Finite Group Databasebeta

← Group #13156309

Character table — Group #13156309

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size111122222222222222222244444444444444444444444488888888881212121212121212121212121212121212121212121212121212121212121212121212121212181824242424242424243636363636727272727272108108
order12223334466666666612121212333666666666121212121212121212121212366612121212121222888824242424242424242424242424242424242424242424242424242424242424244466666666412121212441212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111111111-1-1-1-1-1-11-1-111-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-111
χ511111111111111111111111111111111111111111111111111111111-1-111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000000000002200000000-222-2-200000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-200000000000000000000000000000000000000-2-2000000002-2-22200000000
χ11222222-1222-122-1222-122222-1-122-1-1-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-122002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-10022-1-1-1-1-1-1000000200-1-100
χ12222222-1222-122-1222-122222-1-122-1-1-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-12200-2-20000-2-2-2-20000000000001111111111110022-1-1-1-1-1-1000000-2001100
χ13222222-1222-122-1222-122222-1-122-1-1-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100-2-2111111000000-2001100
χ14222222-1222-122-1222-122222-1-122-1-1-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-20000-2-2-2-200000000000011111111111100-2-2111111000000200-1-100
χ1522222-1222-122-1222-122222-12-1-1-122-1-1-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-122220022220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000-1-122-1-1-1-10000020-1-10000
χ1622222-1222-122-1222-122222-12-1-1-122-1-1-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-122-2-200-2-2-2-2000011111111111100000000000000-1-122-1-1-1-100000-20110000
χ1722222-1222-122-1222-122222-12-1-1-122-1-1-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1-2-2220022220000-1-1-1-1-1-1-1-1-1-1-1-10000000000000011-2-2111100000-20110000
χ1822222-1222-122-1222-122222-12-1-1-122-1-1-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-200-2-2-2-200001111111111110000000000000011-2-211110000020-1-10000
χ192222-1222222-122-1-122-1-1-1-1-1-12-1-1-1-122-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1002222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122000000002-1-1-1-100000000
χ202222-1222222-122-1-122-1-1-1-1-1-12-1-1-1-122-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10022-2-2-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-200000000-2111100000000
χ212222-1222222-122-1-122-1-1-1-1-1-12-1-1-1-122-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-2-2221111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-200000000-2111100000000
χ222222-1222222-122-1-122-1-1-1-1-1-12-1-1-1-122-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-2-2-2-211111111-2-2-2-211111111-2-2-2-21111111122000000002-1-1-1-100000000
χ232222-122-2-222-122-1-1221111-1-12-1-1-1-122-1-12-2-21111-2-21111-1-1-1-1-2-2111100000033−3−333−3−300003333−3−3−3−300003333−3−3−3−32200000000-2-1-11100000000
χ242222-122-2-222-122-1-1221111-1-12-1-1-1-122-1-12-2-21111-2-21111-1-1-1-1-2-2111100000033−3−3−3−33300003333−3−3−3−30000−3−3−3−33333-2-200000000211-1-100000000
χ252222-122-2-222-122-1-1221111-1-12-1-1-1-122-1-12-2-21111-2-21111-1-1-1-1-2-21111000000−3−33333−3−30000−3−3−3−3333300003333−3−3−3−3-2-200000000211-1-100000000
