Finite Group Databasebeta

← Group #13178290

Character table — Group #13178290

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818181836363636363636363636363636363636363636363636363672727272
order1222333446666666662333334666666666666666661212121212121212666666666666121212121212121212121212121212121212121212122244121212122224444444666612121212121212121212661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-11-11-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-111-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-1-1-111-1-1-1-1111-1-11
χ5111111111111111111-111111-1-1-111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-11-11-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111-111111-1-1-111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-11-1-11-1-11-111111-1-11111-1-111-1-1-1-1
χ7111111111111111111-111111-1-1-111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-11-1-1-1-11111-1-11111-111-1
χ8111111111111111111-111111-1-1-111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-111-1-1-11111-1-11111-1-11-1-11
χ91111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111-1-1-11-1111-1-111-1-111-1-11111-1-1
χ101111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-111-11-11-111111111-1-1-1-1-1-1-1-111
χ111111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-111-111-1-1-1-1-1-1-1111111-1-1-11-11
χ121111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-111-1-11-1-111-1-1-1-1-1-111111-11-1
χ131111111-1-1111111111-1111111-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111-111-1-1-1-11111-1-111-1-111-1-111-1-1
χ141111111-1-1111111111-1111111-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1111111-1-111
χ151111111-1-1111111111-1111111-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111111111-11-1-1-1-111-1-11111-1-1-1-1-1-111-11-11
χ161111111-1-1111111111-1111111-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1111-111-1-1-1-1-1-1111111-1-1-1-11-11-1
χ17222222-122-12222-1-12222-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-12222-1-1222-122-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000220000220000-1-10000-1-100000-1-10
χ18222222-122-12222-1-12222-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-12222-1-1222-122-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000-2-20000-2-200001100001100000110
χ19222222-122-12222-1-122-22-1-1-1-1-2-2-22-1-1-1-122-1-1-1-1-1-1-1-122-2-2-1-122-21-2-2111111111-222-1-1-1-1-1-1-1-1-2-211111111000000002-200002-200001100001100000-1-10
χ20222222-122-12222-1-122-22-1-1-1-1-2-2-22-1-1-1-122-1-1-1-1-1-1-1-122-2-2-1-122-21-2-2111111111-222-1-1-1-1-1-1-1-1-2-21111111100000000-220000-220000-1-10000-1-100000110
χ21222222-1-2-2-12222-1-12222-1-1-1-1-2222-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211-2-22-122-1-1-1-1-1-1-1-11-2-2-211111111-2-211111111000000002-20000-220000110000-1-100000-110
χ22222222-1-2-2-12222-1-12222-1-1-1-1-2222-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211-2-22-122-1-1-1-1-1-1-1-11-2-2-211111111-2-21111111100000000-2200002-20000-1-1000011000001-10
