Finite Group Databasebeta

← Group #11780439

Character table — Group #11780439

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size1111222222222222222244444444444444444444444888888888888888888881212121212121212121212121212121212122424242424242424242424242424247272144
order1222334444666666121212123444666121212121212121212121212121212122666666661212121212121212121212226666888824242424242424244448812121212121224242424884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-111-1-1-1-1-1-11111-1-1-1
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
χ5111111111111111111111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1111111111111111111-1-11-1-111-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-11
χ7111111111111111111111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11111-1-1-1-1-1-11
χ8111111111111111111111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111111111-1
χ92222222-22-22222222222200-2222-2-2-2-22200002222-2-2000000000-200-2-2-2-2000022222200000000000000-200-2-200000000000
χ102222222-22-22222222222200-2222-2-2-2-22200002222-2-2000000000-200-2-2-2-20000-2-2-2-2-2-2000000000000002002200000000000
χ11222222-22-22222222-2-2-2-2222-22222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222000000000000000000000000000000000000
χ12222222-22-22222222-2-2-2-22-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2222222222-2-2-222-2-2-2-2-2-2000000000000000000000000000000000000
χ13222222-2-2-2-2222222-2-2-2-22002222-2-2-2-2-2-20000-2-2-2-222000000000200-2-22200000000000000000000002-20000022-2-20000000
χ14222222-2-2-2-2222222-2-2-2-22002222-2-2-2-2-2-20000-2-2-2-222000000000200-2-2220000000000000000000000-2200000-2-2220000000
χ1522222-1222222-12-1-12222-1222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000000022200-1-1-1-1-1-10000000
χ1622222-1222222-12-1-12222-1222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-21111000000000000-2-2-2001111110000000
χ1722222-1222222-12-1-12222-1-2-22-1-1-122-1-1-1-11111-1-1-1-122-2-2-2111111-1-2-2-1-1-1-1111122-1-1-1-1000000000000-2-2200-1-111110000000
χ1822222-1222222-12-1-12222-1-2-22-1-1-122-1-1-1-11111-1-1-1-122-2-2-2111111-1-2-2-1-1-1-11111-2-2111100000000000022-20011-1-1-1-10000000
χ1922222-12-22-222-12-1-12222-100-2-1-1-1-2-211-1-1−i3−i3i3i3-1-1-1-1-2-2000−i3i3−i3−i3i3i31001111−i3−i3i3i322-1-1-1-100000000000000-20011−i3i3−i3i30000000
χ2022222-12-22-222-12-1-12222-100-2-1-1-1-2-211-1-1−i3−i3i3i3-1-1-1-1-2-2000−i3i3−i3−i3i3i31001111−i3−i3i3i3-2-2111100000000000000200-1-1i3−i3i3−i30000000
χ2122222-12-22-222-12-1-12222-100-2-1-1-1-2-211-1-1i3i3−i3−i3-1-1-1-1-2-2000i3−i3i3i3−i3−i31001111i3i3−i3−i322-1-1-1-100000000000000-20011i3−i3i3−i30000000
χ2222222-12-22-222-12-1-12222-100-2-1-1-1-2-211-1-1i3i3−i3−i3-1-1-1-1-2-2000i3−i3i3i3−i3−i31001111i3i3−i3−i3-2-2111100000000000000200-1-1−i3i3−i3i30000000
χ2322222-1-22-2222-12-1-1-2-2-2-2-122-2-1-1-122-1-111-1-1-1-11111-2-2-2-2-2111111122-1-111-1-1-1-100−i3−i3i3i300000000000000000−i3i3−i3i3i3−i30000000
