Finite Group Databasebeta

← Group #11780257

Character table — Group #11780257

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size1111222222222222222244444444444444444444444888888888888888888881212121212121212121212121212121212122424242424242424242424242424247272144
order12223344446666661212121234446661212121212121212121212121212121241212121212121212121212121212121212121244888812121212242424242424242424466881212121224242424884
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
χ5111111111111111111111-1-1111111-1-1-1-11111111111-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-1111111-1-1-1-11111111111-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-11
χ7111111111111111111111-1-1111111-1-1-1-11111111111-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-111-1-1-1-11111-1-1-1-1-1-11
χ8111111111111111111111-1-1111111-1-1-1-11111111111-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1
χ92222222-2-22222222-2-2-2-2222-222222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-222-2-22222-2-2-2-2000000000000000000000000000000000000
χ102222222-2-22222222-2-2-2-22-2-2-222222-2-2-2-222-2-2-2-2-2-2-2-22-2-2-2222222-2-2-2-2-2-22222000000000000000000000000000000000000
χ11222222-222-22222222222200-2222-2-20000-2-2222222-2-20-2000000-2-2-2-200000000220000222200000000-200-2-20000000000000
χ12222222-222-22222222222200-2222-2-20000-2-2222222-2-20-2000000-2-2-2-200000000-2-20000-2-2-2-200000000200220000000000000
χ13222222-2-2-2-2222222-2-2-2-22002222-2-20000-2-2-2-2-2-2-2-22202000000-2-2220000000000000000000000000002-2000022-2-20000000
χ14222222-2-2-2-2222222-2-2-2-22002222-2-20000-2-2-2-2-2-2-2-22202000000-2-222000000000000000000000000000-220000-2-2220000000
χ1522222-12222222-1-1-12222-1222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1220000-1-1-1-100000000222-1-100-1-1-1-10000000
χ1622222-12222222-1-1-12222-1222-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20000111100000000-2-2-2110011110000000
χ1722222-12222222-1-1-12222-1-2-22-1-1-1221111-1-1-1-1-1-1-1-122-2-1-2-2-2-211-1-1-1-111111111220000-1-1-1-1000000002-2-2-1-10011110000000
χ1822222-12222222-1-1-12222-1-2-22-1-1-1221111-1-1-1-1-1-1-1-122-2-1-2-2-2-211-1-1-1-111111111-2-20000111100000000-2221100-1-1-1-10000000
χ1922222-12-2-22222-1-1-1-2-2-2-2-122-2-1-1-122-1-1-1-1-1-1111111-2-2-2122-2-211-1-111-1-1-1-11111000000−i3−i3i3i300000000000−i3i300−i3i3−i3i30000000
χ2022222-12-2-22222-1-1-1-2-2-2-2-122-2-1-1-122-1-1-1-1-1-1111111-2-2-2122-2-211-1-111-1-1-1-11111000000i3i3−i3−i300000000000i3−i300i3−i3i3−i30000000
χ2122222-12-2-22222-1-1-1-2-2-2-2-1-2-2-2-1-1-1221111-1-1111111-2-221-2-222-1-1-1-1111111-1-1-1-1000000−i3−i3i3i300000000000−i3i300i3−i3i3−i30000000
χ2222222-12-2-22222-1-1-1-2-2-2-2-1-2-2-2-1-1-1221111-1-1111111-2-221-2-222-1-1-1-1111111-1-1-1-1000000i3i3−i3−i300000000000i3−i300−i3i3−i3i30000000
χ2322222-1-222-2222-1-1-12222-100-2-1-1-1-2-2−i3−i3i3i311-1-1-1-1-1-1-2-2010000−i3i31111−i3−i3i3i3−i3−i3i3i3220000-1-1-1-100000000-2001100−i3i3i3−i30000000
χ2422222-1-222-2222-1-1-12222-100-2-1-1-1-2-2−i3−i3i3i311-1-1-1-1-1-1-2-2010000−i3i31111−i3−i3i3i3−i3−i3i3i3-2-20000111100000000200-1-100i3−i3−i3i30000000
