Finite Group Databasebeta

← Group #13170648

Character table — Group #13170648

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size1111222222222222222222444444444444444444444444666666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121224242424242436363636363636363636363636367272108108
order12442333466666121212121212121233366666666612121212121212121212121222446612123666612121212122466666666688121212121212121212242424242424242424242424242424246661212122244668812122424242461224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-11-111-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1111-1-1111111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1111-1-11111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-111-1-1-1-111-1-1-111-1-1-1-11111111111111111111111-11-11-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11-11-111-1-111-1-1-1-1-1-111
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ911-1-1-11111-1-1111-1-1-1-1-1-111111-1-1-1-1-1-11111-1-111-1-1-1-11111-11-111-1-11-1-1-11111-1-11-11-1-11111-1-11-11-11-1-111-1-111-1-1111111-1-1-1-1-1-1111-1-1-111-1-1111-1-1-111-1-11-1-11
χ1011-1-1-11111-1-1111-1-1-1-1-1-111111-1-1-1-1-1-11111-1-111-1-1-1-11111-11-111-1-11-1-1-11111-1-11-11-1-11111-1-1-111-11-1-111-1-1-1-111-1-1-1-1-1-1111111111-1-1-11-1-1111-11-1-1-1-111-111-1
χ1111-1-1-11111-1-1111-1-1-1-1-1-111111-1-1-1-1-1-11111-1-111-1-1-1-11111-11-111-1-11-1-1-11111-1-1-111-1-1-1-111-1-11-11-111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1111-1-111-1-11-11111-1-1-111-1
χ1211-1-1-11111-1-1111-1-1-1-1-1-111111-1-1-1-1-1-11111-1-111-1-1-1-11111-11-111-1-11-1-1-11111-1-1-111-1-1-1-111-1-1-111-111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1111-111-1-1-1-1111-1-1111-1-11
χ1311-1-1-11111-1-1111-1-1-1-1-1-111111-1-1-1-1-1-11111-1-111-1-1-1-1111-11-11-1-1111-1-1-11111-1-11-1-11111-1-1111-1-11-1-1-1-1-11111-1-1111111-1-1-1-1-1-1111-1-1-1-111-1-1-1-1111-1-1111-11-1
χ1411-1-1-11111-1-1111-1-1-1-1-1-111111-1-1-1-1-1-11111-1-111-1-1-1-1111-11-11-1-1111-1-1-11111-1-11-1-11111-1-111-11-11-1-1-1-1-111-1-111-1-1-1-1-1-1111111111-1-1-1-1-111-1-11-11111-1-1-11-11
χ1511-1-1-11111-1-1111-1-1-1-1-1-111111-1-1-1-1-1-11111-1-111-1-1-1-1111-11-11-1-1111-1-1-11111-1-1-11-111-1-1-1-1111-1-11-111-1-11111-1-1111111-1-1-1-1-1-1-1-1-11111-1-1111-11-1-1-1-111-11-11
χ1611-1-1-11111-1-1111-1-1-1-1-1-111111-1-1-1-1-1-11111-1-111-1-1-1-1111-11-11-1-1111-1-1-11111-1-1-11-111-1-1-1-111-11-11-111-1-111-1-111-1-1-1-1-1-1111111-1-1-111111-1-1111-1-1-111-1-11-11-1
χ172222222-122222-12222-1-1222-1-12-122-1-12-1-1-122-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-10022-1-1-1-1-1-1-100000000000000002-1-12-1-12020-1-100-1-100000000
χ182222222-122222-12222-1-1222-1-12-122-1-12-1-1-122-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-111-1-1-1-10022-111-1-1-1-10000000000000000-211-211-20-2011001100000000
χ192222222-122222-12222-1-1222-1-12-122-1-12-1-1-122-1-1-1-1-1-1222-2-2-2-21111-1-1-1-1-1-1-1-1-1-122-2-21-1-1111100-2-21-1-1111100000000000000002-1-12-1-1-20-2011001100000000
