Finite Group Databasebeta

← Group #11779965

Character table — Group #11779965

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size1111222222222222222244444444444444444444444888888888888888888881212121212121212121212121212121212122424242424242424242424242424247272144
order122233444466666612121212344466612121212121212121212121212121212412121212121212121212121212121212121212226666888824242424242424244448812121212121224242424884
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
χ5111111111111111111111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111111111111111111-1-11-1-111-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1-11
χ7111111111111111111111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11111-1-1-1-1-1-11
χ8111111111111111111111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111111111-1
χ92222222-22-22222222222200-222222-2-2-2-200002222-2-20000000-2-2-2-2-20000000022222200000000000000-200-2-200000000000
χ102222222-22-22222222222200-222222-2-2-2-200002222-2-20000000-2-2-2-2-200000000-2-2-2-2-2-2000000000000002002200000000000
χ11222222-22-22222222-2-2-2-2222-2222-2-222222222-2-2-2-2-2-2-222-2-2-2-2-222-2-22222-2-2-2-2000000000000000000000000000000000000
χ12222222-22-22222222-2-2-2-22-2-2-2222-2-22222-2-2-2-2-2-2-2-2-2-22-2-22222-222-2-2-2-2-2-22222000000000000000000000000000000000000
χ13222222-2-2-2-2222222-2-2-2-22002222-2-2-2-2-2-20000-2-2-2-22200000002-2-222000000000000000000000000002-20000022-2-20000000
χ14222222-2-2-2-2222222-2-2-2-22002222-2-2-2-2-2-20000-2-2-2-22200000002-2-22200000000000000000000000000-2200000-2-2220000000
χ1522222-122222-122-1-12222-1222-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000000022200-1-1-1-1-1-10000000
χ1622222-122222-122-1-12222-1222-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111000000000000-2-2-2001111110000000
χ1722222-122222-122-1-12222-1-2-22-1-1-1-1-122-1-11111-1-1-1-122-2-2-2-2-211-1-1-1-1-11111111122-1-1-1-1000000000000-2-2200-1-111110000000
χ1822222-122222-122-1-12222-1-2-22-1-1-1-1-122-1-11111-1-1-1-122-2-2-2-2-211-1-1-1-1-111111111-2-2111100000000000022-20011-1-1-1-10000000
χ1922222-12-22-22-122-1-12222-100-2-1-1-1-1-1-2-211−i3−i3i3i3-1-1-1-1-2-200000−i3i311111−i3−i3i3i3−i3−i3i3i322-1-1-1-100000000000000-20011−i3i3−i3i30000000
χ2022222-12-22-22-122-1-12222-100-2-1-1-1-1-1-2-211−i3−i3i3i3-1-1-1-1-2-200000−i3i311111−i3−i3i3i3−i3−i3i3i3-2-2111100000000000000200-1-1i3−i3i3−i30000000
χ2122222-12-22-22-122-1-12222-100-2-1-1-1-1-1-2-211i3i3−i3−i3-1-1-1-1-2-200000i3−i311111i3i3−i3−i3i3i3−i3−i322-1-1-1-100000000000000-20011i3−i3i3−i30000000
χ2222222-12-22-22-122-1-12222-100-2-1-1-1-1-1-2-211i3i3−i3−i3-1-1-1-1-2-200000i3−i311111i3i3−i3−i3i3i3−i3−i3-2-2111100000000000000200-1-1−i3i3−i3i30000000
χ2322222-1-22-222-122-1-1-2-2-2-2-122-2-1-1-11122-1-1-1-1-1-11111-2-2-222-2-2111-1-111-1-1-1-1111100−i3−i3i3i300000000000000000−i3i3−i3i3i3−i30000000
χ2422222-1-22-222-122-1-1-2-2-2-2-122-2-1-1-11122-1-1-1-1-1-11111-2-2-222-2-2111-1-111-1-1-1-1111100i3i3−i3−i300000000000000000i3−i3i3−i3−i3i30000000
χ2522222-1-22-222-122-1-1-2-2-2-2-1-2-2-2-1-1-11122-1-111111111-2-22-2-222-1-11-1-1111111-1-1-1-100−i3−i3i3i300000000000000000−i3i3i3−i3−i3i30000000
χ2622222-1-22-222-122-1-1-2-2-2-2-1-2-2-2-1-1-11122-1-111111111-2-22-2-222-1-11-1-1111111-1-1-1-100i3i3−i3−i300000000000000000i3−i3−i3i3i3−i30000000
