Finite Group Databasebeta

← Group #13178214

Character table — Group #13178214

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size111122222222222244444444444444444444444444444888888888888888888888888888888888888181818181818181818181818363636363636363636363636363636363636727272727272
order12223336666666662333334466666666666666666121212126666666666661212121212121212121212121212121212121212121212122244444444444444446612121212121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11-11-1-1-111-1-1-1-111-1-1-1-11-1-1-11-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-11-11-1-1-1-11111-1-1-1-1-1-1-11-11-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11-1-11
χ51111111111111111111111-1-111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111-1-11111-11-1-11-1
χ61111111111111111111111-1-111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-1111-1-1-1-11111-1-1-1-1111-1-11
χ81111111111111111111111-1-111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-11111111-1-11-1-1
χ91111111111111111-1111111-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11-1-1-11-1111111-1-111-1-11-11-1-1-1
χ101111111111111111-1111111-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-11-1111-1-1-1-1-1-1-1-11111-11-11
χ111111111111111111-1111111-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11-1-11-1-1111111-1-111-1-1-1-111
χ121111111111111111-1111111-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-11111-1-1-1-1-1-1-11111-1-1-11111-1
χ131111111111111111-111111-11-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-11-1-1-1111-1-1111111-1-1-1-1-11-11
χ141111111111111111-111111-11-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-111-1-1-111-11111-1-111-1-111-111-1-1-1
χ151111111111111111-111111-11-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111111-11-1-1-1-1-111-1-1-1-1111-1111-1
χ161111111111111111-111111-11-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-11-111-11-1-111-1-1-1-111-1-111-1-111
χ17222222-12-1-12222-1222-1-1-1-122222-1-1-1-122-1-1-1-1-1-1-1-122-1-12-122-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1220022000000202000-1-10000-1-10000-1000-10
χ18222222-12-1-12222-1222-1-1-1-122222-1-1-1-122-1-1-1-1-1-1-1-122-1-12-122-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-200-2-2000000-20-2000110000110000100010
χ19222222-12-1-12222-1222-1-1-1-1-2-2222-1-1-1-122-1-1-1-1-1-1-1-1-2-2112-122-1-1-1-1-1-1-1-11-2-2-2-2-211111111-2-2111111112200-2-2000000-202000-1-100001100001000-10
χ20222222-12-1-12222-1222-1-1-1-1-2-2222-1-1-1-122-1-1-1-1-1-1-1-1-2-2112-122-1-1-1-1-1-1-1-11-2-2-2-2-211111111-2-211111111-2-2002200000020-2000110000-1-10000-100010
χ21222222-12-1-12222-12-22-1-1-1-12-2-2-22-1-1-1-122-1-1-1-1-1-1-1-12211-21-2-211111111-1-2-2222-1-1-1-1-1-1-1-1-2-2111111112200-2-200000020-2000-1-10000110000-100010
χ22222222-12-1-12222-12-22-1-1-1-12-2-2-22-1-1-1-122-1-1-1-1-1-1-1-12211-21-2-211111111-1-2-2222-1-1-1-1-1-1-1-1-2-211111111-2-20022000000-202000110000-1-100001000-10
χ23222222-12-1-12222-12-22-1-1-1-1-22-2-22-1-1-1-122-1-1-1-1-1-1-1-1-2-2-1-1-21-2-211111111122-2-2-21111111122-1-1-1-1-1-1-1-1220022000000-20-2000-1-10000-1-10000100010
χ24222222-12-1-12222-12-22-1-1-1-1-22-2-22-1-1-1-122-1-1-1-1-1-1-1-1-2-2-1-1-21-2-211111111122-2-2-21111111122-1-1-1-1-1-1-1-1-2-200-2-2000000202000110000110000-1000-10