χ23222222-1-2-2-12222-1-122-22-1-1-1-12-2-22-1-1-1-122-1-1-1-1-1-1-1-1-2-22211-2-2-21-2-211111111-12-2-21111111122-1-1-1-1-1-1-1-100000000220000-2-20000-1-100001100000-110
χ24222222-1-2-2-12222-1-122-22-1-1-1-12-2-22-1-1-1-122-1-1-1-1-1-1-1-1-2-22211-2-2-21-2-211111111-12-2-21111111122-1-1-1-1-1-1-1-100000000-2-20000220000110000-1-1000001-10
χ2522222-122222-12-1222-12-12-1-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-1222222-12-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000020200022000000-1-10000-1-1-100-1
χ2622222-122222-12-1222-12-12-1-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-1222222-12-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000000000-20-2000-2-2000000110000111001
χ2722222-122222-12-1222-1-2-12-1-1-1-2-2-2-12-1-1-1-1-122-1-1-1-1-1-1-1-1-2-222221-211-2-2111111-21-1-122-1-1-1-1-1-111-2-2111111000000000020-20002-200000011000011-100-1
χ2822222-122222-12-1222-1-2-12-1-1-1-2-2-2-12-1-1-1-1-122-1-1-1-1-1-1-1-1-2-222221-211-2-2111111-21-1-122-1-1-1-1-1-111-2-21111110000000000-202000-22000000-1-10000-1-11001
χ2922222-12-2-222-12-1222-12-12-1-1-1-222-12-1-1-1-1-122-1-1-1-1-1-111-2-2-2-2-2-2-12-1-122-1-1-1-1-1-1-2111-2-211111111-2-2111111000000000020-2000-22000000110000-1-1-1001
χ3022222-12-2-222-12-1222-12-12-1-1-1-222-12-1-1-1-1-122-1-1-1-1-1-111-2-2-2-2-2-2-12-1-122-1-1-1-1-1-1-2111-2-211111111-2-21111110000000000-2020002-2000000-1-1000011100-1
χ3122222-12-2-222-12-1222-1-2-12-1-1-12-2-2-12-1-1-1-1-122-1-1-1-1-1-11122-2-2-2-21-211-2-21111112-111-2-2111111-1-122-1-1-1-1-1-10000000000202000-2-2000000-1-1000011-1001
χ3222222-12-2-222-12-1222-1-2-12-1-1-12-2-2-12-1-1-1-1-122-1-1-1-1-1-11122-2-2-2-21-211-2-21111112-111-2-2111111-1-122-1-1-1-1-1-10000000000-20-200022000000110000-1-1100-1
χ332222-122222-12-1222-122-1-12-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-122-1-122-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-10002020000-1-100-1-10000-1-1000000
χ342222-122222-12-1222-122-1-12-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-122-1-122-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-21111000-20-20000110011000011000000
χ352222-122222-12-1222-12-2-1-12-1-1-211-1-12-1-1-1-1-1-122-1-1-1-1221122-1-1-2-21111-2-21111-2-2-1-1-1-122-1-1-1-11111-2-211112222-1-1-1-1000-20-20000-1-10011000011000000
χ362222-122222-12-1222-12-2-1-12-1-1-211-1-12-1-1-1-1-1-122-1-1-1-1221122-1-1-2-21111-2-21111-2-2-1-1-1-122-1-1-1-11111-2-21111-2-2-2-2111100020200001100-1-10000-1-1000000
χ372222-122-2-22-12-1222-122-1-12-1-1-2-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-211-2-21122-1-1-1-122-1-1-1-1-2-21111-2-211111111-2-2111122-2-2111100020-20000-1-100-1-1000011000000
χ382222-122-2-22-12-1222-122-1-12-1-1-2-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-211-2-21122-1-1-1-122-1-1-1-1-2-21111-2-211111111-2-21111-2-222-1-1-1-1000-20200001100110000-1-1000000
χ392222-122-2-22-12-1222-12-2-1-12-1-1211-1-12-1-1-1-1-1-122-1-1-1-1-2-2-1-1-2-211-2-21111-2-21111221111-2-21111-1-1-1-122-1-1-1-122-2-21111000-2020000-1-100110000-1-1000000
