Finite Group Databasebeta

← Group #11779499

Character table — Group #11779499

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size1111222222222222222244444444444444444444444888888888888888888881212121212121212121212121212121212122424242424242424242424242424247272144
order122233444466666612121212344466612121212121212121212121212121212266666666121212121212121212121244888812121212242424242424242424466881212121224242424884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-111111111-1-1-1-1-111-1-1-1-11111-1-1-1
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
χ5111111111111111111111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-11
χ7111111111111111111111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-111111111-111-1-1-1-11111-1-1-1-1-1-11
χ8111111111111111111111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1
χ92222222-22-22222222222200-2222-2-2220000-2-22222-2-200000000000-2-2-2-2-20000220000222200000000-200-2-20000000000000
χ102222222-22-22222222222200-2222-2-2220000-2-22222-2-200000000000-2-2-2-2-20000-2-20000-2-2-2-200000000200220000000000000
χ11222222-22-22222222-2-2-2-2222-222222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-222-2-22222000000000000000000000000000000000000
χ12222222-22-22222222-2-2-2-22-2-2-222222-2-2-2-2-2-222-2-2-2-2-2-2222222222-2-2-222-2-2-2-2-2-2000000000000000000000000000000000000
χ13222222-2-2-2-2222222-2-2-2-22002222-2-2-2-20000-2-2-2-2-2-222000000000002-2-222000000000000000000000002-2000022-2-20000000
χ14222222-2-2-2-2222222-2-2-2-22002222-2-2-2-20000-2-2-2-2-2-222000000000002-2-22200000000000000000000000-220000-2-2220000000
χ1522222-12222222-1-1-12222-1222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1220000-1-1-1-100000000222-1-100-1-1-1-10000000
χ1622222-12222222-1-1-12222-1222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-2-20000111100000000-2-2-2110011110000000
χ1722222-12222222-1-1-12222-1-2-22-1-1-122-1-11111-1-1-1-1-1-122-2-2-2111111-2-2-1-1-1-1-11111220000-1-1-1-1000000002-2-2-1-10011110000000
χ1822222-12222222-1-1-12222-1-2-22-1-1-122-1-11111-1-1-1-1-1-122-2-2-2111111-2-2-1-1-1-1-11111-2-20000111100000000-2221100-1-1-1-10000000
χ1922222-12-22-2222-1-1-12222-100-2-1-1-1-2-2-1-1−i3−i3i3i311-1-1-1-1-2-2000−i3i3−i3−i3i3i30011111−i3−i3i3i3220000-1-1-1-100000000-2001100−i3i3−i3i30000000
χ2022222-12-22-2222-1-1-12222-100-2-1-1-1-2-2-1-1−i3−i3i3i311-1-1-1-1-2-2000−i3i3−i3−i3i3i30011111−i3−i3i3i3-2-20000111100000000200-1-100i3−i3i3−i30000000
χ2122222-12-22-2222-1-1-12222-100-2-1-1-1-2-2-1-1i3i3−i3−i311-1-1-1-1-2-2000i3−i3i3i3−i3−i30011111i3i3−i3−i3220000-1-1-1-100000000-2001100i3−i3i3−i30000000
χ2222222-12-22-2222-1-1-12222-100-2-1-1-1-2-2-1-1i3i3−i3−i311-1-1-1-1-2-2000i3−i3i3i3−i3−i30011111i3i3−i3−i3-2-20000111100000000200-1-100−i3i3−i3i30000000
χ2322222-1-22-22222-1-1-1-2-2-2-2-122-2-1-1-12211-1-1-1-1-1-11111-2-2-2-2-2111111221-1-111-1-1-1-1000000−i3−i3i3i300000000000−i3i300−i3i3i3−i30000000