χ2522222-122222-1-1-1222-12-1-1-12222-12-1-1-1-1-122-1-1-1-1-1-1-1-122-12-1-122-1-1-1-1-1-122-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100220022000002020000-1-1-1-10000000-10-100
χ2622222-122222-1-1-1222-12-1-1-12222-12-1-1-1-1-122-1-1-1-1-1-1-1-122-12-1-122-1-1-1-1-1-122-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100-2-200-2-200000-20-200001111000000010100
χ2722222-122222-1-1-1222-12-1-1-1-2-222-12-1-1-1-1-122-1-1-1-1-1-111-2-2-12-1-122-1-1-1-1-1-1-2-21-211-2-211111111-2-2111111002200-2-200000-202000011-1-10000000-10100
χ2822222-122222-1-1-1222-12-1-1-1-2-222-12-1-1-1-1-122-1-1-1-1-1-111-2-2-12-1-122-1-1-1-1-1-1-2-21-211-2-211111111-2-211111100-2-200220000020-20000-1-111000000010-100
χ2922222-122222-1-1-122-2-12-1-1-12-2-2-2-12-1-1-1-1-122-1-1-1-1-1-1-1-1-2-21-211-2-21111112-212-1-122-1-1-1-1-1-111-2-21111110022002200000-20-20000-1-1-1-1000000010100
χ3022222-122222-1-1-122-2-12-1-1-12-2-2-2-12-1-1-1-1-122-1-1-1-1-1-1-1-1-2-21-211-2-21111112-212-1-122-1-1-1-1-1-111-2-211111100-2-200-2-200000202000011110000000-10-100
χ3122222-122222-1-1-122-2-12-1-1-1-22-2-2-12-1-1-1-1-122-1-1-1-1-1-111221-211-2-2111111-22-1-211-2-2111111-1-122-1-1-1-1-1-1002200-2-20000020-2000011-1-1000000010-100
χ3222222-122222-1-1-122-2-12-1-1-1-22-2-2-12-1-1-1-1-122-1-1-1-1-1-111221-211-2-2111111-22-1-211-2-2111111-1-122-1-1-1-1-1-100-2-2002200000-2020000-1-1110000000-10100
χ332222-122-122-12222-12-1-12-1-122-1-1-1-12-1-1-1-1-1-122-1-1-1-1222222-1-1-1-122-1-1-1-12-12-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000222200002200000000-1-1-1-100-100-1
χ342222-122-122-12222-12-1-12-1-122-1-1-1-12-1-1-1-1-1-122-1-1-1-1222222-1-1-1-122-1-1-1-12-12-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000-2-2-2-20000-2-2000000001111001001
χ352222-122-122-12222-12-1-12-1-1-2-2-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-2-2-222-1-1-1-122-1-1-1-1-21-211111-2-211111111-2-211110000000022220000-2-200000000-1-1-1-1001001
χ362222-122-122-12222-12-1-12-1-1-2-2-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-2-2-222-1-1-1-122-1-1-1-1-21-211111-2-211111111-2-2111100000000-2-2-2-200002200000000111100-100-1
χ372222-122-122-12222-1-2-1-12-1-12-211-1-12-1-1-1-1-1-122-1-1-1-122-2-2-2-21111-2-2111121-2-1-1-1-1-122-1-1-1-11111-2-211110000000022-2-200002-200000000-1-11100-1001
χ382222-122-122-12222-1-2-1-12-1-12-211-1-12-1-1-1-1-1-122-1-1-1-122-2-2-2-21111-2-2111121-2-1-1-1-1-122-1-1-1-11111-2-2111100000000-2-2220000-220000000011-1-100100-1
χ392222-122-122-12222-1-2-1-12-1-1-2211-1-12-1-1-1-1-1-122-1-1-1-1-2-222-2-21111-2-21111-2-1211111-2-21111-1-1-1-122-1-1-1-10000000022-2-20000-2200000000-1-11100100-1
χ402222-122-122-12222-1-2-1-12-1-1-2211-1-12-1-1-1-1-1-122-1-1-1-1-2-222-2-21111-2-21111-2-1211111-2-21111-1-1-1-122-1-1-1-100000000-2-22200002-20000000011-1-100-1001
χ412-22-2222-22-2-22-2-2-220222220000-2-2-2-2-22-22-22-222-2-2000000000000000000000000000000000000000000002i−2i2i−2i002-2000000002i−2i002i−2i002-2000000
χ422-22-2222-22-2-22-2-2-220222220000-2-2-2-2-22-22-22-222-2-2000000000000000000000000000000000000000000002i−2i−2i2i00-2200000000−2i2i002i−2i00-22000000
