Finite Group Databasebeta

← Group #11780448

Character table — Group #11780448

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size1111222222222222222244444444444444444444444888888888888888888881212121212121212121212121212121212122424242424242424242424242424247272144
order1222334444666666121212122234666666612121212121212121212121246666661212121212121212121212121244888812121212242424242424242424466881212121224242424884
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
χ511111111111111111111-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-11111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1
χ611111111111111111111-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-11
χ711111111111111111111-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-111-1-1-1-11111-1-1-1-1-1-11
χ811111111111111111111-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1
χ92222222-2-22222222-2-2-2-2222-2222222222-2-222-2-2-2-2-2-2-2222222-2-2-2-2-222-2-2-2-2-2-2000000000000000000000000000000000000
χ102222222-2-22222222-2-2-2-2-2-22-2-2-2-2-222222-2-222-2-2-2-2-2-22-2-2-2-2-2-2-2222222-2-22222000000000000000000000000000000000000
χ11222222-222-22222222222002-20000222-2-222-2-22222-2-20000000-20000-2-2-2-20000220000222200000000-200-2-20000000000000
χ12222222-222-22222222222002-20000222-2-222-2-22222-2-20000000-20000-2-2-2-20000-2-20000-2-2-2-200000000200220000000000000
χ13222222-2-2-2-2222222-2-2-2-200220000222-2-2-2-2-2-2-2-2-2-222000000020000-2-222000000000000000000000002-2000022-2-20000000
χ14222222-2-2-2-2222222-2-2-2-200220000222-2-2-2-2-2-2-2-2-2-222000000020000-2-22200000000000000000000000-220000-2-2220000000
χ1522222-1222222-12-1-1222222-12-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1220000-1-1-1-100000000222-1-100-1-1-1-10000000
χ1622222-1222222-12-1-1222222-12-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-20000111100000000-2-2-2110011110000000
χ1722222-1222222-12-1-12222-2-2-121111-1-1-122-1-1-1-1-1-1-1-122-2-2-21111-1-2-211-1-1-1-11111220000-1-1-1-1000000002-2-2-1-10011110000000
χ1822222-1222222-12-1-12222-2-2-121111-1-1-122-1-1-1-1-1-1-1-122-2-2-21111-1-2-211-1-1-1-11111-2-20000111100000000-2221100-1-1-1-10000000
χ1922222-12-2-2222-12-1-1-2-2-2-222-1-2-1-1-1-1-1-1-12211-1-11111-2-2-222-1-1-1-11-2-211-1-1111111000000−i3−i3i3i300000000000−i3i300−i3i3−i3i30000000
χ2022222-12-2-2222-12-1-1-2-2-2-222-1-2-1-1-1-1-1-1-12211-1-11111-2-2-222-1-1-1-11-2-211-1-1111111000000i3i3−i3−i300000000000i3−i300i3−i3i3−i30000000
χ2122222-12-2-2222-12-1-1-2-2-2-2-2-2-1-21111-1-1-12211-1-11111-2-22-2-21111122-1-1-1-111-1-1-1-1000000−i3−i3i3i300000000000−i3i300i3−i3i3−i30000000
χ2222222-12-2-2222-12-1-1-2-2-2-2-2-2-1-21111-1-1-12211-1-11111-2-22-2-21111122-1-1-1-111-1-1-1-1000000i3i3−i3−i300000000000i3−i300−i3i3−i3i30000000
χ2322222-1-222-222-12-1-1222200-1-2−i3−i3i3i3-1-1-1-2-2-1-111-1-1-1-1-2-2000−i3−i3i3i3100−i3i31111−i3−i3i3i3220000-1-1-1-100000000-2001100−i3i3i3−i30000000
χ2422222-1-222-222-12-1-1222200-1-2−i3−i3i3i3-1-1-1-2-2-1-111-1-1-1-1-2-2000−i3−i3i3i3100−i3i31111−i3−i3i3i3-2-20000111100000000200-1-100i3−i3−i3i30000000
χ2522222-1-222-222-12-1-1222200-1-2i3i3−i3−i3-1-1-1-2-2-1-111-1-1-1-1-2-2000i3i3−i3−i3100i3−i31111i3i3−i3−i3220000-1-1-1-100000000-2001100i3−i3−i3i30000000
χ2622222-1-222-222-12-1-1222200-1-2i3i3−i3−i3-1-1-1-2-2-1-111-1-1-1-1-2-2000i3i3−i3−i3100i3−i31111i3i3−i3−i3-2-20000111100000000200-1-100−i3i3i3−i30000000
