Finite Group Databasebeta

← Group #13172194

Character table — Group #13172194

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222444444444444444444444466668888888888889999121212121212121212121212121212121212121212121212121212121818181818182424242424242424242424243636363636365454545472727272
order122222333666666666333666666666666666666644443666666666664444224466661212121212121212121212121212121212121212441212121266666612121212121244441212222212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11-11-111-1-11111111111-1-111111111-1-1-1-1-1-11-111-1-11-111-1-111-1-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-11-11-1-11111111111-1-11111111111-1-1-1-1-1-1-11-1-111-11-1-111-1-111-1-1-1-1-1-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-11-11-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-111-1-1-1-111-1-11111-1-111
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-11-11-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-11111-1-1-1-1111111-1-1
χ91111-1-1111111111111111-1-1-1-1-1-111-1-1-1-1111111111-1-11-1-1-1-1111-1-1-1-111111-1-1111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111111-111-1-1-11-1-1111-11-1-1-111-1-11-11-1
χ101111-1-1111111111111111-1-1-1-1-1-111-1-1-1-1111111111-1-11-1-1-1-1111-1-1-1-11111-111-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-11111-11-1-1111-111-1-1-11-11-1-111-1-1-11-11
χ111111-1-1111111111111111-1-1-1-1-1-111-1-1-1-1111111111-1-11-1-1-1-1111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11-1-1111-1-1111-1-11
χ121111-1-1111111111111111-1-1-1-1-1-111-1-1-1-1111111111-1-11-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-111-111-1-111-111-1
χ131111-1-1111111111111111-1-1-1-1-1-111-1-1-1-11111111-1-1111-1-1-1-1111-1-1-1-111111-1-1111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111111-111-1-1-11-1-111-11-11-1-1-1-111-11-11
χ141111-1-1111111111111111-1-1-1-1-1-111-1-1-1-11111111-1-1111-1-1-1-1111-1-1-1-11111-111-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-11111-11-1-1111-111-1-11-11-1-1-1-1-1111-11-1
χ151111-1-1111111111111111-1-1-1-1-1-111-1-1-1-11111111-1-1111-1-1-1-1111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-111-11111-1-1-111-1
χ161111-1-1111111111111111-1-1-1-1-1-111-1-1-1-11111111-1-1111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111-1-111111-1-11-1-11
χ1722222222-1-1-1222222-12-1-12222-1-1222222-1-1-1-1-1-120000-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-100000000-1-1-1-10000000022-1-1-1-122-1-1-1-122-1-1-1-10000-1-100000000
χ1822222222-1-1-1222222-12-1-12222-1-1222222-1-1-1-1-1-120000-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211110000000011110000000022-1-1-1-1-2-21111-2-211110000-1-100000000
χ1922222222-1-1-1222222-12-1-12222-1-1222222-1-1-1-1-1-120000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22-22-2-1-11100000000-1-11100000000-2-211112-2-1-1112-2-1-11100001100000000
