Finite Group Databasebeta

← Group #11780012

Character table — Group #11780012

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size1111222222222222222244444444444444444444444888888888888888888881212121212121212121212121212121212122424242424242424242424242424247272144
order1222334444666666121212123444666121212121212121212121212121212124121212121212121212121212121212121212124488881212121224242424242424244448812121212121224242424884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-111111111-1-1-111-1-1-1-1-1-11111-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ5111111111111111111111-1-111111111-1-1-1-111111111-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-111111111-1-1-1-111111111-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-11
χ7111111111111111111111-1-111111111-1-1-1-111111111-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-111-1-1-1-11111-1-1-1-1-1-11
χ8111111111111111111111-1-111111111-1-1-1-111111111-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1
χ92222222-22-22222222222200-2222-2-2-2-20000222222-2-200000-200-2-2-2-200000000220000222200000000-20000-2-200000000000
χ102222222-22-22222222222200-2222-2-2-2-20000222222-2-200000-200-2-2-2-200000000-2-20000-2-2-2-200000000200002200000000000
χ11222222-22-22222222-2-2-2-2222-222222222222-2-2-2-2-2-2-2-2-222-2-2-2-2-222-2-22222-2-2-2-2000000000000000000000000000000000000
χ12222222-22-22222222-2-2-2-22-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-22-2-222-22222-2-2-2-2-2-22222000000000000000000000000000000000000
χ13222222-2-2-2-2222222-2-2-2-22002222-2-2-2-20000-2-2-2-2-2-22200000200-2-2220000000000000000000000000002-2000022-2-20000000
χ14222222-2-2-2-2222222-2-2-2-22002222-2-2-2-20000-2-2-2-2-2-22200000200-2-222000000000000000000000000000-220000-2-2220000000
χ1522222-12222222-1-1-12222-1222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1220000-1-1-1-10000000022200-1-1-1-1-1-10000000
χ1622222-12222222-1-1-12222-1222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20000111100000000-2-2-2001111110000000
χ1722222-12222222-1-1-12222-1-2-22-1-1-122-1-11111-1-1-1-1-1-122-2-2-2-2-2-111-1-1-1-111111111220000-1-1-1-1000000002-2-200-1-111110000000
χ1822222-12222222-1-1-12222-1-2-22-1-1-122-1-11111-1-1-1-1-1-122-2-2-2-2-2-111-1-1-1-111111111-2-20000111100000000-2220011-1-1-1-10000000
χ1922222-12-22-2222-1-1-12222-100-2-1-1-1-2-211−i3−i3i3i3-1-1-1-1-1-1-2-2000001−i3i31111−i3−i3i3i3−i3−i3i3i3220000-1-1-1-100000000-2000011−i3i3−i3i30000000
χ2022222-12-22-2222-1-1-12222-100-2-1-1-1-2-211−i3−i3i3i3-1-1-1-1-1-1-2-2000001−i3i31111−i3−i3i3i3−i3−i3i3i3-2-2000011110000000020000-1-1i3−i3i3−i30000000
χ2122222-12-22-2222-1-1-12222-100-2-1-1-1-2-211i3i3−i3−i3-1-1-1-1-1-1-2-2000001i3−i31111i3i3−i3−i3i3i3−i3−i3220000-1-1-1-100000000-2000011i3−i3i3−i30000000
χ2222222-12-22-2222-1-1-12222-100-2-1-1-1-2-211i3i3−i3−i3-1-1-1-1-1-1-2-2000001i3−i31111i3i3−i3−i3i3i3−i3−i3-2-2000011110000000020000-1-1−i3i3−i3i30000000
χ2322222-1-22-22222-1-1-1-2-2-2-2-122-2-1-1-122-1-1-1-1-1-1111111-2-2-222-2-2111-1-111-1-1-1-11111000000−i3−i3i3i30000000000000−i3i3−i3i3i3−i30000000
χ2422222-1-22-22222-1-1-1-2-2-2-2-122-2-1-1-122-1-1-1-1-1-1111111-2-2-222-2-2111-1-111-1-1-1-11111000000i3i3−i3−i30000000000000i3−i3i3−i3−i3i30000000
χ2522222-1-22-22222-1-1-1-2-2-2-2-1-2-2-2-1-1-122-1-11111111111-2-22-2-2221-1-1-1-1111111-1-1-1-1000000−i3−i3i3i30000000000000−i3i3i3−i3−i3i30000000
χ2622222-1-22-22222-1-1-1-2-2-2-2-1-2-2-2-1-1-122-1-11111111111-2-22-2-2221-1-1-1-1111111-1-1-1-1000000i3i3−i3−i30000000000000i3−i3−i3i3i3−i30000000
χ2722222-1-2-2-2-2222-1-1-1-2-2-2-2-1002-1-1-1-2-211−i3−i3i3i31111112200000-1i3−i311-1-1−i3−i3i3i3i3i3−i3−i3000000−i3−i3i3i30000000002-200i3−i3-1-1110000000