χ2422222-1-22-2222-12-1-1-2-2-2-2-122-2-1-1-122-1-111-1-1-1-11111-2-2-2-2-2111111122-1-111-1-1-1-100i3i3−i3−i300000000000000000i3−i3i3−i3−i3i30000000
χ2522222-1-22-2222-12-1-1-2-2-2-2-1-2-2-2-1-1-122-1-11111111111-2-2222-1-1-1-1-1-11-2-2-1-111111100−i3−i3i3i300000000000000000−i3i3i3−i3−i3i30000000
χ2622222-1-22-2222-12-1-1-2-2-2-2-1-2-2-2-1-1-122-1-11111111111-2-2222-1-1-1-1-1-11-2-2-1-111111100i3i3−i3−i300000000000000000i3−i3−i3i3i3−i30000000
χ2722222-1-2-2-2-222-12-1-1-2-2-2-2-1002-1-1-1-2-21111−i3−i3i3i3111122000i3−i3i3i3−i3−i3-10011-1-1−i3−i3i3i300−i3−i3i3i30000000000002-2000i3−i3-1-1110000000
χ2822222-1-2-2-2-222-12-1-1-2-2-2-2-1002-1-1-1-2-21111−i3−i3i3i3111122000i3−i3i3i3−i3−i3-10011-1-1−i3−i3i3i300i3i3−i3−i3000000000000-22000−i3i311-1-10000000
χ2922222-1-2-2-2-222-12-1-1-2-2-2-2-1002-1-1-1-2-21111i3i3−i3−i3111122000−i3i3−i3−i3i3i3-10011-1-1i3i3−i3−i300−i3−i3i3i3000000000000-22000i3−i311-1-10000000
χ3022222-1-2-2-2-222-12-1-1-2-2-2-2-1002-1-1-1-2-21111i3i3−i3−i3111122000−i3i3−i3−i3i3i3-10011-1-1i3i3−i3−i300i3i3−i3−i30000000000002-2000−i3i3-1-1110000000
χ312222-122222-1-12-122-1-1-1-1-1222-1-1-1-1-122222222-1-1-1-1-1-12-1-122-1-1-1-12-1-1-1-1-1-1-1-1-1-10000002222-1-1-1-1-1-1-1-100022000000-1-1-1-1000
χ322222-122222-1-12-122-1-1-1-1-1222-1-1-1-1-122222222-1-1-1-1-1-12-1-122-1-1-1-12-1-1-1-1-1-1-1-1-1-1000000-2-2-2-211111111000-2-20000001111000
χ332222-122222-1-12-122-1-1-1-1-1-2-22-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-211-2-21111211-1-1-1-111110000002222-1-1-1-1-1-1-1-1000-2-20000001111000
χ342222-122222-1-12-122-1-1-1-1-1-2-22-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-211-2-21111211-1-1-1-11111000000-2-2-2-21111111100022000000-1-1-1-1000
χ352222-12-22-22-1-12-1221111-122-2-1-1-1-1-122-2-22222111111-211-2-21111-2-1-1-1-111-1-1-1-100000000003333−3−3−3−30000000000033−3−3000
χ362222-12-22-22-1-12-1221111-122-2-1-1-1-1-122-2-22222111111-211-2-21111-2-1-1-1-111-1-1-1-10000000000−3−3−3−3333300000000000−3−333000
χ372222-12-22-22-1-12-1221111-1-2-2-2-1-1-1-1-122-2-2-2-2-2-21111112-1-122-1-1-1-1-211-1-111111100000000003333−3−3−3−300000000000−3−333000
χ382222-12-22-22-1-12-1221111-1-2-2-2-1-1-1-1-122-2-2-2-2-2-21111112-1-122-1-1-1-1-211-1-11111110000000000−3−3−3−333330000000000033−3−3000
χ392-22-22220-20-2-2-22-2222-2-22000-2-2200002-2000022-2-200000000000000000000002-22-22-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000−i2i20
χ402-22-22220-20-2-2-22-2222-2-22000-2-2200002-2000022-2-200000000000000000000002-22-22-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000i2−i20
χ412-22-22220-20-2-2-22-2222-2-22000-2-2200002-2000022-2-20000000000000000000000-22-22-22−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000i2−i20
χ422-22-22220-20-2-2-22-2222-2-22000-2-2200002-2000022-2-20000000000000000000000-22-22-22i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000−i2i20
χ432-2-2222020-22-2-2-22-2000022i−2i02-2-22-22-2002i−2i2i−2i00000000000000002i−2i2-2002i−2i2i−2i000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20002−20000002−22−2000
