Finite Group Databasebeta

← Group #13178349

Character table — Group #13178349

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size111122222222222244444444444444444444444444444888888888888888888888888888888888888181818181818181818181818363636363636363636363636363636363636727272727272
order122233366666666633333444666666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212224444444444244444661212121212121212121261212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11-1-11-1-111-1-111-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-111-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-111
χ51111111111111111111111-1-111111111111111111-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111-1-1-1-1111111-111-1-1-1
χ61111111111111111111111-1-111111111111111111-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-11-11111111-1-1-1-1-1-1-1-1-11-1111
χ71111111111111111111111-1-111111111111111111-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-11-111-1-1-1-111-1-111-1-11-11-111
χ81111111111111111111111-1-111111111111111111-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1111-1-11-1-1
χ9111111111111111111111-11-1111111111111111-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-11-1-11-111-1-111-1-11111-1-1-111-1
χ10111111111111111111111-11-1111111111111111-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11-1-1111111111-1-1-1-1-1-11-1-11
χ11111111111111111111111-11-1111111111111111-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-11-11-1-1-1-1-1-11111-1-111-11-11
χ12111111111111111111111-11-1111111111111111-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1111-1-1-111-1-1-1-1-1-111111-11-1
χ13111111111111111111111-1-11111111111111111-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111111-1-1-1-111111-1-1-1-111111-1-1-1-11
χ14111111111111111111111-1-11111111111111111-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1111-11-111-1-1-1-111-1-1-1-11-1111-1
χ15111111111111111111111-1-11111111111111111-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111111111-1-1-1-1-111-1-1-111111111-1-1-11-1-11-1
χ16111111111111111111111-1-11111111111111111-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-1111-11-1-1-1-111-1-1-1-111-1111-11
χ17222222-12-12-122-1222-1-1-1-12222-1-1-1-12-1-1-1-12-1-1-1-122-1-122-1222-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1220022000000200200-1-100-1-1000000-1-10000
χ18222222-12-12-122-1222-1-1-1-12222-1-1-1-12-1-1-1-12-1-1-1-122-1-122-1222-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-200-2-2000000-200-200110011000000110000
χ19222222-12-12-122-1222-1-1-1-12-2-22-1-1-1-12-1-1-1-12-1-1-1-12211-2-2-1-2-2-21222-1-1-1-1-1-1-1-1-2-211111111-2-2111111112200-2-2000000-200200-1-100110000001-10000
χ20222222-12-12-122-1222-1-1-1-12-2-22-1-1-1-12-1-1-1-12-1-1-1-12211-2-2-1-2-2-21222-1-1-1-1-1-1-1-1-2-211111111-2-211111111-2-20022000000200-2001100-1-1000000-110000
χ21222222-12-12-122-1222-1-1-1-1-22-22-1-1-1-12-1-1-1-12-1-1-1-1-2-2-1-1-2-2122-21-2-2-21111111122-1-1-1-1-1-1-1-1-2-211111111220022000000-200-200-1-100-1-1000000110000