χ2822222-1-2-2-2-2222-1-1-1-2-2-2-2-1002-1-1-1-2-211−i3−i3i3i31111112200000-1i3−i311-1-1−i3−i3i3i3i3i3−i3−i3000000i3i3−i3−i3000000000-2200−i3i311-1-10000000
χ2922222-1-2-2-2-2222-1-1-1-2-2-2-2-1002-1-1-1-2-211i3i3−i3−i31111112200000-1−i3i311-1-1i3i3−i3−i3−i3−i3i3i3000000−i3−i3i3i3000000000-2200i3−i311-1-10000000
χ3022222-1-2-2-2-2222-1-1-1-2-2-2-2-1002-1-1-1-2-211i3i3−i3−i31111112200000-1−i3i311-1-1i3i3−i3−i3−i3−i3i3i3000000i3i3−i3−i30000000002-200−i3i3-1-1110000000
χ312222-122222-1-1-1222-1-1-1-1-1222-1-1-1-1-122222222-1-1-1-1-1-12-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-10022220000-1-1-1-1-1-1-1-100022000000-1-1-1-1000
χ322222-122222-1-1-1222-1-1-1-1-1222-1-1-1-1-122222222-1-1-1-1-1-12-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-2000011111111000-2-20000001111000
χ332222-122222-1-1-1222-1-1-1-1-1-2-22-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-211112-2-2-1-1-1-1111111110022220000-1-1-1-1-1-1-1-1000-2-20000001111000
χ342222-122222-1-1-1222-1-1-1-1-1-2-22-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-211112-2-2-1-1-1-11111111100-2-2-2-200001111111100022000000-1-1-1-1000
χ352222-12-22-22-1-1-12221111-122-2-1-1-1-1-1222222-2-2111111-2-1-111-2-2-2-1-111-1-1-1-1111100000000003333−3−3−3−30000000000033−3−3000
χ362222-12-22-22-1-1-12221111-122-2-1-1-1-1-1222222-2-2111111-2-1-111-2-2-2-1-111-1-1-1-111110000000000−3−3−3−3333300000000000−3−333000
χ372222-12-22-22-1-1-12221111-1-2-2-2-1-1-1-1-122-2-2-2-2-2-2111111211-1-1-222-1-1111111-1-1-1-100000000003333−3−3−3−300000000000−3−333000
χ382222-12-22-22-1-1-12221111-1-2-2-2-1-1-1-1-122-2-2-2-2-2-2111111211-1-1-222-1-1111111-1-1-1-10000000000−3−3−3−333330000000000033−3−3000
χ3922-2-22220-202-2-2-22-222-2-220002-2-2000000002-222-2-200000000000000000000002-222−2−22-22-222−2−222−2−20000000000000002−20
χ4022-2-22220-202-2-2-22-222-2-220002-2-2000000002-222-2-200000000000000000000002-2−2−2222-22-2−2−222−2−222000000000000000−220
χ4122-2-22220-202-2-2-22-222-2-220002-2-2000000002-222-2-20000000000000000000000-2222−2−2-22-2222−2−222−2−2000000000000000−220
χ4222-2-22220-202-2-2-22-222-2-220002-2-2000000002-222-2-20000000000000000000000-22−2−222-22-22−2−222−2−2220000000000000002−20
χ432-2-22220-202-22-22-2-2000022-20-22-22-22-22-22-20000000002-2000002-2002-22-2000000−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2000−i2i2000000−i2i2−i2i2000
χ442-2-22220-202-22-22-2-2000022-20-22-22-22-22-22-20000000002-2000002-2002-22-2000000i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2000i2−i2000000i2−i2i2−i2000
χ452-2-22220-202-22-22-2-200002-220-22-22-22-2-22-22000000000-22000002-200-22-22000000−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2000i2−i2000000i2−i2i2−i2000
χ462-2-22220-202-22-22-2-200002-220-22-22-22-2-22-22000000000-22000002-200-22-22000000i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2000−i2i2000000−i2i2−i2i2000
χ472-2-22-120-2021-112-2-23−33−3-12-201-11-112-22-22-2003−33−33−30-113−3000-113−3-11-113−33−300−i2i2−i2i20000ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000−i2i2000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000
χ482-2-22-120-2021-112-2-23−33−3-12-201-11-112-22-22-2003−33−33−30-113−3000-113−3-11-113−33−300i2−i2i2−i20000−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000i2−i2000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000
χ492-2-22-120-2021-112-2-23−33−3-1-2201-11-112-2-22-22003−33−33−301-1−33000-113−31-11-1−33−3300−i2i2−i2i20000ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000i2−i2000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000