χ2022222222-1-1-1222222-12-1-12222-1-1222222-1-1-1-1-1-120000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-22-2211-1-10000000011-1-100000000-2-21111-2211-1-1-2211-1-100001100000000
χ212222222-1222222-1-1-12-12-122-1-122-1-1-1-1-1-122-1-12-1-12222-122-1-1-1-1-1-1-1-1-100000202002222-1-122-1-10022-1-1-1-1-1-1-1-10000000-100-1-10-100-1-1002200000000-1-1
χ222222222-1222222-1-1-12-12-122-1-122-1-1-1-1-1-122-1-12-1-12222-122-1-1-1-1-1-1-1-1-100000-20-200-2-222-1-122-1-100-2-2-1-1-1-1-1-1-1-100000001001101001100-2-20000000011
χ232222222-1222222-1-1-12-12-122-1-122-1-1-1-1-1-122-1-12-1-1-2-2-2-2-122-1-1-1-1-1-1-1-1-1000002020022-2-211-2-2110022111111110000000-100-1-10-100-1-100-2-20000000011
χ242222222-1222222-1-1-12-12-122-1-122-1-1-1-1-1-122-1-12-1-1-2-2-2-2-122-1-1-1-1-1-1-1-1-100000-20-200-2-2-2-211-2-21100-2-211111111000000010011010011002200000000-1-1
χ25222222-12222-1-1-12222-1-12-1-12222-1-1-1-1-1-1-1-122-12-12222-1-1-122-1-1-1-1-1-1-1000020202200-1-122-1-1222200-1-1-1-1-1-1-1-1000000-10-1-100-10-1-1002200000000-1-100
χ26222222-12222-1-1-12222-1-12-1-12222-1-1-1-1-1-1-1-122-12-12222-1-1-122-1-1-1-1-1-1-10000-20-20-2-200-1-122-1-122-2-200-1-1-1-1-1-1-1-1000000101100101100-2-2000000001100
χ27222222-12222-1-1-12222-1-12-1-12222-1-1-1-1-1-1-1-122-12-1-2-2-2-2-1-1-122-1-1-1-1-1-1-100002020220011-2-211-2-2220011111111000000-10-1-100-10-1-100-2-2000000001100
χ28222222-12222-1-1-12222-1-12-1-12222-1-1-1-1-1-1-1-122-12-1-2-2-2-2-1-1-122-1-1-1-1-1-1-10000-20-20-2-20011-2-211-2-2-2-200111111110000001011001011002200000000-1-100
χ292222-2-222-1-1-1222222-12-1-1-2-2-2-21122-2-2-2-2-1-1-1-1-1-120000-11111-1-1-1111122222-2-22-1-1110000000011-1-100000000-2-2-1-1-1-12-2-1-111-2211-1-100001100000000
χ302222-2-222-1-1-1222222-12-1-1-2-2-2-21122-2-2-2-2-1-1-1-1-1-120000-11111-1-1-111112222-222-211-1-100000000-1-11100000000-2-2-1-1-1-1-2211-1-12-2-1-11100001100000000
χ312222-2-222-1-1-1222222-12-1-1-2-2-2-21122-2-2-2-2-1-1-1-1-1-120000-11111-1-1-11111-2-2-2-222-2-2-1-1-1-10000000011110000000022111122-1-1-1-1-2-211110000-1-100000000
χ322222-2-222-1-1-1222222-12-1-1-2-2-2-21122-2-2-2-2-1-1-1-1-1-120000-11111-1-1-11111-2-2-2-2-2-222111100000000-1-1-1-100000000221111-2-2111122-1-1-1-10000-1-100000000
χ332222-2-22-1222222-1-1-12-12-1-2-211-2-2-1-1111122-1-12-1-122-2-2-1-2-211-1-1-111110000020-2002222-1-1-2-21100-2-2-1-1-1-111110000000-100-1-101001100-22000000001-1
χ342222-2-22-1222222-1-1-12-12-1-2-211-2-2-1-1111122-1-12-1-122-2-2-1-2-211-1-1-1111100000-20200-2-222-1-1-2-2110022-1-1-1-111110000000100110-100-1-1002-200000000-11
χ352222-2-22-1222222-1-1-12-12-1-2-211-2-2-1-1111122-1-12-1-1-2-222-1-2-211-1-1-111110000020-20022-2-21122-1-100-2-21111-1-1-1-10000000-100-1-1010011002-200000000-11
χ362222-2-22-1222222-1-1-12-12-1-2-211-2-2-1-1111122-1-12-1-1-2-222-1-2-211-1-1-1111100000-20200-2-2-2-21122-1-100221111-1-1-1-10000000100110-100-1-100-22000000001-1