χ2522222-1-222-2222-1-1-12222-100-2-1-1-1-2-2i3i3−i3−i311-1-1-1-1-1-1-2-2010000i3−i31111i3i3−i3−i3i3i3−i3−i3220000-1-1-1-100000000-2001100i3−i3−i3i30000000
χ2622222-1-222-2222-1-1-12222-100-2-1-1-1-2-2i3i3−i3−i311-1-1-1-1-1-1-2-2010000i3−i31111i3i3−i3−i3i3i3−i3−i3-2-20000111100000000200-1-100−i3i3i3−i30000000
χ2722222-1-2-2-2-2222-1-1-1-2-2-2-2-1002-1-1-1-2-2−i3−i3i3i311111111220-10000i3−i311-1-1−i3−i3i3i3i3i3−i3−i3000000−i3−i3i3i30000000002-2i3−i300-1-1110000000
χ2822222-1-2-2-2-2222-1-1-1-2-2-2-2-1002-1-1-1-2-2−i3−i3i3i311111111220-10000i3−i311-1-1−i3−i3i3i3i3i3−i3−i3000000i3i3−i3−i3000000000-22−i3i30011-1-10000000
χ2922222-1-2-2-2-2222-1-1-1-2-2-2-2-1002-1-1-1-2-2i3i3−i3−i311111111220-10000−i3i311-1-1i3i3−i3−i3−i3−i3i3i3000000−i3−i3i3i3000000000-22i3−i30011-1-10000000
χ3022222-1-2-2-2-2222-1-1-1-2-2-2-2-1002-1-1-1-2-2i3i3−i3−i311111111220-10000−i3i311-1-1i3i3−i3−i3−i3−i3i3i3000000i3i3−i3−i30000000002-2−i3i300-1-1110000000
χ312222-122222-1-1-1222-1-1-1-1-1222-1-1-1-1-122222222-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-10022220000-1-1-1-1-1-1-1-100000220000-1-1-1-1000
χ322222-122222-1-1-1222-1-1-1-1-1222-1-1-1-1-122222222-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-200001111111100000-2-200001111000
χ332222-122222-1-1-1222-1-1-1-1-1-2-22-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-221111-2-2-1-1-1-1111111110022220000-1-1-1-1-1-1-1-100000-2-200001111000
χ342222-122222-1-1-1222-1-1-1-1-1-2-22-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-221111-2-2-1-1-1-11111111100-2-2-2-200001111111100000220000-1-1-1-1000
χ352222-122-2-22-1-1-12221111-122-2-1-1-1-1-1222222-2-2111111-2-2-1-111-2-2-1-111-1-1-1-1111100000000003333−3−3−3−30000000000033−3−3000
χ362222-122-2-22-1-1-12221111-122-2-1-1-1-1-1222222-2-2111111-2-2-1-111-2-2-1-111-1-1-1-111110000000000−3−3−3−3333300000000000−3−333000
χ372222-122-2-22-1-1-12221111-1-2-2-2-1-1-1-1-1-2-2-2-222-2-21111112-211-1-122-1-1111111-1-1-1-100000000003333−3−3−3−300000000000−3−333000
χ382222-122-2-22-1-1-12221111-1-2-2-2-1-1-1-1-1-2-2-2-222-2-21111112-211-1-122-1-1111111-1-1-1-10000000000−3−3−3−333330000000000033−3−3000
χ392-22-222-2002-22-2-22-2000022i−2i0-22-22-22i−2i2i−2i2-200000000002i−2i00002-2002i−2i2i−2i00000022−2−2000022−2−222−2−200000−i2i20000−i2i2−i2i2000
χ402-22-222-2002-22-2-22-2000022i−2i0-22-22-22i−2i2i−2i2-200000000002i−2i00002-2002i−2i2i−2i000000−2−2220000−2−222−2−22200000i2−i20000i2−i2i2−i2000
χ412-22-222-2002-22-2-22-200002−2i2i0-22-22-2−2i2i−2i2i2-20000000000−2i2i00002-200−2i2i−2i2i00000022−2−2000022−2−222−2−200000i2−i20000i2−i2i2−i2000
χ422-22-222-2002-22-2-22-200002−2i2i0-22-22-2−2i2i−2i2i2-20000000000−2i2i00002-200−2i2i−2i2i000000−2−2220000−2−222−2−22200000−i2i20000−i2i2−i2i2000
χ432-22-2-12-20021-11-22-23−33−3-12i−2i01-11-112i−2i2i−2i2-20033−3−33−300−ii−i3i300-113−3−ii−ii−i3i3−i3i30022−2−20000ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300000−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000
χ442-22-2-12-20021-11-22-23−33−3-12i−2i01-11-112i−2i2i−2i2-20033−3−33−300−ii−i3i300-113−3−ii−ii−i3i3−i3i300−2−2220000−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300000i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000