χ2722222-1-2-2-2-222-12-1-1-2-2-2-200-12−i3−i3i3i3-1-1-1-2-21111111122000−i3−i3i3i3-100i3−i311-1-1i3i3−i3−i3000000−i3−i3i3i30000000002-2i3−i300-1-1110000000
χ2822222-1-2-2-2-222-12-1-1-2-2-2-200-12−i3−i3i3i3-1-1-1-2-21111111122000−i3−i3i3i3-100i3−i311-1-1i3i3−i3−i3000000i3i3−i3−i3000000000-22−i3i30011-1-10000000
χ2922222-1-2-2-2-222-12-1-1-2-2-2-200-12i3i3−i3−i3-1-1-1-2-21111111122000i3i3−i3−i3-100−i3i311-1-1−i3−i3i3i3000000−i3−i3i3i3000000000-22i3−i30011-1-10000000
χ3022222-1-2-2-2-222-12-1-1-2-2-2-200-12i3i3−i3−i3-1-1-1-2-21111111122000i3i3−i3−i3-100−i3i311-1-1−i3−i3i3i3000000i3i3−i3−i30000000002-2−i3i300-1-1110000000
χ312222-122222-1-12-122-1-1-1-122-122222-1-1-1-1-12222-1-1-1-1-1-12-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-10022220000-1-1-1-1-1-1-1-100000220000-1-1-1-1000
χ322222-122222-1-12-122-1-1-1-122-122222-1-1-1-1-12222-1-1-1-1-1-12-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-100-2-2-2-200001111111100000-2-200001111000
χ332222-122222-1-12-122-1-1-1-1-2-2-12-2-2-2-2-1-1-1-1-12222-1-1-1-1-1-1-2111111211-2-2-1-1-1-111110022220000-1-1-1-1-1-1-1-100000-2-200001111000
χ342222-122222-1-12-122-1-1-1-1-2-2-12-2-2-2-2-1-1-1-1-12222-1-1-1-1-1-1-2111111211-2-2-1-1-1-1111100-2-2-2-200001111111100000220000-1-1-1-1000
χ352222-122-2-22-1-12-122111122-1-22222-1-1-1-1-1-2-222111111-2-1-1-1-1-1-1-211-2-2-1-111111100000000003333−3−3−3−30000000000033−3−3000
χ362222-122-2-22-1-12-122111122-1-22222-1-1-1-1-1-2-222111111-2-1-1-1-1-1-1-211-2-2-1-11111110000000000−3−3−3−3333300000000000−3−333000
χ372222-122-2-22-1-12-1221111-2-2-1-2-2-2-2-2-1-1-1-1-1-2-2221111112111111-2-1-122-1-111-1-1-1-100000000003333−3−3−3−300000000000−3−333000
χ382222-122-2-22-1-12-1221111-2-2-1-2-2-2-2-2-1-1-1-1-1-2-2221111112111111-2-1-122-1-111-1-1-1-10000000000−3−3−3−333330000000000033−3−3000
χ392-22-222200-22-2-2-2-2200002-2202-22-22-2-22-2002-200000002-22-22-2000002-200000000−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i200000−i2i20000−i2i2−i2i2000
χ402-22-222200-22-2-2-2-2200002-2202-22-22-2-22-2002-200000002-22-22-2000002-200000000i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i200000i2−i20000i2−i2i2−i2000
χ412-22-222200-22-2-2-2-220000-2220-22-222-2-22-2002-20000000-22-22-22000002-200000000−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i200000i2−i20000i2−i2i2−i2000
χ422-22-222200-22-2-2-2-220000-2220-22-222-2-22-2002-20000000-22-22-22000002-200000000i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i200000−i2i20000−i2i2−i2i2000
χ432-22-2-12200-2-11-21-223−33−32-2-102-22-2-111-11002-233−3−33−30-11-11-1103−300-113−33−33−300−i2−i2i2i20000ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300000−i2i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000
χ442-22-2-12200-2-11-21-223−33−32-2-102-22-2-111-11002-233−3−33−30-11-11-1103−300-113−33−33−300i2i2−i2−i20000−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300000i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000
χ452-22-2-12200-2-11-21-223−33−3-22-10-22-22-111-11002-233−3−33−301-11-11-10−3300-113−3−33−3300−i2−i2i2i20000ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300000i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000
χ462-22-2-12200-2-11-21-223−33−3-22-10-22-22-111-11002-233−3−33−301-11-11-10−3300-113−3−33−3300i2i2−i2−i20000−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300000−i2i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000