χ262222-122-2-222-122-1-1221111-1-12-1-1-1-122-1-12-2-21111-2-21111-1-1-1-1-2-21111000000−3−333−3−3330000−3−3−3−333330000−3−3−3−333332200000000-2-1-11100000000
χ2722-2-22222-2-2-2222-2-2-2-222-2-2222-2-2-2-2-2-2222222222-2-2-2-2-2-22-2-222-222-2-22-2000000000000000000000000000000000000002-22-222-2-20000000000000
χ2822-2-22222-2-2-2222-2-2-2-222-2-2222-2-2-2-2-2-2222222222-2-2-2-2-2-22-2-222-222-2-2-2200000000000000000000000000000000000000-22-22-2-2220000000000000
χ2922-2-2222-22-2-2222-2-2-2-2-2-222222-2-2-2-2-2-2222-2-2-2-2-2-22222222-2-22-22-2-222000000000000000000000000000000000000000000000000000000000002i−2i
χ3022-2-2222-22-2-2222-2-2-2-2-2-222222-2-2-2-2-2-2222-2-2-2-2-2-22222222-2-22-22-2-22200000000000000000000000000000000000000000000000000000000000−2i2i
χ3122-2-222-12-2-2122-1-2-2-2122-2-22-1-1-2-211112-1-12-122-1-1-21-2-211-111-1-11-1-1112-200000000000000000000000033−3−333−3−333−3−3002-2-11-1-1110000000003−300
χ3222-2-222-12-2-2122-1-2-2-2122-2-22-1-1-2-211112-1-12-122-1-1-21-2-211-111-1-11-1-1112-2000000000000000000000000−3−333−3−333−3−333002-2-11-1-111000000000−3300
χ3322-2-222-12-2-2122-1-2-2-2122-2-22-1-1-2-211112-1-12-122-1-1-21-2-211-111-1-11-1-111-2200000000000000000000000033−3−333−3−333−3−300-221-111-1-1000000000−3300
χ3422-2-222-12-2-2122-1-2-2-2122-2-22-1-1-2-211112-1-12-122-1-1-21-2-211-111-1-11-1-111-22000000000000000000000000−3−333−3−333−3−33300-221-111-1-10000000003−300
χ3522-2-22-122-21-22-12-2-21-222-2-2-12-111-2-211-12-1-12-1-1221-211-2-2-111-1-11-1-1112-200000000000033−3−333−3−333−3−300000000000000-112-2-1-11100000003−30000
χ3622-2-22-122-21-22-12-2-21-222-2-2-12-111-2-211-12-1-12-1-1221-211-2-2-111-1-11-1-1112-2000000000000−3−333−3−333−3−33300000000000000-112-2-1-1110000000−330000
χ3722-2-22-122-21-22-12-2-21-222-2-2-12-111-2-211-12-1-12-1-1221-211-2-2-111-1-11-1-111-2200000000000033−3−333−3−333−3−3000000000000001-1-2211-1-10000000−330000
χ3822-2-22-122-21-22-12-2-21-222-2-2-12-111-2-211-12-1-12-1-1221-211-2-2-111-1-11-1-111-22000000000000−3−333−3−333−3−333000000000000001-1-2211-1-100000003−30000
χ392-2-222220022-2-2-22-2-2-200002222-22-22-2-2-2-200000000000022-2-200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22-20000000002-20000000000
χ402-2-222220022-2-2-22-2-2-200002222-22-22-2-2-2-200000000000022-2-200000000−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2-22000000000-220000000000
χ412-2-222220022-2-2-22-2-2-200002222-22-22-2-2-2-200000000000022-2-200000000i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2-22000000000-220000000000
χ422-2-222220022-2-2-22-2-2-200002222-22-22-2-2-2-200000000000022-2-200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22-20000000002-20000000000
χ432-2-22-12200221-2-2-11-2-23−33−3-1-12-11-112-211-2003−33−3003−33−3-1-111003−33−300−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ232-2000000000-113−300000000
χ442-2-22-12200221-2-2-11-2-23−33−3-1-12-11-112-211-2003−33−3003−33−3-1-111003−33−300−i2i2i2−i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23-220000000001-1−3300000000
χ452-2-22-12200221-2-2-11-2-23−33−3-1-12-11-112-211-2003−33−3003−33−3-1-111003−33−300i2−i2−i2i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23-220000000001-1−3300000000
χ462-2-22-12200221-2-2-11-2-23−33−3-1-12-11-112-211-2003−33−3003−33−3-1-111003−33−300i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ232-2000000000-113−300000000
χ472-2-22-12200221-2-2-11-2-2−33−33-1-12-11-112-211-200−33−3300−33−33-1-11100−33−3300−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ72-2000000000-11−3300000000