χ432-22-2222-22-2-22-2-2-220222220000-2-2-2-2-22-22-22-222-2-200000000000000000000000000000000000000000000−2i2i2i−2i00-22000000002i−2i00−2i2i00-22000000
χ442-22-2222-22-2-22-2-2-220222220000-2-2-2-2-22-22-22-222-2-200000000000000000000000000000000000000000000−2i2i−2i2i002-200000000−2i2i00−2i2i002-2000000
χ452-2-22222-2-2-22-22-22-20222220000-2-2-2-2-2-22-22-22-2-22200000000000000000000000000000000000000002-22i−2i00002i−2i000000002-2002i−2i002i−2i00000000
χ462-2-22222-2-2-22-22-22-20222220000-2-2-2-2-2-22-22-22-2-22200000000000000000000000000000000000000002-2−2i2i0000−2i2i000000002-200−2i2i00−2i2i00000000
χ472-2-22222-2-2-22-22-22-20222220000-2-2-2-2-2-22-22-22-2-2220000000000000000000000000000000000000000-222i−2i0000−2i2i00000000-22002i−2i00−2i2i00000000
χ482-2-22222-2-2-22-22-22-20222220000-2-2-2-2-2-22-22-22-2-2220000000000000000000000000000000000000000-22−2i2i00002i−2i00000000-2200−2i2i002i−2i00000000
χ4944444-2-24-2-24-2-2-2-244-2-21114444-2-2111-2-2-2-2111111-2-2-2-2-2-2-2-2-2-2111111-24-24-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000000000
χ5044444-2-24-2-24-2-2-2-244-2-2111-4-444-2-2111-2-2-2-21111112222-2-2-2-2-2-21111112-42-42222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000000000000000
χ5144444-2-24-2-24-2-2-2-24-4-2-21114-4-4-4-2-2111-2-2-2-2111111-2-222222222-1-1-1-1-1-1-2-424-2-2-2-21111112222-1-1-1-1-1-1000000000000000000000000000000000000
χ5244444-2-24-2-24-2-2-2-24-4-2-2111-44-4-4-2-2111-2-2-2-211111122-2-2222222-1-1-1-1-1-124-2-42222-1-1-1-1-1-1-2-2-2-2111111000000000000000000000000000000000000
χ534444-24-2-2-2-2-2444-2-24-21-21144-2-2-21-211-2-211-2-2111144-2-24-2-2-211-2-21111-2-24-2-2-211-2-21111-2-211-2-21111000000000000000000000000000000000000
χ544444-24-2-2-2-2-2444-2-24-21-211-4-4-2-2-21-211-2-211-2-21111-4-4224-2-2-211-2-2111122-4222-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000000000000000000000
χ554444-24-2-2-2-2-2444-2-2-4-21-2114-422-21-211-2-211-2-211114422-4222-1-122-1-1-1-1-22-4-2-2-211-2-2111122-1-122-1-1-1-1000000000000000000000000000000000000
χ564444-24-2-2-2-2-2444-2-2-4-21-211-4422-21-211-2-211-2-21111-4-4-2-2-4222-1-122-1-1-1-12-24222-1-122-1-1-1-1-2-211-2-21111000000000000000000000000000000000000
χ574444-2-24-244-2-2-2-24-241-2-21144-2-21-2-21111-2-2-2-21111-2-244-2411-2-2-2-211114-2-2-211-2-2-2-2111111-2-2-2-21111000000000000000000000000000000000000
χ584444-2-24-244-2-2-2-24-241-2-211-4-4-2-21-2-21111-2-2-2-2111122-4-4-2411-2-2-2-21111-4222-1-12222-1-1-1-1-1-12222-1-1-1-1000000000000000000000000000000000000
χ594444-2-24-244-2-2-2-24-2-41-2-2114-4221-2-21111-2-2-2-21111-2-2-4-42-4-1-12222-1-1-1-1422-211-2-2-2-21111-1-12222-1-1-1-1000000000000000000000000000000000000
χ604444-2-24-244-2-2-2-24-2-41-2-211-44221-2-21111-2-2-2-2111122442-4-1-12222-1-1-1-1-4-2-22-1-12222-1-1-1-111-2-2-2-21111000000000000000000000000000000000000
χ614444-2-2-2-2-2-2-2-2-2-2-2-24111−1−3i32−1+3i3244-2-2111−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32-2-2-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111111−1−3i32−1−3i32−1+3i32−1+3i32000000000000000000000000000000000000
χ624444-2-2-2-2-2-2-2-2-2-2-2-24111−1−3i32−1+3i32-4-4-2-2111−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i322222-2-2111111−1−3i32−1−3i32−1+3i32−1+3i322222-1-1-1-1-1-11+3i321+3i321−3i321−3i32-1-1-1-1-1-11+3i321+3i321−3i321−3i32000000000000000000000000000000000000
