Finite Group Databasebeta

← Group #11781445

Character table — Group #11781445

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111222222222222222244444444444444444444444444444666666666666888888888888888881212121212121212121212121212121212122424242424244848487272144
order1222334444666666121212122234446666666121212121212121212121212121212128888242424242424242466666612121212121212121212128888882424242424242424242424248824242424266884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ511111111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-111111111111111111-1-1-1-1-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-111-1
χ611111111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-111111111111111111-1-1-1-1-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ711111111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-11
χ811111111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111111-1
χ92222222-2-22222222-2-2-2-2222-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-22000000000000222222-2-2-222-2-2-2-2-2-2000000000000000000000000000000
χ102222222-2-22222222-2-2-2-2-2-22-222-2-2-2-2222222-2-2-2-22222-2-2-2-22000000000000-2-2-2-2-2-2-22222-2-22222000000000000000000000000000000
χ11222222-222-22222222222002-2000000222-2-2-2-2-22200002222-2222222222222000000-200-2-2-2-20000-2-20000-2-2-2-200000000000000000000
χ12222222-222-22222222222002-2000000222-2-2-2-2-22200002222-2-2-2-2-2-2-2-2-2-2-2-2-2000000-200-2-2-2-20000220000222200000000000000000000
χ13222222-2-2-2-2222222-2-2-2-20022000000222-2-2-222-2-20000-2-2-2-2-2000000000000000000200-2-2220000002i2i−2i−2i00002i2i2i2i−2i−2i−2i−2i000000000000
χ14222222-2-2-2-2222222-2-2-2-20022000000222-2-2-222-2-20000-2-2-2-2-2000000000000000000200-2-222000000−2i−2i2i2i0000−2i−2i−2i−2i2i2i2i2i000000000000
χ1522222-1222222-1-12-1222222-12222222-1-1-122-122-1-12222-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000022-1-1-1-12-1-1000
χ1622222-1222222-1-12-1222222-12222222-1-1-122-122-1-12222-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-21111-211000
χ1722222-1222222-1-12-12222-2-2-12-2-2-2-2-2-2-1-1-122-122-1-1-2-2-2-2-1-1-1-1-1000000000000111111-111-1-1-1-1111100000000000000000022-1-1-1-1-211000
χ1822222-1222222-1-12-12222-2-2-12-2-2-2-2-2-2-1-1-122-122-1-1-2-2-2-2-1-1-1-1-1000000000000111111-111-1-1-1-11111000000000000000000-2-211112-1-1000
χ1922222-12-2-2222-1-12-1-2-2-2-222-1-2-2-22222-1-1-122-1-2-211-2-2-2-21111-1000000000000-1-1-1-1-1-1111-1-111111100000000000000000000−i3−i3i3i30−i3i3000
χ2022222-12-2-2222-1-12-1-2-2-2-222-1-2-2-22222-1-1-122-1-2-211-2-2-2-21111-1000000000000-1-1-1-1-1-1111-1-111111100000000000000000000i3i3−i3−i30i3−i3000
χ2122222-12-2-2222-1-12-1-2-2-2-2-2-2-1-222-2-2-2-2-1-1-122-1-2-21122221111-10000000000001111111-1-1-1-111-1-1-1-100000000000000000000−i3−i3i3i30i3−i3000
χ2222222-12-2-2222-1-12-1-2-2-2-2-2-2-1-222-2-2-2-2-1-1-122-1-2-21122221111-10000000000001111111-1-1-1-111-1-1-1-100000000000000000000i3i3−i3−i30−i3i3000
χ232222-122222-1-122-12-1-1-1-122-1222-1-1-1-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ242222-122222-1-122-12-1-1-1-122-1222-1-1-1-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-12-2-2-2-21111111122-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111111111000000000000
χ252222-122222-1-122-12-1-1-1-1-2-2-12-2-21111-1-1-1-1-12-1-1221111-1-1-1-122222-1-1-1-1-1-1-1-1-2-211112-2-2-1-1-1-1111122-2-2-2-2-1-1-1-111111111000000000000
χ262222-122222-1-122-12-1-1-1-1-2-2-12-2-21111-1-1-1-1-12-1-1221111-1-1-1-12-2-2-2-211111111-2-211112-2-2-1-1-1-11111-2-222221111-1-1-1-1-1-1-1-1000000000000