χ22222222-12-12-122-1222-1-1-1-1-22-22-1-1-1-12-1-1-1-12-1-1-1-1-2-2-1-1-2-2122-21-2-2-21111111122-1-1-1-1-1-1-1-1-2-211111111-2-200-2-2000000200200110011000000-1-10000
χ23222222-12-12-122-1222-1-1-1-1-2-222-1-1-1-12-1-1-1-12-1-1-1-1-2-211221-2-22-1-2-2-211111111-2-21111111122-1-1-1-1-1-1-1-12200-2-2000000200-200-1-10011000000-110000
χ24222222-12-12-122-1222-1-1-1-1-2-222-1-1-1-12-1-1-1-12-1-1-1-1-2-211221-2-22-1-2-2-211111111-2-21111111122-1-1-1-1-1-1-1-1-2-20022000000-2002001100-1-10000001-10000
χ2522222-1222-122-12-12-12-1-1-1222-12-1-1-1-12-1-1-1-12-1-1-12222-1-122-122-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100220000220002200000-1-10000-1-10000-1-100
χ2622222-1222-122-12-12-12-1-1-1222-12-1-1-1-12-1-1-1-12-1-1-12222-1-122-122-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100-2-20000-2-2000-2-2000001100001100001100
χ2722222-1222-122-12-12-12-1-1-12-2-2-12-1-1-1-12-1-1-1-12-1-1-122-2-2112-21-2-2-1-1-122-1-1-1-1-1-111-2-211111111-2-211111100220000-2-2000-2200000110000-1-10000-1100
χ2822222-1222-122-12-12-12-1-1-12-2-2-12-1-1-1-12-1-1-1-12-1-1-122-2-2112-21-2-2-1-1-122-1-1-1-1-1-111-2-211111111-2-211111100-2-20000220002-200000-1-100001100001-100
χ2922222-1222-122-12-12-12-1-1-1-22-2-12-1-1-1-12-1-1-1-12-1-1-1-2-22211-22-1-2-2111-2-2111111-1-122-1-1-1-1-1-111-2-211111100220000-2-20002-200000110000-1-100001-100
χ3022222-1222-122-12-12-12-1-1-1-22-2-12-1-1-1-12-1-1-1-12-1-1-1-2-22211-22-1-2-2111-2-2111111-1-122-1-1-1-1-1-111-2-211111100-2-2000022000-2200000-1-10000110000-1100
χ3122222-1222-122-12-12-12-1-1-1-2-22-12-1-1-1-12-1-1-1-12-1-1-1-2-2-2-2-1-1-2-2122111-2-211111111-2-2111111-1-122-1-1-1-1-1-10022000022000-2-200000-1-10000-1-100001100
χ3222222-1222-122-12-12-12-1-1-1-2-22-12-1-1-1-12-1-1-1-12-1-1-1-2-2-2-2-1-1-2-2122111-2-211111111-2-2111111-1-122-1-1-1-1-1-100-2-20000-2-20002200000110000110000-1-100
χ332222-122-1222-1222-1-1-12-1-1222-1-12-1-1-1-12-1-1-1-12-1-1-1-122222-12-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1000000220022000022000000-1-100-1-10000-1-1
χ342222-122-1222-1222-1-1-12-1-1222-1-12-1-1-1-12-1-1-1-12-1-1-1-122222-12-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1000000-2-200-2-20000-2-2000000110011000011
χ352222-122-1222-1222-1-1-12-1-12-2-2-1-12-1-1-1-12-1-1-1-12-1-1-1-1-2-2-2-221-21-22-1-1-1-122-1-1-1-11111-2-211111111-2-211110000002200220000-2-2000000-1-100-1-1000011
χ362222-122-1222-1222-1-1-12-1-12-2-2-1-12-1-1-1-12-1-1-1-12-1-1-1-1-2-2-2-221-21-22-1-1-1-122-1-1-1-11111-2-211111111-2-21111000000-2-200-2-20000220000001100110000-1-1
χ372222-122-1222-1222-1-1-12-1-1-22-2-1-12-1-1-1-12-1-1-1-12-1-11122-2-2-2-121-2-21111-2-21111-1-1-1-122-1-1-1-11111-2-211110000002200-2-20000-22000000-1-1001100001-1
χ382222-122-1222-1222-1-1-12-1-1-22-2-1-12-1-1-1-12-1-1-1-12-1-11122-2-2-2-121-2-21111-2-21111-1-1-1-122-1-1-1-11111-2-21111000000-2-2002200002-20000001100-1-10000-11