χ202222222-122222-12222-1-1222-1-12-122-1-12-1-1-122-1-1-1-1-1-1222-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111100-2-211111110000000000000000-211-2112020-1-100-1-100000000
χ21222222-122222-1222-1-12222-12-1-12-1-122-12-12-1-12222-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-122000220000220002200002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-102020000000000-1-100
χ22222222-122222-1222-1-12222-12-1-12-1-122-12-12-1-12222-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-122000220000-2-2000220000-2-2-2-2111111111111-1-1-1-1-1-10-20-200000000001100
χ23222222-122222-1222-1-12222-12-1-12-1-122-12-12-1-12222-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-2-2000-2-2000022000-2-200002222-1-1-1-1-1-1-1-1-1-1-1-11111110-20-200000000001100
χ24222222-122222-1222-1-12222-12-1-12-1-122-12-12-1-12222-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-2-2000-2-20000-2-2000-2-20000-2-2-2-211111111111111111102020000000000-1-100
χ2522222-1222-1-1-122-1-12222-1-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-1222-1-122222222-12-1-1-12-1-1-1-100-1-1200-1-1-1-122-1-1200-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-10000000000002200-1-1-1-10000
χ2622222-1222-1-1-122-1-12222-1-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-1222-1-122222222-12-1-1-12-1-1-1-100-1-1200-1-1-1-1-2-2-1-1200-1-1-1-11111-2-21111-2-21111000000000000-2-20011110000
χ2722222-1222-1-1-122-1-12222-1-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-1222-1-1-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-10011-20011112211-2001111-1-1-1-122-1-1-1-122-1-1-1-1000000000000-2-20011110000
χ2822222-1222-1-1-122-1-12222-1-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-1222-1-1-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-10011-2001111-2-211-20011111111-2-21111-2-211110000000000002200-1-1-1-10000
χ292222-2222-2-2-2222222222-2-2222-2-2-2-2-2-2222-222-2-22222-2-2-22-2-2222222-2-2-22-2-2-222002-2-20022-2-200-22-200-2-2220000000000000000000000000000000000000000
χ302222-2222-2-2-2222222222-2-2222-2-2-2-2-2-2222-222-2-22222-2-2-2-222-2-2-2-2-22-2-2-22-2-2-22200-22200-2-222002-220022-2-20000000000000000000000000000000000000000
χ312222-222-1-2-2-222-12222-1-1-2-22-1-1-21-2-2112-1-112211-1-1-1-1-2-2-22-2-22-1-1-1-1-1111-1111-1-1002-21−i3i3-1-11100-221−i3i311-1-100000000000000000−i3i30−i3i30000−i3i300−i3i300000000
χ322222-222-1-2-2-222-12222-1-1-2-22-1-1-21-2-2112-1-112211-1-1-1-1-2-2-22-2-22-1-1-1-1-1111-1111-1-1002-21i3−i3-1-11100-221i3−i311-1-100000000000000000i3−i30i3−i30000i3−i300i3−i300000000
χ332222-222-1-2-2-222-12222-1-1-2-22-1-1-21-2-2112-1-112211-1-1-1-1-2-2-2-222-21111-1111-1111-1-100-22-1−i3i311-1-1002-2-1−i3i3-1-11100000000000000000−i3i30−i3i30000i3−i300i3−i300000000
χ342222-222-1-2-2-222-12222-1-1-2-22-1-1-21-2-2112-1-112211-1-1-1-1-2-2-2-222-21111-1111-1111-1-100-22-1i3−i311-1-1002-2-1i3−i3-1-11100000000000000000i3−i30i3−i30000−i3i300−i3i300000000