χ2722222-1-2-2-2-22-122-1-1-2-2-2-2-1002-1-1-111-2-211−i3−i3i3i311112200000i3−i3-111-1-1−i3−i3i3i3i3i3−i3−i300−i3−i3i3i30000000000002-2000i3−i3-1-1110000000
χ2822222-1-2-2-2-22-122-1-1-2-2-2-2-1002-1-1-111-2-211−i3−i3i3i311112200000i3−i3-111-1-1−i3−i3i3i3i3i3−i3−i300i3i3−i3−i3000000000000-22000−i3i311-1-10000000
χ2922222-1-2-2-2-22-122-1-1-2-2-2-2-1002-1-1-111-2-211i3i3−i3−i311112200000−i3i3-111-1-1i3i3−i3−i3−i3−i3i3i300−i3−i3i3i3000000000000-22000i3−i311-1-10000000
χ3022222-1-2-2-2-22-122-1-1-2-2-2-2-1002-1-1-111-2-211i3i3−i3−i311112200000−i3i3-111-1-1i3i3−i3−i3−i3−i3i3i300i3i3−i3−i30000000000002-2000−i3i3-1-1110000000
χ312222-122222-12-1-122-1-1-1-1-1222-1-1-122-1-1222222-1-1-1-1-1-12-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-10000002222-1-1-1-1-1-1-1-100022000000-1-1-1-1000
χ322222-122222-12-1-122-1-1-1-1-1222-1-1-122-1-1222222-1-1-1-1-1-12-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1000000-2-2-2-211111111000-2-20000001111000
χ332222-122222-12-1-122-1-1-1-1-1-2-22-1-1-122-1-122-2-2-2-2-1-1-1-1-1-1-21111-2-22-1-1-1-1111111110000002222-1-1-1-1-1-1-1-1000-2-20000001111000
χ342222-122222-12-1-122-1-1-1-1-1-2-22-1-1-122-1-122-2-2-2-2-1-1-1-1-1-1-21111-2-22-1-1-1-111111111000000-2-2-2-21111111100022000000-1-1-1-1000
χ352222-12-22-22-12-1-1221111-122-2-1-1-1-2-2-1-1222222111111-2-1-111-2-2-2-1-111-1-1-1-1111100000000003333−3−3−3−30000000000033−3−3000
χ362222-12-22-22-12-1-1221111-122-2-1-1-1-2-2-1-1222222111111-2-1-111-2-2-2-1-111-1-1-1-111110000000000−3−3−3−3333300000000000−3−333000
χ372222-12-22-22-12-1-1221111-1-2-2-2-1-1-1-2-2-1-122-2-2-2-2111111211-1-122-2-1-1111111-1-1-1-100000000003333−3−3−3−300000000000−3−333000
χ382222-12-22-22-12-1-1221111-1-2-2-2-1-1-1-2-2-1-122-2-2-2-2111111211-1-122-2-1-1111111-1-1-1-10000000000−3−3−3−333330000000000033−3−3000
χ3922-2-22220-2022-2-2-2-222-2-220002-2-22-20000000022-2-200000000000000000000002-22-22-222−2−222−2−222−2−20000000000000002−20
χ4022-2-22220-2022-2-2-2-222-2-220002-2-22-20000000022-2-200000000000000000000002-22-22-2−2−222−2−222−2−222000000000000000−220
χ4122-2-22220-2022-2-2-2-222-2-220002-2-22-20000000022-2-20000000000000000000000-22-22-2222−2−222−2−222−2−2000000000000000−220
χ4222-2-22220-2022-2-2-2-222-2-220002-2-22-20000000022-2-20000000000000000000000-22-22-22−2−222−2−222−2−2220000000000000002−20
χ432-2-2222020-2-2-22-22-2000022i−2i0-22-2002-22-22i−2i2i−2i00000002i−2i000002-2002i−2i2i−2i0000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20002−20000002−22−2000
χ442-2-2222020-2-2-22-22-2000022i−2i0-22-2002-22-22i−2i2i−2i00000002i−2i000002-2002i−2i2i−2i0000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000−22000000−22−22000
χ452-2-2222020-2-2-22-22-200002−2i2i0-22-2002-22-2−2i2i−2i2i0000000−2i2i000002-200−2i2i−2i2i0000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000−22000000−22−22000
χ462-2-2222020-2-2-22-22-200002−2i2i0-22-2002-22-2−2i2i−2i2i0000000−2i2i000002-200−2i2i−2i2i0000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20002−20000002−22−2000
χ472-2-22-12020-21-2-112-23−33−3-12i−2i01-1100-112-22i−2i2i−2i3−33−33−30−ii−i3i3000-113−3−ii−ii−i3i3−i3i3000000−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ230002−2000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000
χ482-2-22-12020-21-2-112-23−33−3-12i−2i01-1100-112-22i−2i2i−2i3−33−33−30−ii−i3i3000-113−3−ii−ii−i3i3−i3i3000000i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000−22000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000