χ482-2-22-12200221-2-2-11-2-2−33−33-1-12-11-112-211-200−33−3300−33−33-1-11100−33−3300−i2i2i2−i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7-220000000001-13−300000000
χ492-2-22-12200221-2-2-11-2-2−33−33-1-12-11-112-211-200−33−3300−33−33-1-11100−33−3300i2−i2−i2i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7-220000000001-13−300000000
χ502-2-22-12200221-2-2-11-2-2−33−33-1-12-11-112-211-200−33−3300−33−33-1-11100−33−3300i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ72-2000000000-11−3300000000
χ51444444-2-4-44-244-2444-2-4-4-4-44-2-244-2-2-2-24-2-2-42-4-422-42-4-422-2-2-2-22222220000000000000000000000000000000000000000000000000000000000000
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χ5344444-2-244-2-24-2-244-2-24444-2-21-2-2-2-211-2-21-2-2-2-2-2-2-2-2-2-2-2-211111111114400000000000000000000000000000000000000-2-2-2-211110000000000000
χ5444444-2-244-2-24-2-244-2-24444-2-21-2-2-2-211-2-21-2-2-2-2-2-2-2-2-2-2-2-21111111111-4-4000000000000000000000000000000000000002222-1-1-1-10000000000000
χ5544444-2-2-4-4-2-24-2-244-2-2-4-4-4-4-2-21-2-2-2-211-2-212222222222221111-1-1-1-1-1-1000000000000000000000000000000000000000000003-33-30000000000000
χ5644444-2-2-4-4-2-24-2-244-2-2-4-4-4-4-2-21-2-2-2-211-2-212222222222221111-1-1-1-1-1-100000000000000000000000000000000000000000000-33-330000000000000
χ574444-24-2444-2-24-2-2-24-2-2-2-2-2-21-2-2-211-2-2-21-24-2-2-2114-2-2-2111111-2-211110000440000-2-2-2-2000000000000-2-2-2-21111111100000000000000000000000
χ584444-24-2444-2-24-2-2-24-2-2-2-2-2-21-2-2-211-2-2-21-24-2-2-2114-2-2-2111111-2-211110000-4-4000022220000000000002222-1-1-1-1-1-1-1-100000000000000000000000
χ594444-24-2-4-44-2-24-2-2-24-22222-21-2-2-211-2-2-21-2-4222-1-1-4222-1-1111122-1-1-1-100000000002323−23−230000000000000000−3−3−3−3333300000000000000000000000
χ604444-24-2-4-44-2-24-2-2-24-22222-21-2-2-211-2-2-21-2-4222-1-1-4222-1-1111122-1-1-1-10000000000−23−23232300000000000000003333−3−3−3−300000000000000000000000
χ614444-2-2444-24-2-24-2-2-24-2-2-2-21-2-211-2-2-2-21-2-2-2411-2-2-2411-2-21111-2-21111004400-2-2-2-20000-2-2-2-21111111100000000000000000000000000000000000
χ624444-2-2444-24-2-24-2-2-24-2-2-2-21-2-211-2-2-2-21-2-2-2411-2-2-2411-2-21111-2-2111100-4-400222200002222-1-1-1-1-1-1-1-100000000000000000000000000000000000
χ634444-2-24-4-4-24-2-24-2-2-2422221-2-211-2-2-2-21-2-22-4-1-1222-4-1-122111122-1-1-1-10000002323−23−2300000000−3−3−3−3333300000000000000000000000000000000000
χ644444-2-24-4-4-24-2-24-2-2-2422221-2-211-2-2-2-21-2-22-4-1-1222-4-1-122111122-1-1-1-1000000−23−232323000000003333−3−3−3−300000000000000000000000000000000000
χ6544-4-444-2-44-4244-2-4-4-42-4-4444-2-2-4-422224-2-2-42-4-4224-244-2-2-222-22-222-2-20000000000000000000000000000000000000000000000000000000000000
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χ6744-4-44-2-24-4224-2-2-4-42244-4-4-2-212222-1-1-2-21-2-2-2-2-2-22222221-1-111-111-1-14-400000000000000000000000000000000000000-22-2211-1-10000000000000
χ6844-4-44-2-24-4224-2-2-4-42244-4-4-2-212222-1-1-2-21-2-2-2-2-2-22222221-1-111-111-1-1-44000000000000000000000000000000000000002-22-2-1-1110000000000000
χ6944-4-44-2-2-44224-2-2-4-422-4-444-2-212222-1-1-2-21222222-2-2-2-2-2-21-1-11-11-1-111000000000000000000000000000000000000000000003-3-330000000000000
χ7044-4-44-2-2-44224-2-2-4-422-4-444-2-212222-1-1-2-21222222-2-2-2-2-2-21-1-11-11-1-11100000000000000000000000000000000000000000000-333-30000000000000
χ7144-4-4-2444-4-4-4-24422-4-4-2-222-2-242222-4-4-2-2444-2-2-2-2-4-42222-222-24-4-2-2220000000000000000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.