χ352222-2-122-211-122-1-1222211-1-12-2-21111-1-12-2-1-111-1-122-2112-2-222222-1-211-1-211-1-100-11-200-1-111001-1-20011-1-13−33−30033−3−30033−3−300000000000000003−33−30000
χ362222-2-122-211-122-1-1222211-1-12-2-21111-1-12-2-1-111-1-122-2112-2-222222-1-211-1-211-1-100-11-200-1-111001-1-20011-1-1−33−3300−3−33300−3−3330000000000000000−33−330000
χ372222-2-122-211-122-1-1222211-1-12-2-21111-1-12-2-1-111-1-122-211-222-2-2-2-2-2-1-211-1-211-1-1001-120011-1-100-11200-1-1113−33−30033−3−30033−3−30000000000000000−33−330000
χ382222-2-122-211-122-1-1222211-1-12-2-21111-1-12-2-1-111-1-122-211-222-2-2-2-2-2-1-211-1-211-1-1001-120011-1-100-11200-1-111−33−3300−3−33300−3−33300000000000000003−33−30000
χ3922-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222222-2-2-2-2-20022200222200-2-2-200-2-2-2-20000000000000000000000000000000000000000
χ4022-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22222222-2-2-2-2-200-2-2-200-2-2-2-2002220022220000000000000000000000000000000000000000
χ4122-2-2222-1-22222-1-2-2-2-211-2-22-1-12-122-1-12-1-11-2-2111111-2-2-222-2-2-1-111-1-1-1-1-1111110022-1−i3i3-1-1-1-100-2-21i3−i3111100000000000000000−i3i30i3−i30000−i3i300i3−i300000000
χ4222-2-2222-1-22222-1-2-2-2-211-2-22-1-12-122-1-12-1-11-2-2111111-2-2-222-2-2-1-111-1-1-1-1-1111110022-1i3−i3-1-1-1-100-2-21−i3i3111100000000000000000i3−i30−i3i30000i3−i300−i3i300000000
χ4322-2-2222-1-22222-1-2-2-2-211-2-22-1-12-122-1-12-1-11-2-2111111-2-2-2-2-22211-1-1-1-1-1-1-11111100-2-21−i3i311110022-1i3−i3-1-1-1-100000000000000000−i3i30i3−i30000i3−i300−i3i300000000
χ4422-2-2222-1-22222-1-2-2-2-211-2-22-1-12-122-1-12-1-11-2-2111111-2-2-2-2-22211-1-1-1-1-1-1-11111100-2-21i3−i311110022-1−i3i3-1-1-1-100000000000000000i3−i30−i3i30000−i3i300i3−i300000000
χ4522-2-22-122-2-1-1-12211-2-2-2-211-1-1222-1-1-1-1-1-12-2111111-2-2-21122-2-222-2-2-12-1-1-1-2111100-1-1200-1-1-1-10011-20011113−3−330033−3−300−3−33300000000000000003−3−330000
χ4622-2-22-122-2-1-1-12211-2-2-2-211-1-1222-1-1-1-1-1-12-2111111-2-2-21122-2-222-2-2-12-1-1-1-2111100-1-1200-1-1-1-10011-2001111−333−300−3−3330033−3−30000000000000000−333−30000
χ4722-2-22-122-2-1-1-12211-2-2-2-211-1-1222-1-1-1-1-1-12-2111111-2-2-211-2-222-2-222-12-1-1-1-211110011-200111100-1-1200-1-1-1-13−3−330033−3−300−3−3330000000000000000−333−30000
χ4822-2-22-122-2-1-1-12211-2-2-2-211-1-1222-1-1-1-1-1-12-2111111-2-2-211-2-222-2-222-12-1-1-1-211110011-200111100-1-1200-1-1-1-1−333−300−3−3330033−3−300000000000000003−3−330000
χ4922-2-2-222-12-2-222-1-2-2-2-211222-1-1-21-2-2112-1-1-1-2-2-1-111112222-22-2-1-111-1111-1-1-1-1112-22-21-1-1-1-111002-2-111-1-11100000000000000002-1-1-21120-20-1-1001100000000
χ5022-2-2-222-12-2-222-1-2-2-2-211222-1-1-21-2-2112-1-1-1-2-2-1-111112222-22-2-1-111-1111-1-1-1-111-222-2111-1-111002-2-1-1-1-1-1110000000000000000-2112-1-1-20201100-1-100000000
χ5122-2-2-222-12-2-222-1-2-2-2-211222-1-1-21-2-2112-1-1-1-2-2-1-11111222-22-2211-1-1-1111-1-1-1-1112-2-22-1-1-111-1-100-2211111-1-100000000000000002-1-1-211-20201100-1-100000000