χ452-22-2-12-20021-11-22-23−33−3-1−2i2i01-11-11−2i2i−2i2i2-20033−3−33−300i−ii3−i300-113−3i−ii−ii3−i3i3−i30022−2−20000ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300000i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000
χ462-22-2-12-20021-11-22-23−33−3-1−2i2i01-11-11−2i2i−2i2i2-20033−3−33−300i−ii3−i300-113−3i−ii−ii3−i3i3−i300−2−2220000−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300000−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000
χ472-22-2-12-20021-11-22-2−33−33-12i−2i01-11-112i−2i2i−2i2-200−3−333−3300−iii3−i300-11−33−ii−iii3−i3i3−i30022−2−20000ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700000−i2i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000
χ482-22-2-12-20021-11-22-2−33−33-12i−2i01-11-112i−2i2i−2i2-200−3−333−3300−iii3−i300-11−33−ii−iii3−i3i3−i300−2−2220000−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700000i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000
χ492-22-2-12-20021-11-22-2−33−33-1−2i2i01-11-11−2i2i−2i2i2-200−3−333−3300i−i−i3i300-11−33i−ii−i−i3i3−i3i30022−2−20000ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700000i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000
χ502-22-2-12-20021-11-22-2−33−33-1−2i2i01-11-11−2i2i−2i2i2-200−3−333−3300i−i−i3i300-11−33i−ii−i−i3i3−i3i300−2−2220000−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700000−i2i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000
χ512-2-222202-202-2-2-2-2222-2-220002-2-2000000002-22-22-200000000000000000000002i−2i2−22−22i−2i2i−2i2−22−22−22−2000000000000000−i2i20
χ522-2-222202-202-2-2-2-2222-2-220002-2-2000000002-22-22-200000000000000000000002i−2i−22−222i−2i2i−2i−22−22−22−22000000000000000i2−i20
χ532-2-222202-202-2-2-2-2222-2-220002-2-2000000002-22-22-20000000000000000000000−2i2i2−22−2−2i2i−2i2i2−22−22−22−2000000000000000i2−i20
χ542-2-222202-202-2-2-2-2222-2-220002-2-2000000002-22-22-20000000000000000000000−2i2i−22−22−2i2i−2i2i−22−22−22−22000000000000000−i2i20
χ554444-24-444-4-2-2-2444-2-2-2-2-200-4-2-2-2220000-4-444-2-2-2-2220-4000000222200000000000000000000000000000000000000000000
χ564444-24-4-4-4-4-2-2-24442222-2004-2-2-2220000-4-4-4-42222-2-20400000022-2-200000000000000000000000000000000000000000000
χ574444-2-24444-2-2-2-2-2-2-2-2-2-21444111-2-2-2-2-2-2-2-2-2-21111-2-24-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000
χ584444-2-24444-2-2-2-2-2-2-2-2-2-21-4-44111-2-22222-2-2-2-21111-2-2-4-22222221111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ594444-2-24-4-44-2-2-2-2-2-22222144-4111-2-2-2-2-2-2-2-222-1-1-1-122-42-2-2222211-1-11111-1-1-1-1000000000000000000000000000000000000
χ604444-2-24-4-44-2-2-2-2-2-222221-4-4-4111-2-22222-2-222-1-1-1-1224222-2-2-2-211-1-1-1-1-1-11111000000000000000000000000000000000000
χ614444-2-2-444-4-2-2-2-2-2-2-2-2-2-2100-411122−2i3−2i32i32i322-2-2111122020000−2i32i3-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000000000000000000000000000000000
χ624444-2-2-444-4-2-2-2-2-2-2-2-2-2-2100-4111222i32i3−2i3−2i322-2-21111220200002i3−2i3-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000000000
χ634444-2-2-4-4-4-4-2-2-2-2-2-22222100411122−2i3−2i32i32i32222-1-1-1-1-2-20-200002i3−2i3-1-111i3i3−i3−i3−i3−i3i3i3000000000000000000000000000000000000
χ644444-2-2-4-4-4-4-2-2-2-2-2-222221004111222i32i3−2i3−2i32222-1-1-1-1-2-20-20000−2i32i3-1-111−i3−i3i3i3i3i3−i3−i3000000000000000000000000000000000000