χ272222-122-2-22-1-122-12111122-1-2-2-2-1-1-1-1-1-1-1-1-1211-2-211111111200003333−3−3−3−322-1-1-1-1-2-2-2-1-111111100000033−3−333−3−333−3−3000000000000
χ282222-122-2-22-1-122-12111122-1-2-2-2-1-1-1-1-1-1-1-1-1211-2-21111111120000−3−3−3−3333322-1-1-1-1-2-2-2-1-1111111000000−3−333−3−333−3−333000000000000
χ292222-122-2-22-1-122-121111-2-2-1-2221111-1-1-1-1-1211-2-2-1-1-1-11111200003333−3−3−3−3-2-21111-222-1-111-1-1-1-100000033−3−3−3−333−3−333000000000000
χ302222-122-2-22-1-122-121111-2-2-1-2221111-1-1-1-1-1211-2-2-1-1-1-1111120000−3−3−3−33333-2-21111-222-1-111-1-1-1-1000000−3−33333−3−333−3−3000000000000
χ312222-12-222-2-1-122-12-1-1-1-100-1-200−i3−i3i3i3-1-1-111-21122−i3−i3i3i3-1-1-1-1-22222-1-1-1-1-1-1-1-100−i3−i3i3i3-2001111−i3−i3i3i3-2-200001111−i3−i3i3i3i3i3−i3−i3000000000000
χ322222-12-222-2-1-122-12-1-1-1-100-1-200−i3−i3i3i3-1-1-111-21122−i3−i3i3i3-1-1-1-1-2-2-2-2-21111111100−i3−i3i3i3-2001111−i3−i3i3i3220000-1-1-1-1i3i3−i3−i3−i3−i3i3i3000000000000
χ332222-12-222-2-1-122-12-1-1-1-100-1-200i3i3−i3−i3-1-1-111-21122i3i3−i3−i3-1-1-1-1-22222-1-1-1-1-1-1-1-100i3i3−i3−i3-2001111i3i3−i3−i3-2-200001111i3i3−i3−i3−i3−i3i3i3000000000000
χ342222-12-222-2-1-122-12-1-1-1-100-1-200i3i3−i3−i3-1-1-111-21122i3i3−i3−i3-1-1-1-1-2-2-2-2-21111111100i3i3−i3−i3-2001111i3i3−i3−i3220000-1-1-1-1−i3−i3i3i3i3i3−i3−i3000000000000
χ352222-12-2-2-2-2-1-122-12111100-1200−i3−i3i3i3-1-1-111-2-1-1-2-2i3i3−i3−i31111-200003333−3−3−3−300−i3−i3i3i320011-1-1i3i3−i3−i3002i2i−2i−2i−3−333−i−i−i−iiiii000000000000
χ362222-12-2-2-2-2-1-122-12111100-1200−i3−i3i3i3-1-1-111-2-1-1-2-2i3i3−i3−i31111-20000−3−3−3−3333300−i3−i3i3i320011-1-1i3i3−i3−i300−2i−2i2i2i33−3−3iiii−i−i−i−i000000000000
χ372222-12-2-2-2-2-1-122-12111100-1200i3i3−i3−i3-1-1-111-2-1-1-2-2−i3−i3i3i31111-200003333−3−3−3−300i3i3−i3−i320011-1-1−i3−i3i3i300−2i−2i2i2i−3−333iiii−i−i−i−i000000000000
χ382222-12-2-2-2-2-1-122-12111100-1200i3i3−i3−i3-1-1-111-2-1-1-2-2−i3−i3i3i31111-20000−3−3−3−3333300i3i3−i3−i320011-1-1−i3−i3i3i3002i2i−2i−2i33−3−3−i−i−i−iiiii000000000000
χ392-22-22202-20-2-2-2-22222-2-20020000000-2-22000002-2000022-2-202i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000002−22−22−2000−i2i20
χ402-22-22202-20-2-2-2-22222-2-20020000000-2-22000002-2000022-2-202i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000−22−22−22000i2−i20
χ412-22-22202-20-2-2-2-22222-2-20020000000-2-22000002-2000022-2-20−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000002−22−22−2000i2−i20
χ422-22-22202-20-2-2-2-22222-2-20020000000-2-22000002-2000022-2-20−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000−22−22−22000−i2i20
χ432-2-2222200-22-22-2-2-2000000202i−2i00002-2-22-2200002i−2i2i−2i0000-22−22−22−22−22−22−200000002i−2i2-2002i−2i2i−2i2−2−i2i2−i2i22−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ442-2-2222200-22-22-2-2-2000000202i−2i00002-2-22-2200002i−2i2i−2i0000-2−22−22−22−22−22−2200000002i−2i2-2002i−2i2i−2i−22i2−i2i2−i2−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ452-2-2222200-22-22-2-2-200000020−2i2i00002-2-22-220000−2i2i−2i2i0000-22−22−22−22−22−22−20000000−2i2i2-200−2i2i−2i2i2−2i2−i2i2−i22−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ462-2-2222200-22-22-2-2-200000020−2i2i00002-2-22-220000−2i2i−2i2i0000-2−22−22−22−22−22−220000000−2i2i2-200−2i2i−2i2i−22−i2i2−i2i2−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ472-2-2222-20022-22-2-2-200002-220002-22-22-2-2-22-200000000000022−22−22−22−22−22−22-22-22-2000-22000000−222−2−22−22−222−22−2−22−22000000000000
χ482-2-2222-20022-22-2-2-200002-220002-22-22-2-2-22-20000000000002−22−22−22−22−22−222-22-22-2000-220000002−2−222−22−22−2−22−222−22−2000000000000