χ442-2-2222020-22-2-2-22-2000022i−2i02-2-22-22-2002i−2i2i−2i00000000000000002i−2i2-2002i−2i2i−2i000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000−22000000−22−22000
χ452-2-2222020-22-2-2-22-200002−2i2i02-2-22-22-200−2i2i−2i2i0000000000000000−2i2i2-200−2i2i−2i2i000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000−22000000−22−22000
χ462-2-2222020-22-2-2-22-200002−2i2i02-2-22-22-200−2i2i−2i2i0000000000000000−2i2i2-200−2i2i−2i2i000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20002−20000002−22−2000
χ472-2-22-12020-2-11-212-23−33−3-12i−2i0-111-112-2002i−2i2i−2i3−33−33−30−i3i300−i3i3−i3i30−ii-113−3−ii−ii000000−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ230002−2000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000
χ482-2-22-12020-2-11-212-23−33−3-12i−2i0-111-112-2002i−2i2i−2i3−33−33−30−i3i300−i3i3−i3i30−ii-113−3−ii−ii000000i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000−22000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000
χ492-2-22-12020-2-11-212-23−33−3-1−2i2i0-111-112-200−2i2i−2i2i3−33−33−30i3−i300i3−i3i3−i30i−i-113−3i−ii−i000000−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000−22000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000
χ502-2-22-12020-2-11-212-23−33−3-1−2i2i0-111-112-200−2i2i−2i2i3−33−33−30i3−i300i3−i3i3−i30i−i-113−3i−ii−i000000i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ230002−2000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000
χ512-2-22-12020-2-11-212-2−33−33-12i−2i0-111-112-2002i−2i2i−2i−33−33−330i3−i300i3−i3i3−i30−ii-11−33−ii−ii000000−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ70002−2000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000
χ522-2-22-12020-2-11-212-2−33−33-12i−2i0-111-112-2002i−2i2i−2i−33−33−330i3−i300i3−i3i3−i30−ii-11−33−ii−ii000000i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000−22000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000
χ532-2-22-12020-2-11-212-2−33−33-1−2i2i0-111-112-200−2i2i−2i2i−33−33−330−i3i300−i3i3−i3i30i−i-11−33i−ii−i000000−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000−22000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000
χ542-2-22-12020-2-11-212-2−33−33-1−2i2i0-111-112-200−2i2i−2i2i−33−33−330−i3i300−i3i3−i3i30i−i-11−33i−ii−i000000i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ70002−2000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000
χ554444-244-44-4-2-24-244-2-2-2-2-200-4-2-2-222-4-4440000-2-2-2-222000000000-40022220000000000000000000000000000000000000000
χ564444-24-4-4-4-4-2-24-2442222-2004-2-2-222-4-4-4-400002222-2-200000000040022-2-20000000000000000000000000000000000000000
χ574444-2-24444-2-2-2-2-2-2-2-2-2-21444111-2-2-2-2-2-2-2-2-2-21111-2-24-2-2-2-21111-2-2-211111111000000000000000000000000000000000000
χ584444-2-24444-2-2-2-2-2-2-2-2-2-21-4-44111-2-2-2-2-2-222221111-2-2-42222-1-1-1-1-2221111-1-1-1-1000000000000000000000000000000000000
χ594444-2-24-44-4-2-2-2-2-2-2-2-2-2-2100-41112222-2-2−2i3−2i32i32i3111122000−2i32i3i3i3−i3−i3200-1-1-1-1i3i3−i3−i3000000000000000000000000000000000000