χ472-22-2-12200-2-11-21-22−33−332-2-102-22-2-111-11002-2−3−333−330-11-11-110−3300-11−33−33−3300−i2−i2i2i20000ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700000−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000
χ482-22-2-12200-2-11-21-22−33−332-2-102-22-2-111-11002-2−3−333−330-11-11-110−3300-11−33−33−3300i2i2−i2−i20000−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700000i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000
χ492-22-2-12200-2-11-21-22−33−33-22-10-22-22-111-11002-2−3−333−3301-11-11-103−300-11−333−33−300−i2−i2i2i20000ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700000i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000
χ502-22-2-12200-2-11-21-22−33−33-22-10-22-22-111-11002-2−3−333−3301-11-11-103−300-11−333−33−300i2i2−i2−i20000−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700000−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000
χ512-2-222202-20-2-2-222-222-2-200200000-2-22002-2002-22-200000000000000000000002i−2i−i2i2−i2i22i−2i2i−2i−i2i2−i2i2−i2i2−i2i20000000000000002−20
χ522-2-222202-20-2-2-222-222-2-200200000-2-22002-2002-22-200000000000000000000002i−2ii2−i2i2−i22i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000000000000000−220
χ532-2-222202-20-2-2-222-222-2-200200000-2-22002-2002-22-20000000000000000000000−2i2i−i2i2−i2i2−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000000000000000−220
χ542-2-222202-20-2-2-222-222-2-200200000-2-22002-2002-22-20000000000000000000000−2i2ii2−i2i2−i2−2i2i−2i2ii2−i2i2−i2i2−i2i2−i20000000000000002−20
χ554444-24-444-4-2-24-244-2-2-2-200-2-40000-2-2-22244-4-4-2-2-2-2220000000-4000022220000000000000000000000000000000000000000
χ564444-24-4-4-4-4-2-24-244222200-240000-2-2-222-4-4-4-42222-2-200000004000022-2-20000000000000000000000000000000000000000
χ574444-2-24444-2-2-2-2-2-2-2-2-2-24414-2-2-2-2111-2-2-2-2-2-21111-2-24-2-21111-2-2-2-2-211111111000000000000000000000000000000000000
χ584444-2-24444-2-2-2-2-2-2-2-2-2-2-4-4142222111-2-2-2-2-2-21111-2-2-422-1-1-1-1-222221111-1-1-1-1000000000000000000000000000000000000
χ594444-2-24-4-44-2-2-2-2-2-22222441-4-2-2-2-2111-2-222-2-2-1-1-1-122-4-2-211112222211-1-1-1-1-1-1000000000000000000000000000000000000
χ604444-2-24-4-44-2-2-2-2-2-22222-4-41-42222111-2-222-2-2-1-1-1-122422-1-1-1-12-2-2-2-211-1-11111000000000000000000000000000000000000
χ614444-2-2-444-4-2-2-2-2-2-2-2-2-2-2001-4−2i3−2i32i32i311122-2-222111122000i3i3−i3−i3200−2i32i3-1-1-1-1i3i3−i3−i3000000000000000000000000000000000000
χ624444-2-2-444-4-2-2-2-2-2-2-2-2-2-2001-42i32i3−2i3−2i311122-2-222111122000−i3−i3i3i32002i3−2i3-1-1-1-1−i3−i3i3i3000000000000000000000000000000000000
χ634444-2-2-4-4-4-4-2-2-2-2-2-222220014−2i3−2i32i32i3111222222-1-1-1-1-2-2000i3i3−i3−i3-2002i3−2i3-1-111−i3−i3i3i3000000000000000000000000000000000000
χ644444-2-2-4-4-4-4-2-2-2-2-2-2222200142i32i3−2i3−2i3111222222-1-1-1-1-2-2000−i3−i3i3i3-200−2i32i3-1-111i3i3−i3−i3000000000000000000000000000000000000
χ6544-4-4440000-444-4-4-4000000400000-44-400000000000000000000000000000000002-2-2200002-2-222-2-22000000000000000000
χ6644-4-4440000-444-4-4-4000000400000-44-40000000000000000000000000000000000-222-20000-222-2-222-2000000000000000000
χ6744-4-4-2400002-242-4-423−23−232300-2000002-2200000023−23−23230000000000000000000000002-2-220000−1−31+31+3−1−3−1+31−31−3−1+3000000000000000000
χ6844-4-4-2400002-242-4-423−23−232300-2000002-2200000023−23−2323000000000000000000000000-222-200001+3−1−3−1−31+31−3−1+3−1+31−3000000000000000000
χ6944-4-4-2400002-242-4-4−232323−2300-2000002-22000000−232323−230000000000000000000000002-2-220000−1+31−31−3−1+3−1−31+31+3−1−3000000000000000000