χ5222-2-2-222-12-2-222-1-2-2-2-211222-1-1-21-2-2112-1-1-1-2-2-1-11111222-22-2211-1-1-1111-1-1-1-111-22-22-11111-1-100-221-1-111-1-10000000000000000-2112-1-120-20-1-1001100000000
χ5322-2-2-22-122-2-22-12-2-211-2-222-12-11-211-2-2-12-121122-2-211-1-1-100000000-1111-1-1-1-1112-20002200002-2000-2-2000022-2-2-1-1-1-1-1-1111111-1-1-1111020-20000000000-1100
χ5422-2-2-22-122-2-22-12-2-211-2-222-12-11-211-2-2-12-121122-2-211-1-1-100000000-1111-1-1-1-1112-2000220000-22000-2-20000-2-222111111-1-1-1-1-1-1-1-1-11110-20200000000001-100
χ5522-2-2-22-122-2-22-12-2-211-2-222-12-11-211-2-2-12-121122-2-211-1-1-100000000-1111-1-1-1-111-22000-2-200002-200022000022-2-2-1-1-1-1-1-1111111111-1-1-10-20200000000001-100
χ5622-2-2-22-122-2-22-12-2-211-2-222-12-11-211-2-2-12-121122-2-211-1-1-100000000-1111-1-1-1-111-22000-2-20000-22000220000-2-222111111-1-1-1-1-1-1111-1-1-1020-20000000000-1100
χ5722-2-2-2-122211-12211-2-2-2-2-1-1-1-12-2-21111-1-12211-1-111-2-22-1-12-22-222-2-2-1-211-12-1-11100-11-200-1-1112-2-11200-1-111-1-11122-1-1-1-1-2-211110000000000002-200-1-1110000
χ5822-2-2-2-122211-12211-2-2-2-2-1-1-1-12-2-21111-1-12211-1-111-2-22-1-12-22-222-2-2-1-211-12-1-11100-11-200-1-111-22-11200-1-11111-1-1-2-2111122-1-1-1-1000000000000-220011-1-10000
χ5922-2-2-2-122211-12211-2-2-2-2-1-1-1-12-2-21111-1-12211-1-111-2-22-1-1-22-22-2-222-1-211-12-1-111001-120011-1-12-21-1-20011-1-1-1-11122-1-1-1-1-2-21111000000000000-220011-1-10000
χ6022-2-2-2-122211-12211-2-2-2-2-1-1-1-12-2-21111-1-12211-1-111-2-22-1-1-22-22-2-222-1-211-12-1-111001-120011-1-1-221-1-20011-1-111-1-1-2-2111122-1-1-1-10000000000002-200-1-1110000
χ61444444-2-24444-2-244-2-2-2-244-2-21-2-2-2-2-2-2-2-21-2-2-2-2-2-2-211-2-2-200000000111111111144000-2-2000000000-2-200000000000000000000-211-211000000000000000000
χ62444444-2-24444-2-244-2-2-2-244-2-21-2-2-2-2-2-2-2-21-2-2-2-2-2-2-211-2-2-2000000001111111111-4-40002200000000022000000000000000000002-1-12-1-1000000000000000000
χ6344444-24-24-2-2-24-2-2-244-2-2-2-2-21-24-2-2-211-21-2-2-2-21111-2-24-2-24444-2-2-2-21-2111-2111100-2-2-200111100-2-2-20011110000000000000000000000000000000000000000
χ6444444-24-24-2-2-24-2-2-244-2-2-2-2-21-24-2-2-211-21-2-2-2-21111-2-24-2-2-4-4-4-422221-2111-211110022200-1-1-1-10022200-1-1-1-10000000000000000000000000000000000000000
χ6544444-2-244-2-2-2-24-2-2-2-244-2-21-2-2-2411-2-21-2-2411-2-2-2-2-2-2-211000000001-2111-211110000000000044000000000-2-2-2-2-2-21111-2-21111000000000000000000000000
χ6644444-2-244-2-2-2-24-2-2-2-244-2-21-2-2-2411-2-21-2-2411-2-2-2-2-2-2-211000000001-2111-2111100000000000-4-4000000000222222-1-1-1-122-1-1-1-1000000000000000000000000
χ674444-44-24-4-4-44-2444-2-244-4-4-24-22-422-4-4-24-2-4-2-2-4-444-2-222200000000-2222-2222-2-200000000000000000000000000000000000000000000000000000000000000
χ684444-44-2-2-4-4-44-2-244-2-2-2-2-4-4-2-21222222-2-212-2-222-2-211222000000001-1-1-11-1-1-11100000−2i32i3000000000−2i32i3000000000000000000000i3−i30i3−i3000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.