χ2422222-1-22-22222-1-1-1-2-2-2-2-122-2-1-1-12211-1-1-1-1-1-11111-2-2-2-2-2111111221-1-111-1-1-1-1000000i3i3−i3−i300000000000i3−i300i3−i3−i3i30000000
χ2522222-1-22-22222-1-1-1-2-2-2-2-1-2-2-2-1-1-122111111-1-11111-2-2222-1-1-1-1-1-1-2-21-1-1111111000000−i3−i3i3i300000000000−i3i300i3−i3−i3i30000000
χ2622222-1-22-22222-1-1-1-2-2-2-2-1-2-2-2-1-1-122111111-1-11111-2-2222-1-1-1-1-1-1-2-21-1-1111111000000i3i3−i3−i300000000000i3−i300−i3i3i3−i30000000
χ2722222-1-2-2-2-2222-1-1-1-2-2-2-2-1002-1-1-1-2-211−i3−i3i3i311111122000i3−i3i3i3−i3−i300-111-1-1−i3−i3i3i3000000−i3−i3i3i30000000002-2i3−i300-1-1110000000
χ2822222-1-2-2-2-2222-1-1-1-2-2-2-2-1002-1-1-1-2-211−i3−i3i3i311111122000i3−i3i3i3−i3−i300-111-1-1−i3−i3i3i3000000i3i3−i3−i3000000000-22−i3i30011-1-10000000
χ2922222-1-2-2-2-2222-1-1-1-2-2-2-2-1002-1-1-1-2-211i3i3−i3−i311111122000−i3i3−i3−i3i3i300-111-1-1i3i3−i3−i3000000−i3−i3i3i3000000000-22i3−i30011-1-10000000
χ3022222-1-2-2-2-2222-1-1-1-2-2-2-2-1002-1-1-1-2-211i3i3−i3−i311111122000−i3i3−i3−i3i3i300-111-1-1i3i3−i3−i3000000i3i3−i3−i30000000002-2−i3i300-1-1110000000
χ312222-122222-1-1-1222-1-1-1-1-1222-1-1-1-1-122222222-1-1-1-1-1-12-1-122-1-1-1-1-1-12-1-1-1-1-1-1-1-10022220000-1-1-1-1-1-1-1-100000220000-1-1-1-1000
χ322222-122222-1-1-1222-1-1-1-1-1222-1-1-1-1-122222222-1-1-1-1-1-12-1-122-1-1-1-1-1-12-1-1-1-1-1-1-1-100-2-2-2-200001111111100000-2-200001111000
χ332222-122222-1-1-1222-1-1-1-1-1-2-22-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-211-2-21111112-1-1-1-111110022220000-1-1-1-1-1-1-1-100000-2-200001111000
χ342222-122222-1-1-1222-1-1-1-1-1-2-22-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-211-2-21111112-1-1-1-1111100-2-2-2-200001111111100000220000-1-1-1-1000
χ352222-12-22-22-1-1-12221111-122-2-1-1-1-1-1-2-2222222111111-211-2-21111-1-1-2-1-111-1-1-1-100000000003333−3−3−3−30000000000033−3−3000
χ362222-12-22-22-1-1-12221111-122-2-1-1-1-1-1-2-2222222111111-211-2-21111-1-1-2-1-111-1-1-1-10000000000−3−3−3−3333300000000000−3−333000
χ372222-12-22-22-1-1-12221111-1-2-2-2-1-1-1-1-1-2-2-2-2-2-2221111112-1-122-1-1-1-111-2-1-111111100000000003333−3−3−3−300000000000−3−333000
χ382222-12-22-22-1-1-12221111-1-2-2-2-1-1-1-1-1-2-2-2-2-2-2221111112-1-122-1-1-1-111-2-1-11111110000000000−3−3−3−333330000000000033−3−3000
χ3922-2-222-2020-2-222-2-2-2-2222000-2-22002-200000022-2-200000000000000000000002i−2i22−2−22i−2i2i−2i22−2−222−2−2000000000000000−i2i20
χ4022-2-222-2020-2-222-2-2-2-2222000-2-22002-200000022-2-200000000000000000000002i−2i−2−2222i−2i2i−2i−2−222−2−222000000000000000i2−i20
χ4122-2-222-2020-2-222-2-2-2-2222000-2-22002-200000022-2-20000000000000000000000−2i2i22−2−2−2i2i−2i2i22−2−222−2−2000000000000000i2−i20
χ4222-2-222-2020-2-222-2-2-2-2222000-2-22002-200000022-2-20000000000000000000000−2i2i−2−222−2i2i−2i2i−2−222−2−222000000000000000−i2i20