χ7044-4-4-2400002-242-4-4−232323−2300-2000002-22000000−232323−23000000000000000000000000-222-200001−3−1+3−1+31−31+3−1−3−1−31+3000000000000000000
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χ764-44-4-24-4004-22-42-4423−2323−2300-200000-2222-200-442323−23−23−23230000000000002-2−23230000000000000000000000000000000000000000
χ774-44-4-24-4004-22-42-44−2323−232300-200000-2222-200-44−23−23232323−230000000000002-223−230000000000000000000000000000000000000000
χ784-44-4-2-2400-4-22222-223−2323−234-410-22-221-1-1-2200-22−3−33323−230-221-11-1023−23001-1−33−33−33000000000000000000000000000000000000
χ794-44-4-2-2400-4-22222-223−2323−23-44102-22-21-1-1-2200-22−3−33323−2302-2-11-110−2323001-1−333−33−3000000000000000000000000000000000000
χ804-44-4-2-2400-4-22222-2−2323−23234-410-22-221-1-1-2200-2233−3−3−23230-221-11-10−2323001-13−33−33−3000000000000000000000000000000000000
χ814-44-4-2-2400-4-22222-2−2323−2323-44102-22-21-1-1-2200-2233−3−3−232302-2-11-11023−23001-13−3−33−33000000000000000000000000000000000000
χ824-44-4-2-2-4004-22222-223−2323−230010−2i32i32i3−2i31-1-12-2002-2−3−333−2323000i3−i3−i3i300000-113−3−3i3i3i−3i000000000000000000000000000000000000
χ834-44-4-2-2-4004-22222-223−2323−2300102i3−2i3−2i32i31-1-12-2002-2−3−333−2323000−i3i3i3−i300000-113−33i−3i−3i3i000000000000000000000000000000000000
χ844-44-4-2-2-4004-22222-2−2323−23230010−2i32i32i3−2i31-1-12-2002-233−3−323−23000i3−i3−i3i300000-11−333i−3i−3i3i000000000000000000000000000000000000
χ854-44-4-2-2-4004-22222-2−2323−232300102i3−2i3−2i32i31-1-12-2002-233−3−323−23000−i3i3i3−i300000-11−33−3i3i3i−3i000000000000000000000000000000000000
χ864-4-44440-440-4-4-444-4-4-44400400000-4-4400-4400-44-440000000000000000000000000000000000000000000000000000000000
χ874-4-444-204-40-4-424-2244-4-400-20000022-200-2200-22-2200000000000000000000004i−4i0000−2i2i−2i2i00000000000000000000000000
χ884-4-444-204-40-4-424-2244-4-400-20000022-200-2200-22-220000000000000000000000−4i4i00002i−2i2i−2i00000000000000000000000000
χ894-4-444-20-440-4-424-22-4-44400-20000022-2002-2002-22-2000000000000000000000000000023−23−232300000000000000000000000000
χ904-4-444-20-440-4-424-22-4-44400-20000022-2002-2002-22-20000000000000000000000000000−232323−2300000000000000000000000000
χ914-4-44-2404-4022-4-24-4-2-22200-20000022-2004-400-22-22000000000000000000000000−2i22i2−2i22i20000i2−i2i2−i2i2−i2i2−i2000000000000000000
χ924-4-44-2404-4022-4-24-4-2-22200-20000022-2004-400-22-220000000000000000000000002i2−2i22i2−2i20000−i2i2−i2i2−i2i2−i2i2000000000000000000
χ934-4-44-240-44022-4-24-422-2-200-20000022-200-44002-22-200000000000000000000000000000000i6−i6i6−i6−i6i6−i6i6000000000000000000
χ944-4-44-240-44022-4-24-422-2-200-20000022-200-44002-22-200000000000000000000000000000000−i6i6−i6i6i6−i6i6−i6000000000000000000
χ9588-8-88-40000-88-4-844000000-4000004-4400000000000000000000000000000000000000000000000000000000000000000000
χ9688-8-8-4-400004-4-444443−43−434300200000-22-2000000−232323−230000000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-400004-4-4444−434343−4300200000-22-200000023−23−23230000000000000000000000000000000000000000000000000000000000
χ988-8-88-4-408-80444-4-44-4-44400200000-2-2200-44002-22-20000000000000000000000000000000000000000000000000000000000
χ998-8-88-4-40-880444-4-4444-4-400200000-2-22004-400-22-220000000000000000000000000000000000000000000000000000000000

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