χ634444-2-2-2-2-2-2-2-2-2-2-2-24111−1+3i32−1−3i3244-2-2111−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32-2-2-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111111−1+3i32−1+3i32−1−3i32−1−3i32000000000000000000000000000000000000
χ644444-2-2-2-2-2-2-2-2-2-2-2-24111−1+3i32−1−3i32-4-4-2-2111−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i322222-2-2111111−1+3i32−1+3i32−1−3i32−1−3i322222-1-1-1-1-1-11−3i321−3i321+3i321+3i32-1-1-1-1-1-11−3i321−3i321+3i321+3i32000000000000000000000000000000000000
χ654444-2-2-2-2-2-2-2-2-2-2-2-2-4111−1−3i32−1+3i324-422111−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32-2-22222-1-1-1-1-1-11+3i321+3i321−3i321−3i32-222-2111111−1−3i32−1−3i32−1+3i32−1+3i32-1-1-1-1-1-11+3i321+3i321−3i321−3i32000000000000000000000000000000000000
χ664444-2-2-2-2-2-2-2-2-2-2-2-2-4111−1−3i32−1+3i32-4422111−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i3222-2-222-1-1-1-1-1-11+3i321+3i321−3i321−3i322-2-22-1-1-1-1-1-11+3i321+3i321−3i321−3i32111111−1−3i32−1−3i32−1+3i32−1+3i32000000000000000000000000000000000000
χ674444-2-2-2-2-2-2-2-2-2-2-2-2-4111−1+3i32−1−3i324-422111−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32-2-22222-1-1-1-1-1-11−3i321−3i321+3i321+3i32-222-2111111−1+3i32−1+3i32−1−3i32−1−3i32-1-1-1-1-1-11−3i321−3i321+3i321+3i32000000000000000000000000000000000000
χ684444-2-2-2-2-2-2-2-2-2-2-2-2-4111−1+3i32−1−3i32-4422111−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i3222-2-222-1-1-1-1-1-11−3i321−3i321+3i321+3i322-2-22-1-1-1-1-1-11−3i321−3i321+3i321+3i32111111−1+3i32−1+3i32−1−3i32−1−3i32000000000000000000000000000000000000
χ6944-4-44444-44-4-4-44-4-4044444000044444-4-4-4-4-4-4-4-4-4-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ7044-4-444-242-2-4-4-442-404-2-2-2-200004-2-2-2-2-4-4222222220023−23000000000000000000000000000023−2323−2323−2323−23000000000000000000000000000000000000
χ7144-4-444-242-2-4-4-442-404-2-2-2-200004-2-2-2-2-4-42222222200−23230000000000000000000000000000−2323−2323−2323−2323000000000000000000000000000000000000
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χ964-44-444-2-4-22-44-4-42404-2-2-2-20000-422224-4-22-22-2-222000000000000000000000000000000000000000000004i−4i000000000000000000−2i2i0000000000
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χ1118-88-8-4-4-44-444-4444-40222−1−3i3−1+3i30000-2-2-21+3i31−3i32-22-22-2−1−3i3−1+3i31+3i31−3i30000000000000000000000000000000000000000000000000000000000000000000000000000
χ1128-88-8-4-4-44-444-4444-40222−1+3i3−1−3i30000-2-2-21−3i31+3i32-22-22-2−1+3i3−1−3i31−3i31+3i30000000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-888-4-4-84484-44-4-80-4-4222000044-2-2-24-44-4-22-2-2220000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1158-8-88-4-484-8-8-44-448402-4-4220000-244-2-2-224-44-4-2-2220000000000000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-4444-44-44-440222−1−3i3−1+3i30000-2-2-21+3i31−3i3-22-22-221+3i31−3i3−1−3i3−1+3i30000000000000000000000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-4444-44-44-440222−1+3i3−1−3i30000-2-2-21−3i31+3i3-22-22-221−3i31+3i3−1+3i3−1−3i30000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.