χ6544-4-4440000-4-444-4-400004000-4-44000000000000000000000000000000000000002-2-2200002-2-222-2-22000000000000000000
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χ6844-4-4-24000022-24-4-423−23−2323-200022-2000000000023−23−2323000000000000000000000000-222-200001−3−1+3−1+31−31+3−1−3−1−31+3000000000000000000
χ6944-4-4-24000022-24-4-4−232323−23-200022-20000000000−232323−230000000000000000000000002-2-220000−1−31+31+3−1−3−1+31−31−3−1+3000000000000000000
χ7044-4-4-24000022-24-4-4−232323−23-200022-20000000000−232323−23000000000000000000000000-222-200001+3−1−3−1−31+31−3−1+3−1+31−3000000000000000000
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χ754-44-44-2-4004-44-42-220000-2−4i4i02-224-42i−2i2i−2i-220000000000−4i4i0000-22002i−2i2i−2i0000000000000000000000000000000000000000
χ764-44-4-24400-42-22-44-423−2323−23-20002-222-20000-44002323−23−23−2323000000002-2−232300000000000000000000000000000000000000000000
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χ834-44-4-2-2-40042-222-2223−2323−231−4i4i0-11-1-222i−2i2i−2i-2200−3−33323−23002i−2i2i3−2i3001-1−33−ii−ii−i3i3−i3i3000000000000000000000000000000000000
χ844-44-4-2-2-40042-222-22−2323−232314i−4i0-11-1-22−2i2i−2i2i-220033−3−3−232300−2i2i2i3−2i3001-13−3i−ii−i−i3i3−i3i3000000000000000000000000000000000000
χ854-44-4-2-2-40042-222-22−2323−23231−4i4i0-11-1-222i−2i2i−2i-220033−3−3−2323002i−2i−2i32i3001-13−3−ii−iii3−i3i3−i3000000000000000000000000000000000000
χ864-4-44440-4404-4-4-4-44-4-44440004-4-400000000-44-44-440000000000000000000000000000000000000000000000000000000000
χ874-4-444-204-404-4-422-244-4-4-2000-22200000000-22-22-2200000000000000000000004i−4i0000−2i2i−2i2i00000000000000000000000000
χ884-4-444-204-404-4-422-244-4-4-2000-22200000000-22-22-220000000000000000000000−4i4i00002i−2i2i−2i00000000000000000000000000
χ894-4-444-20-4404-4-422-2-4-444-2000-222000000002-22-22-2000000000000000000000000000023−23−232300000000000000000000000000
χ904-4-444-20-4404-4-422-2-4-444-2000-222000000002-22-22-20000000000000000000000000000−232323−2300000000000000000000000000
χ914-4-44-2404-40-222-4-44-2-222-2000-222000000004-4-22-2200000000000000000000000022−2222−220000−22−22−22−22000000000000000000
χ924-4-44-2404-40-222-4-44-2-222-2000-222000000004-4-22-22000000000000000000000000−2222−222200002−22−22−22−2000000000000000000
χ934-4-44-240-440-222-4-4422-2-2-2000-22200000000-442-22-2000000000000000000000000000000006−66−6−66−66000000000000000000
χ944-4-44-240-440-222-4-4422-2-2-2000-22200000000-442-22-200000000000000000000000000000000−66−666−66−6000000000000000000
χ9588-8-88-40000-8-88-4440000-400044-4000000000000000000000000000000000000000000000000000000000000000000000000
χ9688-8-8-4-4000044-4-44443−43−43432000-2-220000000000−232323−230000000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-4000044-4-444−434343−432000-2-22000000000023−23−23230000000000000000000000000000000000000000000000000000000000
χ988-8-88-4-408-80-44444-4-4-44420002-2-200000000-442-22-20000000000000000000000000000000000000000000000000000000000
χ998-8-88-4-40-880-44444-444-4-420002-2-2000000004-4-22-220000000000000000000000000000000000000000000000000000000000

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