χ432-22-2220-2022-2-2-22-2000022i−2i02-2-22-2002i−2i2i−2i2-20000000000000002i−2i02-2002i−2i2i−2i002−22−200002−22−22−22−200000−i2i20000−i2i2−i2i2000
χ442-22-2220-2022-2-2-22-2000022i−2i02-2-22-2002i−2i2i−2i2-20000000000000002i−2i02-2002i−2i2i−2i00−22−220000−22−22−22−2200000i2−i20000i2−i2i2−i2000
χ452-22-2220-2022-2-2-22-200002−2i2i02-2-22-200−2i2i−2i2i2-2000000000000000−2i2i02-200−2i2i−2i2i002−22−200002−22−22−22−200000i2−i20000i2−i2i2−i2000
χ462-22-2220-2022-2-2-22-200002−2i2i02-2-22-200−2i2i−2i2i2-2000000000000000−2i2i02-200−2i2i−2i2i00−22−220000−22−22−22−2200000−i2i20000−i2i2−i2i2000
χ472-22-2-120-202-111-22-23−33−3-12i−2i0-111-11002i−2i2i−2i2-23−33−33−30−i3i300−i3i3−i3i3−ii0-113−3−ii−ii002−22−20000ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300000−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000
χ482-22-2-120-202-111-22-23−33−3-12i−2i0-111-11002i−2i2i−2i2-23−33−33−30−i3i300−i3i3−i3i3−ii0-113−3−ii−ii00−22−220000−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000
χ492-22-2-120-202-111-22-23−33−3-1−2i2i0-111-1100−2i2i−2i2i2-23−33−33−30i3−i300i3−i3i3−i3i−i0-113−3i−ii−i002−22−20000ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300000i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000
χ502-22-2-120-202-111-22-23−33−3-1−2i2i0-111-1100−2i2i−2i2i2-23−33−33−30i3−i300i3−i3i3−i3i−i0-113−3i−ii−i00−22−220000−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000
χ512-22-2-120-202-111-22-2−33−33-12i−2i0-111-11002i−2i2i−2i2-2−33−33−330i3−i300i3−i3i3−i3−ii0-11−33−ii−ii002−22−20000ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700000−i2i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000
χ522-22-2-120-202-111-22-2−33−33-12i−2i0-111-11002i−2i2i−2i2-2−33−33−330i3−i300i3−i3i3−i3−ii0-11−33−ii−ii00−22−220000−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700000i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000
χ532-22-2-120-202-111-22-2−33−33-1−2i2i0-111-1100−2i2i−2i2i2-2−33−33−330−i3i300−i3i3−i3i3i−i0-11−33i−ii−i002−22−20000ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700000i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000
χ542-22-2-120-202-111-22-2−33−33-1−2i2i0-111-1100−2i2i−2i2i2-2−33−33−330−i3i300−i3i3−i3i3i−i0-11−33i−ii−i00−22−220000−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700000−i2i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000
χ554444-244-44-4-2-2-2444-2-2-2-2-200-4-2-2-222440000-4-4-2-2-2-22200000000000-422220000000000000000000000000000000000000000
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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
χ584444-2-24444-2-2-2-2-2-2-2-2-2-21-4-44111-2-2-2-22222-2-21111-2-2-42222-1-1-1-122-21111-1-1-1-1000000000000000000000000000000000000
χ594444-2-24-44-4-2-2-2-2-2-2-2-2-2-2100-411122-2-2−2i3−2i32i32i322111122000−2i32i3i3i3−i3−i3002-1-1-1-1i3i3−i3−i3000000000000000000000000000000000000