χ502-2-22-120-2021-112-2-23−33−3-1-2201-11-112-2-22-22003−33−33−301-1−33000-113−31-11-1−33−3300i2−i2i2−i20000−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000−i2i2000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000
χ512-2-22-120-2021-112-2-2−33−33-12-201-11-112-22-22-200−33−33−330-11−33000-11−33-11-11−33−3300−i2i2−i2i20000ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000−i2i2000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000
χ522-2-22-120-2021-112-2-2−33−33-12-201-11-112-22-22-200−33−33−330-11−33000-11−33-11-11−33−3300i2−i2i2−i20000−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000i2−i2000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000
χ532-2-22-120-2021-112-2-2−33−33-1-2201-11-112-2-22-2200−33−33−3301-13−3000-11−331-11-13−33−300−i2i2−i2i20000ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000i2−i2000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000
χ542-2-22-120-2021-112-2-2−33−33-1-2201-11-112-2-22-2200−33−33−3301-13−3000-11−331-11-13−33−300i2−i2i2−i20000−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000−i2i2000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000
χ554444-244-44-4-2-2-2444-2-2-2-2-200-4-2-2-222-4-4000044-2-2-2-22200000-400222200000000000000000000000000000000000000000000
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χ584444-2-24444-2-2-2-2-2-2-2-2-2-21-4-44111-2-2-2-22222-2-21111-2-2-42222-2221111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
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χ604444-2-24-44-4-2-2-2-2-2-2-2-2-2-2100-411122222i32i3−2i3−2i3-2-21111220000022i3−2i3-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000000000
χ614444-2-2-44-44-2-2-2-2-2-22222144-4111-2-2-2-2-2-2-2-222-1-1-1-122-4-2-22222211-1-11111-1-1-1-1000000000000000000000000000000000000
χ624444-2-2-44-44-2-2-2-2-2-222221-4-4-4111-2-2-2-2222222-1-1-1-122422-2-22-2-211-1-1-1-1-1-11111000000000000000000000000000000000000
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χ644444-2-2-4-4-4-4-2-2-2-2-2-22222100411122222i32i3−2i3−2i322-1-1-1-1-2-200000-2−2i32i3-1-111−i3−i3i3i3i3i3−i3−i3000000000000000000000000000000000000
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χ894-4-44-2-2040-42-22-222−2323−23231000-11-12-22-2−2i32i32i3−2i3003−33−323−2300000000-11−33i3−i3−i3i33i−3i−3i3i000000000000000000000000000000000000
χ904-4-44-2-2040-42-22-222−2323−23231000-11-12-22-22i3−2i3−2i32i3003−33−323−2300000000-11−33−i3i3i3−i3−3i3i3i−3i000000000000000000000000000000000000
χ914-4-44-2-20-4042-22-22223−2323−2314-40-11-1-22-22-22-2200−33−3323−230-2223−230001-1−331-11-1−33−33000000000000000000000000000000000000
χ924-4-44-2-20-4042-22-22223−2323−231-440-11-1-22-222-22-200−33−3323−2302-2−23230001-1−33-11-113−33−3000000000000000000000000000000000000
χ934-4-44-2-20-4042-22-222−2323−232314-40-11-1-22-22-22-22003−33−3−23230-22−23230001-13−31-11-13−33−3000000000000000000000000000000000000
χ944-4-44-2-20-4042-22-222−2323−23231-440-11-1-22-222-22-2003−33−3−232302-223−230001-13−3-11-11−33−33000000000000000000000000000000000000
χ9588-8-8-4-480-80-4444-44-4-44420002-2-200000000-4422-2-20000000000000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-8080-4444-4444-4-420002-2-2000000004-4-2-2220000000000000000000000000000000000000000000000000000000000
χ978-88-88-40000-8-8844-40000-400044-4000000000000000000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4000044-444-443−43−43432000-2-220000000000−232323−230000000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4000044-444-4−434343−432000-2-22000000000023−23−23230000000000000000000000000000000000000000000000000000000000

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