χ402222-122-2-22-12-1222-12-2-1-12-1-1211-1-12-1-1-1-1-1-122-1-1-1-1-2-2-1-1-2-211-2-21111-2-21111221111-2-21111-1-1-1-122-1-1-1-1-2-222-1-1-1-100020-200001100-1-1000011000000
χ4122-2-22222i−2i2-2-222-2-2-2-202222200022222-2-2-2-2-2-2-2-2-2-22i−2i002i−2i2i−2i000000000000002i−2i2i−2i2i−2i2i2i−2i−2i00000000002-22i−2i2i2i−2i−2i00000000002-20000000000000000
χ4222-2-22222i−2i2-2-222-2-2-2-202222200022222-2-2-2-2-2-2-2-2-2-22i−2i002i−2i2i−2i000000000000002i−2i2i−2i2i−2i2i2i−2i−2i0000000000-22−2i2i−2i−2i2i2i0000000000-220000000000000000
χ4322-2-2222−2i2i2-2-222-2-2-2-202222200022222-2-2-2-2-2-2-2-2-2-2−2i2i00−2i2i−2i2i00000000000000−2i2i−2i2i−2i2i−2i−2i2i2i00000000002-2−2i2i−2i−2i2i2i00000000002-20000000000000000
χ4422-2-2222−2i2i2-2-222-2-2-2-202222200022222-2-2-2-2-2-2-2-2-2-2−2i2i00−2i2i−2i2i00000000000000−2i2i−2i2i−2i2i−2i−2i2i2i0000000000-222i−2i2i2i−2i−2i0000000000-220000000000000000
χ4522-2-2-1222i−2i21-2-12-2-21-20-1-12-1-10−i3i3-1-12-1-11111-2-211112i−2i3−32i−2i−ii00−i3i3−i3i300−i3−i3i3i300−ii−ii2i−2i−i−iii3−33−30033−3−32-22i−2i−i−iii0000000000-1100−i3i300003−3000000
χ4622-2-2-1222i−2i21-2-12-2-21-20-1-12-1-10−i3i3-1-12-1-11111-2-211112i−2i3−32i−2i−ii00−i3i3−i3i300−i3−i3i3i300−ii−ii2i−2i−i−iii3−33−30033−3−3-22−2i2iii−i−i00000000001-100i3−i30000−33000000
χ4722-2-2-1222i−2i21-2-12-2-21-20-1-12-1-10i3−i3-1-12-1-11111-2-211112i−2i−332i−2i−ii00i3−i3i3−i300i3i3−i3−i300−ii−ii2i−2i−i−iii−33−3300−3−3332-22i−2i−i−iii0000000000-1100i3−i30000−33000000
χ4822-2-2-1222i−2i21-2-12-2-21-20-1-12-1-10i3−i3-1-12-1-11111-2-211112i−2i−332i−2i−ii00i3−i3i3−i300i3i3−i3−i300−ii−ii2i−2i−i−iii−33−3300−3−333-22−2i2iii−i−i00000000001-100−i3i300003−3000000
χ4922-2-2-122−2i2i21-2-12-2-21-20-1-12-1-10−i3i3-1-12-1-11111-2-21111−2i2i−33−2i2ii−i00−i3i3−i3i300−i3−i3i3i300i−ii−i−2i2iii−i−i−33−3300−3−3332-2−2i2iii−i−i0000000000-1100−i3i30000−33000000
χ5022-2-2-122−2i2i21-2-12-2-21-20-1-12-1-10−i3i3-1-12-1-11111-2-21111−2i2i−33−2i2ii−i00−i3i3−i3i300−i3−i3i3i300i−ii−i−2i2iii−i−i−33−3300−3−333-222i−2i−i−iii00000000001-100i3−i300003−3000000
χ5122-2-2-122−2i2i21-2-12-2-21-20-1-12-1-10i3−i3-1-12-1-11111-2-21111−2i2i3−3−2i2ii−i00i3−i3i3−i300i3i3−i3−i300i−ii−i−2i2iii−i−i3−33−30033−3−32-2−2i2iii−i−i0000000000-1100i3−i300003−3000000
χ5222-2-2-122−2i2i21-2-12-2-21-20-1-12-1-10i3−i3-1-12-1-11111-2-21111−2i2i3−3−2i2ii−i00i3−i3i3−i300i3i3−i3−i300i−ii−i−2i2iii−i−i3−33−30033−3−3-222i−2i−i−iii00000000001-100−i3i30000−33000000
χ5344444-2-244-24-24-2-2-24-24-2-2111444-2-2111-2-2-2-2111111-2-244-2-244-2-2-2-2-2-2111111-2-2-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000000000
χ5444444-2-244-24-24-2-2-24-2-4-2-2111-4-4-4-2-2111-2-2-2-2111111-2-2-4-4-2-244222222-1-1-1-1-1-122-2-2-2-21111112222-1-1-1-1-1-1000000000000000000000000000000000000
χ5544444-2-2-4-4-24-24-2-2-24-24-2-2111-444-2-2111-2-2-2-211111122-4-422-4-4-2-2-2-2-2-2111111222222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000000000000000