χ392222-122-1222-1222-1-1-12-1-1-2-22-1-12-1-1-1-12-1-1-1-12-1-111-2-222-21-2-12-21111-2-211111111-2-21111-1-1-1-122-1-1-1-10000002200-2-200002-2000000-1-100110000-11
χ402222-122-1222-1222-1-1-12-1-1-2-22-1-12-1-1-1-12-1-1-1-12-1-111-2-222-21-2-12-21111-2-211111111-2-21111-1-1-1-122-1-1-1-1000000-2-200220000-220000001100-1-100001-1
χ412-22-2222-2-2-2-2222-2-222222000-2-2-2-2-2-2-2-2-2-2222220000000000000000000000000000000000000000002-22i−2i0000002i−2i0000002-20000002i−2i2i−2i000000
χ422-22-2222-2-2-2-2222-2-222222000-2-2-2-2-2-2-2-2-2-2222220000000000000000000000000000000000000000002-2−2i2i000000−2i2i0000002-2000000−2i2i−2i2i000000
χ432-22-2222-2-2-2-2222-2-222222000-2-2-2-2-2-2-2-2-2-222222000000000000000000000000000000000000000000-222i−2i000000−2i2i000000-220000002i−2i−2i2i000000
χ442-22-2222-2-2-2-2222-2-222222000-2-2-2-2-2-2-2-2-2-222222000000000000000000000000000000000000000000-22−2i2i0000002i−2i000000-22000000−2i2i2i−2i000000
χ452-2-22222-2-222-2-2-2-222222200022222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000002i−2i2i−2i2-200000000002-22i−2i2i−2i0000000000
χ462-2-22222-2-222-2-2-2-222222200022222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000002i−2i−2i2i-220000000000-222i−2i−2i2i0000000000
χ472-2-22222-2-222-2-2-2-222222200022222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000−2i2i2i−2i-220000000000-22−2i2i2i−2i0000000000
χ482-2-22222-2-222-2-2-2-222222200022222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000−2i2i−2i2i2-200000000002-2−2i2i−2i2i0000000000
χ4944444-2-24-2-2-24-2-2-24-2-2111444-2-2111-2-2111-2-211144-2-2-2-2-24-24-2-2-2-2-2-2111111-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000000000
χ5044444-2-24-2-2-24-2-2-24-2-21114-4-4-2-2111-2-2111-2-2111442222-2-42-42-2-2-2-2-21111112222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000000000000000
χ5144444-2-24-2-2-24-2-2-24-2-2111-44-4-2-2111-2-2111-2-2111-4-4-2-22224-2-4222222-1-1-1-1-1-1-2-2-2-21111112222-1-1-1-1-1-1000000000000000000000000000000000000
χ5244444-2-24-2-2-24-2-2-24-2-2111-4-44-2-2111-2-2111-2-2111-4-422-2-22-424-222222-1-1-1-1-1-12222-1-1-1-1-1-1-2-2-2-2111111000000000000000000000000000000000000
χ534444-24-2-2-24-2-24-24-2-21-211444-21-211-21-211-21-211-2-2-2-244-2-24-2-24-2-211-2-21111-2-211-2-21111-2-211-2-21111000000000000000000000000000000000000
χ544444-24-2-2-24-2-24-24-2-21-2114-4-4-21-211-21-211-21-211-2-222-4-4-22-4224-2-211-2-2111122-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000000000000000000000
χ554444-24-2-2-24-2-24-24-2-21-211-44-4-21-211-21-211-21-21122-2-2-4-42-2422-422-1-122-1-1-1-1-2-211-2-2111122-1-122-1-1-1-1000000000000000000000000000000000000
χ564444-24-2-2-24-2-24-24-2-21-211-4-44-21-211-21-211-21-21122224422-4-2-2-422-1-122-1-1-1-122-1-122-1-1-1-1-2-211-2-21111000000000000000000000000000000000000
χ574444-2-24-24-24-2-24-2-21-2-2114441-2-2111-2-2111-2-211-2-244-2-24-2-2-24-211-2-2-2-2111111-2-2-2-2111111-2-2-2-21111000000000000000000000000000000000000
