii
χ3922-2002222-2-2-2-20000000022-200000022-2002222-2-2-2-20000000022-2000000-2-2200-2-2-2-2222200000000-2-22000000
χ4022-2002222-2-2-2-200000000-2-2200000022-2002222-2-2-2-200000000-2-22000000-2-2200-2-2-2-222220000000022-2000000
χ412-202−222-2-200002222−2−2−2−22i−2i0i2−i200002-202−222-2-200002222−2−2−2−22i−2i0i2−i20000-220−22-2-2220000−2−2−2−22222−2i2i0−i2i20000
χ422-202−222-2-200002222−2−2−2−2−2i2i0−i2i200002-202−222-2-200002222−2−2−2−2−2i2i0−i2i20000-220−22-2-2220000−2−2−2−222222i−2i0i2−i20000
χ432-20−2222-2-20000−2−2−2−222222i−2i0−i2i200002-20−2222-2-20000−2−2−2−222222i−2i0−i2i20000-2202−2-2-22200002222−2−2−2−2−2i2i0i2−i20000
χ442-20−2222-2-20000−2−2−2−22222−2i2i0i2−i200002-20−2222-2-20000−2−2−2−22222−2i2i0i2−i20000-2202−2-2-22200002222−2−2−2−22i−2i0−i2i20000
χ45444441-21-211-2-211-2-211-2-2000000000444441-21-211-2-211-2-211-2-2000000000-4-4-4-4-4-12-12-1-122-1-122-1-122000000000
χ4644444-21-21-2-211-2-211-2-21100000000044444-21-21-2-211-2-211-2-211000000000-4-4-4-4-42-12-122-1-122-1-122-1-1000000000
χ47444-4-41-21-211-2-2-1-122-1-122000000000444-4-41-21-211-2-2-1-122-1-122000000000-4-4-444-12-12-1-12211-2-211-2-2000000000
χ48444-4-4-21-21-2-21122-1-122-1-1000000000444-4-4-21-21-2-21122-1-122-1-1000000000-4-4-4442-12-122-1-1-2-211-2-211000000000
χ4944-4001-21-2-1-1223i−3i003i−3i0000000000044-4001-21-2-1-1223i−3i003i−3i00000000000-4-4400-12-1211-2-2−3i3i00−3i3i00000000000
χ5044-4001-21-2-1-122−3i3i00−3i3i0000000000044-4001-21-2-1-122−3i3i00−3i3i00000000000-4-4400-12-1211-2-23i−3i003i−3i00000000000
χ5144-400-21-2122-1-1003i−3i003i−3i00000000044-400-21-2122-1-1003i−3i003i−3i000000000-4-44002-12-1-2-21100−3i3i00−3i3i000000000
χ5244-400-21-2122-1-100−3i3i00−3i3i00000000044-400-21-2122-1-100−3i3i00−3i3i000000000-4-44002-12-1-2-211003i−3i003i−3i000000000
χ534-4022−221-2-123i−3i002ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ3220000000004-4022−221-2-123i−3i002ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ322000000000-440−2222-121-2−3i3i00−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−2000000000
χ544-4022−221-2-12−3i3i00−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ3220000000004-4022−221-2-12−3i3i00−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ322000000000-440−2222-121-23i−3i00ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−2000000000
χ554-4022−22-212-1003i−3i−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ30000000004-4022−22-212-1003i−3i−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3000000000-440−22222-1-2100−3i3i22−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ3000000000
χ564-4022−22-212-100−3i3i−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ30000000004-4022−22-212-100−3i3i−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ3000000000-440−22222-1-21003i−3i22ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ3000000000
χ574-40−22221-2-123i−3i00−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−20000000004-40−22221-2-123i−3i00−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−2000000000-44022−22-121-2−3i3i002ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ322000000000
χ584-40−22221-2-12−3i3i00ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−20000000004-40−22221-2-12−3i3i00ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−2000000000-44022−22-121-23i−3i00−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ322000000000
χ594-40−2222-212-1003i−3i22−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ30000000004-40−2222-212-1003i−3i22−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ3000000000-44022−222-1-2100−3i3i−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3000000000
χ604-40−2222-212-100−3i3i22ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ30000000004-40−2222-212-100−3i3i22ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ3000000000-44022−222-1-21003i−3i−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ3000000000
χ61222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000
χ6222222222222222222222222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111000000000000000000000000000000