χ372222-2-2-12222-1-1-12222-1-1211-2-2-2-2-1-11111-1-122-12-122-2-2-111-2-2-1-1-11111000020-202200-1-12211-2-2-2-200-1-1-1-11111000000-10-1-1001011002-200000000-1100
χ382222-2-2-12222-1-1-12222-1-1211-2-2-2-2-1-11111-1-122-12-122-2-2-111-2-2-1-1-111110000-2020-2-200-1-12211-2-22200-1-1-1-11111000000101100-10-1-100-22000000001-100
χ392222-2-2-12222-1-1-12222-1-1211-2-2-2-2-1-11111-1-122-12-1-2-222-111-2-2-1-1-11111000020-20220011-2-2-1-122-2-2001111-1-1-1-1000000-10-1-100101100-22000000001-100
χ402222-2-2-12222-1-1-12222-1-1211-2-2-2-2-1-11111-1-122-12-1-2-222-111-2-2-1-1-111110000-2020-2-20011-2-2-1-12222001111-1-1-1-1000000101100-10-1-1002-200000000-1100
χ4122-2-2002222-22-2-22-2-2-22220000002-200002-22-2-2-2-2002i−2i200002-2-200002i2i−2i−2i0000000000002i−2i2i−2i000000002i2i−2i−2i002i2i−2i−2i000000000000000000002-20000
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χ4322-2-2002222-22-2-22-2-2-22220000002-200002-22-2-2-2-200−2i2i200002-2-200002i2i−2i−2i000000000000−2i2i−2i2i00000000−2i−2i2i2i002i2i−2i−2i00000000000000000000-220000
χ4422-2-2002222-22-2-22-2-2-22220000002-200002-22-2-2-2-200−2i2i200002-2-20000−2i−2i2i2i000000000000−2i2i−2i2i00000000−2i−2i2i2i00−2i−2i2i2i000000000000000000002-20000
χ452-22-200222-22-22-2-22-2-2222000000-220000-22-22-2-2-22i−2i0020000-22-200002i−2i2i−2i000000002i−2i2i−2i000000002i2i−2i−2i0000002i−2i2i−2i0000000000000000002-2000000
χ462-22-200222-22-22-2-22-2-2222000000-220000-22-22-2-2-22i−2i0020000-22-20000−2i2i−2i2i000000002i−2i2i−2i000000002i2i−2i−2i000000−2i2i−2i2i000000000000000000-22000000
χ472-22-200222-22-22-2-22-2-2222000000-220000-22-22-2-2-2−2i2i0020000-22-200002i−2i2i−2i00000000−2i2i−2i2i00000000−2i−2i2i2i0000002i−2i2i−2i000000000000000000-22000000
χ482-22-200222-22-22-2-22-2-2222000000-220000-22-22-2-2-2−2i2i0020000-22-20000−2i2i−2i2i00000000−2i2i−2i2i00000000−2i−2i2i2i000000−2i2i−2i2i0000000000000000002-2000000
χ492-2-222-2222-2-2-2-22-2-2222222-22-22-2-2-222-2-2-2-2-2-2222000022-22-2-2-2222-2-22-2-2200000000000000000000000000002-22-2-2200000000000000002-200000000
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χ552-2-22-22222-2-2-2-22-2-222222-22-22-22-2-2-2-222-2-2-2-222200002-22-22-2-22-2-2222-2-220000000000000000000000000000-222-2-220000000000000000-2200000000
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χ724444-4-4-2-2444-2-2-2-2-2-241-2-22222-4-411-1-1-1-1-2-2-2-2-2-21-4-44412222111-1-1-1-10000000000002222-2-2-2-20000-1-1-1-1111100000000000000000000000000000000
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χ1084-4-44-44-2-24-4-422-222-241-2-22-22-2-44-1-1-1-1112222-2-21000012-22-2-1-11-1-111000000000000000000000000-333-33-3-3300000000000000000000000000000000
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χ1208-8-88-88-4-4-44444-444-4-42224-44-44-4-2-2-2-222-2-2-2-22220000-1-22-2211-111-1-10000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).