χ492-2-2222-20022-22-2-2-20000-222000-22-222-2-2-22-200000000000022−22−22−22−22−22−2-22-22-22000-22000000−22−222−2−22−22−22−222−22−2000000000000
χ502-2-2222-20022-22-2-2-20000-222000-22-222-2-2-22-20000000000002−22−22−22−22−22−22-22-22-22000-220000002−22−2−222−22−22−22−2−22−22000000000000
χ512-2-22-12200-2-112-21-23−33−300-102i−2i−i3i3i3−i3-111-1123−300−ii−ii3−33−3-22−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700−i3i3i3−i302i−2i-113−3−ii−ii2−2−i2i2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ522-2-22-12200-2-112-21-23−33−300-102i−2i−i3i3i3−i3-111-1123−300−ii−ii3−33−3-2−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700−i3i3i3−i302i−2i-113−3−ii−ii−22i2−i2i2−i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ532-2-22-12200-2-112-21-23−33−300-10−2i2ii3−i3−i3i3-111-1123−300i−ii−i3−33−3-22−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700i3−i3−i3i30−2i2i-113−3i−ii−i2−2i2−i2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ542-2-22-12200-2-112-21-23−33−300-10−2i2ii3−i3−i3i3-111-1123−300i−ii−i3−33−3-2−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700i3−i3−i3i30−2i2i-113−3i−ii−i−22−i2i2−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ552-2-22-12200-2-112-21-2−33−3300-102i−2ii3−i3−i3i3-111-112−3300−ii−ii−33−33-22−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300i3−i3−i3i302i−2i-11−33−ii−ii2−2−i2i2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ562-2-22-12200-2-112-21-2−33−3300-102i−2ii3−i3−i3i3-111-112−3300−ii−ii−33−33-2−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300i3−i3−i3i302i−2i-11−33−ii−ii−22i2−i2i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ572-2-22-12200-2-112-21-2−33−3300-10−2i2i−i3i3i3−i3-111-112−3300i−ii−i−33−33-22−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300−i3i3i3−i30−2i2i-11−33i−ii−i2−2i2−i2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ582-2-22-12200-2-112-21-2−33−3300-10−2i2i−i3i3i3−i3-111-112−3300i−ii−i−33−33-2−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300−i3i3i3−i30−2i2i-11−33i−ii−i−22−i2i2−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ592-2-22-12-2002-112-21-23−33−32-2-1000-11-11-1111-1-2−33003−3−333−33−322−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ72-2-11-110001-1−333−3−33−222−2−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ602-2-22-12-2002-112-21-23−33−32-2-1000-11-11-1111-1-2−33003−3−333−33−32−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ72-2-11-110001-1−333−3−332−2−222−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ612-2-22-12-2002-112-21-23−33−3-22-10001-11-1-1111-1-2−3300−333−33−33−322−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7-221-11-10001-1−33−333−3−22−222−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ622-2-22-12-2002-112-21-23−33−3-22-10001-11-1-1111-1-2−3300−333−33−33−32−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7-221-11-10001-1−33−333−32−22−2−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ632-2-22-12-2002-112-21-2−33−332-2-1000-11-11-1111-1-23−300−333−3−33−3322−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ232-2-11-110001-13−3−333−3−222−2−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ642-2-22-12-2002-112-21-2−33−332-2-1000-11-11-1111-1-23−300−333−3−33−332−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ232-2-11-110001-13−3−333−32−2−222−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
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χ1088-88-8-4-40-8804444-4-444-4-40020000000-2-22000004-40000-2-222000000000000000000000000000000000000000000000000000000000000

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