χ604444-2-24-44-4-2-2-2-2-2-2-2-2-2-2100-411122-2-22i32i3−2i3−2i3221111220002i3−2i3−i3−i3i3i3002-1-1-1-1−i3−i3i3i3000000000000000000000000000000000000
χ614444-2-2-44-44-2-2-2-2-2-22222144-4111-2-222-2-2-2-2-2-2-1-1-1-122-42222-1-1-1-1-2-2211-1-11111000000000000000000000000000000000000
χ624444-2-2-44-44-2-2-2-2-2-222221-4-4-4111-2-2222222-2-2-1-1-1-1224-2-2-2-2111122211-1-1-1-1-1-1000000000000000000000000000000000000
χ634444-2-2-4-4-4-4-2-2-2-2-2-2222210041112222−2i3−2i32i32i322-1-1-1-1-2-20002i3−2i3−i3−i3i3i300-2-1-111i3i3−i3−i3000000000000000000000000000000000000
χ644444-2-2-4-4-4-4-2-2-2-2-2-22222100411122222i32i3−2i3−2i322-1-1-1-1-2-2000−2i32i3i3i3−i3−i300-2-1-111−i3−i3i3i3000000000000000000000000000000000000
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χ854-44-4-2-20-404-2222-2223−2323−2314i−4i01-1-1-2200−2i2i−2i2i-22−33−3323−230−2i32i300i3−i3i3−i3−2i2i01-1−33i−ii−i000000000000000000000000000000000000
χ864-44-4-2-20-404-2222-2223−2323−231−4i4i01-1-1-22002i−2i2i−2i-22−33−3323−2302i3−2i300−i3i3−i3i32i−2i01-1−33−ii−ii000000000000000000000000000000000000
χ874-44-4-2-20-404-2222-22−2323−232314i−4i01-1-1-2200−2i2i−2i2i-223−33−3−232302i3−2i300−i3i3−i3i3−2i2i01-13−3i−ii−i000000000000000000000000000000000000
χ884-44-4-2-20-404-2222-22−2323−23231−4i4i01-1-1-22002i−2i2i−2i-223−33−3−23230−2i32i300i3−i3i3−i32i−2i01-13−3−ii−ii000000000000000000000000000000000000
χ894-4-44440000-44-4-4-4400004000-44-4000000000000000000000000000000000000002-2-2200002-2-222-2-22000000000000000000
χ904-4-44440000-44-4-4-4400004000-44-400000000000000000000000000000000000000-222-20000-222-2-222-2000000000000000000
χ914-4-44-2400002-22-4-4423−23−2323-20002-220000000000−232323−230000000000000000000000002-2-220000−1−31+31+3−1−3−1+31−31−3−1+3000000000000000000
χ924-4-44-2400002-22-4-4423−23−2323-20002-220000000000−232323−23000000000000000000000000-222-200001+3−1−3−1−31+31−3−1+3−1+31−3000000000000000000
χ934-4-44-2400002-22-4-44−232323−23-20002-22000000000023−23−23230000000000000000000000002-2-220000−1+31−31−3−1+3−1−31+31+3−1−3000000000000000000
χ944-4-44-2400002-22-4-44−232323−23-20002-22000000000023−23−2323000000000000000000000000-222-200001−3−1+3−1+31−31+3−1−3−1−31+3000000000000000000
χ9588-8-8-4-480-8044-4-444-4-4442000-2-22004-4000000-2-2220000000000000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-808044-4-44444-4-42000-2-2200-4400000022-2-20000000000000000000000000000000000000000000000000000000000
χ978-8-888-40000-88-844-40000-40004-44000000000000000000000000000000000000000000000000000000000000000000000000
χ988-8-88-4-400004-4444-443−43−43432000-22-2000000000023−23−23230000000000000000000000000000000000000000000000000000000000
χ998-8-88-4-400004-4444-4−434343−432000-22-20000000000−232323−230000000000000000000000000000000000000000000000000000000000

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