χ5644444-2-2-4-4-24-24-2-2-24-2-4-2-21114-4-4-2-2111-2-2-2-2111111224422-4-4222222-1-1-1-1-1-1-2-22222-1-1-1-1-1-1-2-2-2-2111111000000000000000000000000000000000000
χ574444-24-244-2-24-24-2-2-244-21-2114-2-2-21-211-2-211-2-2111144-2-2-2-2-2-24-2-2-211-2-21111-24-2-211-2-21111-2-211-2-21111000000000000000000000000000000000000
χ584444-24-244-2-24-24-2-2-24-4-21-211-422-21-211-2-211-2-211114422-2-2-2-2-4222-1-122-1-1-1-12-4-2-211-2-2111122-1-122-1-1-1-1000000000000000000000000000000000000
χ594444-24-2-4-4-2-24-24-2-2-244-21-211-4-2-2-21-211-2-211-2-21111-4-42222224-2-2-211-2-211112-422-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000000000000000000000
χ604444-24-2-4-4-2-24-24-2-2-24-4-21-211422-21-211-2-211-2-21111-4-4-2-22222-4222-1-122-1-1-1-1-2422-1-122-1-1-1-1-2-211-2-21111000000000000000000000000000000000000
χ614444-2-24444-2-2-2-244-2-241-2-2114-2-21-2-21111-2-2-2-21111-2-2-2-244-2-2-2411-2-2-2-211114-211-2-2-2-2111111-2-2-2-21111000000000000000000000000000000000000
χ624444-2-24444-2-2-2-244-2-2-41-2-211-4221-2-21111-2-2-2-21111-2-22244-2-22-4-1-12222-1-1-1-1-4211-2-2-2-21111-1-12222-1-1-1-1000000000000000000000000000000000000
χ634444-2-24-4-44-2-2-2-244-2-241-2-211-4-2-21-2-21111-2-2-2-211112222-4-422-2411-2-2-2-21111-42-1-12222-1-1-1-1-1-12222-1-1-1-1000000000000000000000000000000000000
χ644444-2-24-4-44-2-2-2-244-2-2-41-2-2114221-2-21111-2-2-2-2111122-2-2-4-4222-4-1-12222-1-1-1-14-2-1-12222-1-1-1-111-2-2-2-21111000000000000000000000000000000000000
χ654444-2-2-244-2-2-2-2-2-2-2-2-24111−1−3i32−1+3i324-2-2111−1−3i32−1+3i32111111−1−3i32−1−3i32−1+3i32−1+3i32-2-2-2-2-2-2-2-2-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000000000000000
χ664444-2-2-244-2-2-2-2-2-2-2-2-24111−1+3i32−1−3i324-2-2111−1+3i32−1−3i32111111−1+3i32−1+3i32−1−3i32−1−3i32-2-2-2-2-2-2-2-2-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000000000000000
χ674444-2-2-244-2-2-2-2-2-2-2-2-2-4111−1−3i32−1+3i32-422111−1−3i32−1+3i32111111−1−3i32−1−3i32−1+3i32−1+3i32-2-222-2-2-2-222-1-1-1-1-1-11+3i321−3i321+3i321−3i3222111111−1−3i32−1+3i32−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000000000000
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χ7544-4-44-244i−4i4-424-2-4-4-420-24-2-2-2000-24-2-2-222-4-4222222−2i2i004i−4i4i−4i00000000000000−2i2i4i−4i−2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000
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χ8644-4-4-2-244i−4i422-2-2-4-42201-2-21102i3−2i31-2-211-1-12222-1-1-1-1−2i2i−23234i−4i−2i2i00−i3i32i3−2i300−i3−i3i3i300i−i−2i2i−2i2iii−i−i3−3−23230033−3−3000000000000000000000000000000000000
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χ1158-88-8-4-4-40044-444-44-440222−1+3i3−1−3i3000-2-2-21−3i31+3i32-22-22-2−1+3i31−3i3−1−3i31+3i3000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1208-8-88-4-4-4004-44444-44-40222−1+3i3−1−3i3000-2-2-21−3i31+3i3-22-22-221−3i3−1+3i31+3i3−1−3i3000000000000000000000000000000000000000000000000000000000000000000000000000000

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