χ63222222222222222222222-2-2-2-2-22i2i−2i−2i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111−i−iii000000000000000000000000000000
χ64222222222222222222222-2-2-2-2-2−2i−2i2i2i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111ii−i−i000000000000000000000000000000
χ65222-2-222222222-2-2-2-2-2-2-2-2222-2-22-22-2-1-1-111-1-1-1-1-1-1-1-111111111-1-1-111-11-11000000000000000000000000000000
χ66222-2-222222222-2-2-2-2-2-2-2-2222-2-2-22-22-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1111-11-1000000000000000000000000000000
χ67222-2-222222222-2-2-2-2-2-2-2-2-2-2-2222i−2i−2i2i-1-1-111-1-1-1-1-1-1-1-111111111111-1-1−iii−i000000000000000000000000000000
χ68222-2-222222222-2-2-2-2-2-2-2-2-2-2-222−2i2i2i−2i-1-1-111-1-1-1-1-1-1-1-111111111111-1-1i−i−ii000000000000000000000000000000
χ6944-4004444-4-4-4-40000000044-4000000-2-2200-2-2-2-2222200000000-2-22000000000000000000000000000000000000
χ7044-4004444-4-4-4-400000000-4-44000000-2-2200-2-2-2-222220000000022-2000000000000000000000000000000000000
χ714-4022−2244-4-4000022222222−22−22−22−224i−4i02i2−2i20000-220−22-2-2220000−2−2−2−22222−2i2i0−i2i20000000000000000000000000000000000
χ724-4022−2244-4-4000022222222−22−22−22−22−4i4i0−2i22i20000-220−22-2-2220000−2−2−2−222222i−2i0i2−i20000000000000000000000000000000000
χ734-40−222244-4-40000−22−22−22−22222222224i−4i0−2i22i20000-2202−2-2-22200002222−2−2−2−2−2i2i0i2−i20000000000000000000000000000000000
χ744-40−222244-4-40000−22−22−22−2222222222−4i4i02i2−2i20000-2202−2-2-22200002222−2−2−2−22i−2i0−i2i20000000000000000000000000000000000
χ75888882-42-422-4-422-4-422-4-4000000000-4-4-4-4-4-12-12-1-122-1-122-1-122000000000000000000000000000000000000000
χ7688888-42-42-4-422-4-422-4-422000000000-4-4-4-4-42-12-122-1-122-1-122-1-1000000000000000000000000000000000000000
χ77888-8-82-42-422-4-4-2-244-2-244000000000-4-4-444-12-12-1-12211-2-211-2-2000000000000000000000000000000000000000
χ78888-8-8-42-42-4-42244-2-244-2-2000000000-4-4-4442-12-122-1-1-2-211-2-211000000000000000000000000000000000000000
χ7988-8002-42-4-2-2446i−6i006i−6i00000000000-4-4400-12-1211-2-2−3i3i00−3i3i00000000000000000000000000000000000000000
χ8088-8002-42-4-2-244−6i6i00−6i6i00000000000-4-4400-12-1211-2-23i−3i003i−3i00000000000000000000000000000000000000000
χ8188-800-42-4244-2-2006i−6i006i−6i000000000-4-44002-12-1-2-21100−3i3i00−3i3i000000000000000000000000000000000000000
χ8288-800-42-4244-2-200−6i6i00−6i6i000000000-4-44002-12-1-2-211003i−3i003i−3i000000000000000000000000000000000000000
χ838-8042−422-4-246i−6i004ζ+2ζ3−2ζ−4ζ3−22−22−4ζ−2ζ32ζ+4ζ32222000000000-440−2222-121-2−3i3i00−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−2000000000000000000000000000000000000000
χ848-8042−422-4-24−6i6i00−2ζ−4ζ34ζ+2ζ3−22−222ζ+4ζ3−4ζ−2ζ32222000000000-440−2222-121-23i−3i00ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−2000000000000000000000000000000000000000
χ858-8042−42-424-2006i−6i−22−224ζ+2ζ3−2ζ−4ζ32222−4ζ−2ζ32ζ+4ζ3000000000-440−22222-1-2100−3i3i22−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ3000000000000000000000000000000000000000
χ868-8042−42-424-200−6i6i−22−22−2ζ−4ζ34ζ+2ζ322222ζ+4ζ3−4ζ−2ζ3000000000-440−22222-1-21003i−3i22ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ3000000000000000000000000000000000000000
χ878-80−42422-4-246i−6i00−4ζ−2ζ32ζ+4ζ322224ζ+2ζ3−2ζ−4ζ3−22−22000000000-44022−22-121-2−3i3i002ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ322000000000000000000000000000000000000000
χ888-80−42422-4-24−6i6i002ζ+4ζ3−4ζ−2ζ32222−2ζ−4ζ34ζ+2ζ3−22−22000000000-44022−22-121-23i−3i00−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ322000000000000000000000000000000000000000
χ898-80−4242-424-2006i−6i2222−4ζ−2ζ32ζ+4ζ3−22−224ζ+2ζ3−2ζ−4ζ3000000000-44022−222-1-2100−3i3i−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3000000000000000000000000000000000000000
χ908-80−4242-424-200−6i6i22222ζ+4ζ3−4ζ−2ζ3−22−22−2ζ−4ζ34ζ+2ζ3000000000-44022−222-1-21003i−3i−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ3000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.