χ604444-2-24-44-4-2-2-2-2-2-2-2-2-2-2100-41112222-2-22i32i3−2i3−2i31111220002i3−2i3−i3−i3i3i3200-1-1-1-1−i3−i3i3i3000000000000000000000000000000000000
χ614444-2-2-44-44-2-2-2-2-2-22222144-4111-2-2-2-222-2-2-2-2-1-1-1-122-42222-1-1-1-12-2-211-1-11111000000000000000000000000000000000000
χ624444-2-2-44-44-2-2-2-2-2-222221-4-4-4111-2-2-2-2222222-1-1-1-1224-2-2-2-2111122211-1-1-1-1-1-1000000000000000000000000000000000000
χ634444-2-2-4-4-4-4-2-2-2-2-2-222221004111222222−2i3−2i32i32i3-1-1-1-1-2-20002i3−2i3−i3−i3i3i3-200-1-111i3i3−i3−i3000000000000000000000000000000000000
χ644444-2-2-4-4-4-4-2-2-2-2-2-2222210041112222222i32i3−2i3−2i3-1-1-1-1-2-2000−2i32i3i3i3−i3−i3-200-1-111−i3−i3i3i3000000000000000000000000000000000000
χ6544-4-4440000-444-4-4-400004000-44-40000000000000000000000000000000000000000002-2-222-2-222-2-22000000000000000000
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χ6844-4-4-2400002-242-4-423−23−2323-20002-22000000000023−23−23230000000000000000000000000000-222-21+3−1−3−1−31+31−3−1+3−1+31−3000000000000000000
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χ7044-4-4-2400002-242-4-4−232323−23-20002-220000000000−232323−230000000000000000000000000000-222-21−3−1+3−1+31−31+3−1−3−1−31+3000000000000000000
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χ834-4-444-20-4044-42-4-220000-2000-222-442-20023−23−23230000000000000000002-20023−23−2323000000000000000000000000000000000000
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χ884-4-44-2-2040-4-2222-2223−2323−231−4i4i01-1-1-22-22002i−2i2i−2i−33−3323−2302i3−2i300−i3i3−i3i302i−2i1-1−33−ii−ii000000000000000000000000000000000000
χ894-4-44-2-2040-4-2222-22−2323−232314i−4i01-1-1-22-2200−2i2i−2i2i3−33−3−232302i3−2i300−i3i3−i3i30−2i2i1-13−3i−ii−i000000000000000000000000000000000000
χ904-4-44-2-2040-4-2222-22−2323−23231−4i4i01-1-1-22-22002i−2i2i−2i3−33−3−23230−2i32i300i3−i3i3−i302i−2i1-13−3−ii−ii000000000000000000000000000000000000
χ914-4-44-2-20-404-2222-2223−2323−2310001-1-12-22-20023−23−2323−33−33−232300000-333-3000-113−3−333−3000000000000000000000000000000000000
χ924-4-44-2-20-404-2222-2223−2323−2310001-1-12-22-200−232323−23−33−33−2323000003-3-33000-113−33−3−33000000000000000000000000000000000000
χ934-4-44-2-20-404-2222-22−2323−232310001-1-12-22-20023−23−23233−33−323−23000003-3-33000-11−33−333−3000000000000000000000000000000000000
χ944-4-44-2-20-404-2222-22−2323−232310001-1-12-22-200−232323−233−33−323−2300000-333-3000-11−333−3−33000000000000000000000000000000000000
χ9588-8-88-40000-88-4-8440000-40004-44000000000000000000000000000000000000000000000000000000000000000000000000
χ9688-8-8-4-400004-4-444443−43−43432000-22-20000000000−232323−230000000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-400004-4-4444−434343−432000-22-2000000000023−23−23230000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-480-80444-44-4-4-4442000-2-220000-44000022-2-20000000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-8080444-44-444-4-42000-2-2200004-40000-2-2220000000000000000000000000000000000000000000000000000000000

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