χ492-2-22-12020-21-2-112-23−33−3-1−2i2i01-1100-112-2−2i2i−2i2i3−33−33−30i−ii3−i3000-113−3i−ii−ii3−i3i3−i3000000−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000−22000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000
χ502-2-22-12020-21-2-112-23−33−3-1−2i2i01-1100-112-2−2i2i−2i2i3−33−33−30i−ii3−i3000-113−3i−ii−ii3−i3i3−i3000000i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ230002−2000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000
χ512-2-22-12020-21-2-112-2−33−33-12i−2i01-1100-112-22i−2i2i−2i−33−33−330−iii3−i3000-11−33−ii−iii3−i3i3−i3000000−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ70002−2000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000
χ522-2-22-12020-21-2-112-2−33−33-12i−2i01-1100-112-22i−2i2i−2i−33−33−330−iii3−i3000-11−33−ii−iii3−i3i3−i3000000i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000−22000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000
χ532-2-22-12020-21-2-112-2−33−33-1−2i2i01-1100-112-2−2i2i−2i2i−33−33−330i−i−i3i3000-11−33i−ii−i−i3i3−i3i3000000−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000−22000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000
χ542-2-22-12020-21-2-112-2−33−33-1−2i2i01-1100-112-2−2i2i−2i2i−33−33−330i−i−i3i3000-11−33i−ii−i−i3i3−i3i3000000i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ70002−2000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000
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χ874-4-44-2-2040-422-22-2223−2323−2314i−4i0-11-100-22-22−2i2i−2i2i−33−3323−230−2i2i−2i32i30001-1−33i−ii−ii3−i3i3−i3000000000000000000000000000000000000
χ884-4-44-2-2040-422-22-2223−2323−231−4i4i0-11-100-22-222i−2i2i−2i−33−3323−2302i−2i2i3−2i30001-1−33−ii−ii−i3i3−i3i3000000000000000000000000000000000000
χ894-4-44-2-2040-422-22-22−2323−232314i−4i0-11-100-22-22−2i2i−2i2i3−33−3−23230−2i2i2i3−2i30001-13−3i−ii−i−i3i3−i3i3000000000000000000000000000000000000
χ904-4-44-2-2040-422-22-22−2323−23231−4i4i0-11-100-22-222i−2i2i−2i3−33−3−232302i−2i−2i32i30001-13−3−ii−iii3−i3i3−i3000000000000000000000000000000000000
χ914-4-44-2-20-40422-22-2223−2323−231000-11-1002-22-223−23−2323−33−33−232300000000-113−3−333−3-333-3000000000000000000000000000000000000
χ924-4-44-2-20-40422-22-2223−2323−231000-11-1002-22-2−232323−23−33−33−232300000000-113−33−3−333-3-33000000000000000000000000000000000000
χ934-4-44-2-20-40422-22-22−2323−23231000-11-1002-22-223−23−23233−33−323−2300000000-11−33−333−33-3-33000000000000000000000000000000000000
χ944-4-44-2-20-40422-22-22−2323−23231000-11-1002-22-2−232323−233−33−323−2300000000-11−333−3−33-333-3000000000000000000000000000000000000
χ9588-8-8-4-480-80-4-44444-4-44420002-2-2-440000000022-2-20000000000000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-8080-4-4444444-4-420002-2-24-400000000-2-2220000000000000000000000000000000000000000000000000000000000
χ978-88-88-40000-84-884-40000-400044-4000000000000000000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-40000444-44-443−43−43432000-2-220000000000−232323−230000000000000000000000000000000000000000000000000000000000
χ998-88-8-4-40000444-44-4−434343−432000-2-22000000000023−23−23230000000000000000000000000000000000000000000000000000000000

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