χ584444-2-24-24-24-2-24-2-21-2-2114-4-41-2-2111-2-2111-2-211-2-2-4-4224222-4-211-2-2-2-21111-1-12222-1-1-1-1-1-12222-1-1-1-1000000000000000000000000000000000000
χ594444-2-24-24-24-2-24-2-21-2-211-44-41-2-2111-2-2111-2-211224422-4-2-22-42-1-12222-1-1-1-111-2-2-2-21111-1-12222-1-1-1-1000000000000000000000000000000000000
χ604444-2-24-24-24-2-24-2-21-2-211-4-441-2-2111-2-2111-2-21122-4-4-2-2-422-242-1-12222-1-1-1-1-1-12222-1-1-1-111-2-2-2-21111000000000000000000000000000000000000
χ614444-2-2-2-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32444111−1−3i32−1+3i32111−1−3i32−1+3i32111−1−3i32−1+3i32-2-2-2-2-2-2-2-2-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111111−1−3i32−1−3i32−1+3i32−1+3i32111111−1−3i32−1−3i32−1+3i32−1+3i32000000000000000000000000000000000000
χ624444-2-2-2-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i324-4-4111−1−3i32−1+3i32111−1−3i32−1+3i32111−1−3i32−1+3i32-2-22222-22222-2111111−1−3i32−1−3i32−1+3i32−1+3i32-1-1-1-1-1-11+3i321+3i321−3i321−3i32-1-1-1-1-1-11+3i321+3i321−3i321−3i32000000000000000000000000000000000000
χ634444-2-2-2-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32-44-4111−1−3i32−1+3i32111−1−3i32−1+3i32111−1−3i32−1+3i3222-2-2222-2-2222-1-1-1-1-1-11+3i321+3i321−3i321−3i32111111−1−3i32−1−3i32−1+3i32−1+3i32-1-1-1-1-1-11+3i321+3i321−3i321−3i32000000000000000000000000000000000000
χ644444-2-2-2-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32-4-44111−1−3i32−1+3i32111−1−3i32−1+3i32111−1−3i32−1+3i322222-2-2222-2-22-1-1-1-1-1-11+3i321+3i321−3i321−3i32-1-1-1-1-1-11+3i321+3i321−3i321−3i32111111−1−3i32−1−3i32−1+3i32−1+3i32000000000000000000000000000000000000
χ654444-2-2-2-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32444111−1+3i32−1−3i32111−1+3i32−1−3i32111−1+3i32−1−3i32-2-2-2-2-2-2-2-2-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111111−1+3i32−1+3i32−1−3i32−1−3i32111111−1+3i32−1+3i32−1−3i32−1−3i32000000000000000000000000000000000000
χ664444-2-2-2-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i324-4-4111−1+3i32−1−3i32111−1+3i32−1−3i32111−1+3i32−1−3i32-2-22222-22222-2111111−1+3i32−1+3i32−1−3i32−1−3i32-1-1-1-1-1-11−3i321−3i321+3i321+3i32-1-1-1-1-1-11−3i321−3i321+3i321+3i32000000000000000000000000000000000000
χ674444-2-2-2-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32-44-4111−1+3i32−1−3i32111−1+3i32−1−3i32111−1+3i32−1−3i3222-2-2222-2-2222-1-1-1-1-1-11−3i321−3i321+3i321+3i32111111−1+3i32−1+3i32−1−3i32−1−3i32-1-1-1-1-1-11−3i321−3i321+3i321+3i32000000000000000000000000000000000000
χ684444-2-2-2-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32-4-44111−1+3i32−1−3i32111−1+3i32−1−3i32111−1+3i32−1−3i322222-2-2222-2-22-1-1-1-1-1-11−3i321−3i321+3i321+3i32-1-1-1-1-1-11−3i321−3i321+3i321+3i32111111−1+3i32−1+3i32−1−3i32−1−3i32000000000000000000000000000000000000
χ6944-4-444444-4-4-4-4-44-444444000-4-4-4-4-444444-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000000000000000000000
χ7044-4-444-24-2-42-4-424-44-2-2-2-2000-422224-2-2-2-2-422220023−230000000000000000000023−2323−2323−2323−230000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.