Finite Group Databasebeta

← Group #13171731

Character table — Group #13171731

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size112222244444466669912121212181122222444444666699121212121822444448888881212121218182424242436224444488888812121212181824242424363366666121212121212181818182727363636365433666661212121212121818181827273636363654
order1223366366666224444661212422266666666662244446612124366336636666666121212126612121266666666666666612121212661212124441212121212121212121244444412121212444412121212121212121212444444121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111-11-1-1-11-11-1-111111111111111-11-1-1-11-11-1-111111111111111-11-1-1-11-11-1-111111111111111-11-1-1-11-11-1-111111111111111-11-1-1-11-11-1-111111111111111-11-1-1-11-11-1-1
χ31111111111111-11-11-1-1-11-11-11111111111111-11-11-1-1-11-11-11111111111111-11-11-1-1-11-11-11111111111111-11-11-1-1-11-11-11111111111111-11-11-1-1-11-11-11111111111111-11-11-1-1-11-11-1
χ41111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-11
χ511-111111-1-11-1-111-1-1-1-111-1-1111-111111-1-11-1-111-1-1-1-111-1-1111-111111-1-11-1-111-1-1-1-111-1-1111-111111-1-11-1-111-1-1-1-111-1-1111-111111-1-11-1-111-1-1-1-111-1-1111-111111-1-11-1-111-1-1-1-111-1-11
χ611-111111-1-11-1-11-1-11111-1-11-111-111111-1-11-1-11-1-11111-1-11-111-111111-1-11-1-11-1-11111-1-11-111-111111-1-11-1-11-1-11111-1-11-111-111111-1-11-1-11-1-11111-1-11-111-111111-1-11-1-11-1-11111-1-11-1
χ711-111111-1-11-1-1-111-111-111-1-111-111111-1-11-1-1-111-111-111-1-111-111111-1-11-1-1-111-111-111-1-111-111111-1-11-1-1-111-111-111-1-111-111111-1-11-1-1-111-111-111-1-111-111111-1-11-1-1-111-111-111-1-1
χ811-111111-1-11-1-1-1-111-1-1-1-111111-111111-1-11-1-1-1-111-1-1-1-111111-111111-1-11-1-1-1-111-1-1-1-111111-111111-1-11-1-1-1-111-1-1-1-111111-111111-1-11-1-1-1-111-1-1-1-111111-111111-1-11-1-1-1-111-1-1-1-1111
χ92222-12-1-12-1-1-1-10202000-10-102222-12-1-12-1-1-1-10202000-10-102222-12-1-12-1-1-1-10202000-10-102222-12-1-12-1-1-1-10202000-10-102222-12-1-12-1-1-1-10202000-10-102222-12-1-12-1-1-1-10202000-10-10
χ102222-12-1-12-1-1-1-10-20-200010102222-12-1-12-1-1-1-10-20-200010102222-12-1-12-1-1-1-10-20-200010102222-12-1-12-1-1-1-10-20-200010102222-12-1-12-1-1-1-10-20-200010102222-12-1-12-1-1-1-10-20-20001010
χ11222-12-12-1-12-1-1-1202000-10-100222-12-12-1-12-1-1-1202000-10-100222-12-12-1-12-1-1-1202000-10-100222-12-12-1-12-1-1-1202000-10-100222-12-12-1-12-1-1-1202000-10-100222-12-12-1-12-1-1-1202000-10-100
χ12222-12-12-1-12-1-1-1-20-200010100222-12-12-1-12-1-1-1-20-200010100222-12-12-1-12-1-1-1-20-200010100222-12-12-1-12-1-1-1-20-200010100222-12-12-1-12-1-1-1-20-200010100222-12-12-1-12-1-1-1-20-200010100
χ1322-22-12-1-1-21-111020-2000-101022-22-12-1-1-21-111020-2000-101022-22-12-1-1-21-111020-2000-101022-22-12-1-1-21-111020-2000-101022-22-12-1-1-21-111020-2000-101022-22-12-1-1-21-111020-2000-1010
χ1422-22-12-1-1-21-1110-20200010-1022-22-12-1-1-21-1110-20200010-1022-22-12-1-1-21-1110-20200010-1022-22-12-1-1-21-1110-20200010-1022-22-12-1-1-21-1110-20200010-1022-22-12-1-1-21-1110-20200010-10
χ1522-2-12-12-11-2-11120-2000-1010022-2-12-12-11-2-11120-2000-1010022-2-12-12-11-2-11120-2000-1010022-2-12-12-11-2-11120-2000-1010022-2-12-12-11-2-11120-2000-1010022-2-12-12-11-2-11120-2000-10100
χ1622-2-12-12-11-2-111-20200010-10022-2-12-12-11-2-111-20200010-10022-2-12-12-11-2-111-20200010-10022-2-12-12-11-2-111-20200010-10022-2-12-12-11-2-111-20200010-10022-2-12-12-11-2-111-20200010-100
χ172-2022-2-2200-20000002i−2i000002-2022-2-2200-20000002i−2i000002-2022-2-2200-20000002i−2i000002-2022-2-2200-20000002i−2i000002-2022-2-2200-20000002i−2i000002-2022-2-2200-20000002i−2i00000
χ182-2022-2-2200-2000000−2i2i000002-2022-2-2200-2000000−2i2i000002-2022-2-2200-2000000−2i2i000002-2022-2-2200-2000000−2i2i000002-2022-2-2200-2000000−2i2i000002-2022-2-2200-2000000−2i2i00000
χ19444-2-2-2-21-2-211100000000000444-2-2-2-21-2-211100000000000444-2-2-2-21-2-211100000000000444-2-2-2-21-2-211100000000000444-2-2-2-21-2-211100000000000444-2-2-2-21-2-211100000000000
χ2044-4-2-2-2-21221-1-10000000000044-4-2-2-2-21221-1-10000000000044-4-2-2-2-21221-1-10000000000044-4-2-2-2-21221-1-10000000000044-4-2-2-2-21221-1-10000000000044-4-2-2-2-21221-1-100000000000
χ214-404-2-42-200200000000000004-404-2-42-200200000000000004-404-2-42-200200000000000004-404-2-42-200200000000000004-404-2-42-200200000000000004-404-2-42-20020000000000000
χ224-40-242-4-200200000000000004-40-242-4-200200000000000004-40-242-4-200200000000000004-40-242-4-200200000000000004-40-242-4-200200000000000004-40-242-4-20020000000000000
χ234-40-2-222100-13-3000000000004-40-2-222100-13-3000000000004-40-2-222100-13-3000000000004-40-2-222100-13-3000000000004-40-2-222100-13-3000000000004-40-2-222100-13-300000000000
χ244-40-2-222100-1-33000000000004-40-2-222100-1-33000000000004-40-2-222100-1-33000000000004-40-2-222100-1-33000000000004-40-2-222100-1-33000000000004-40-2-222100-1-3300000000000
χ25111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ2611111111111111-11-1-1-11-11-1-111111111111111-11-1-1-11-11-1-111111111111111-11-1-1-11-11-1-111111111111111-11-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-11-111
χ271111111111111-11-11-1-1-11-11-11111111111111-11-11-1-1-11-11-11111111111111-11-11-1-1-11-11-11111111111111-11-11-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1111-11-11
χ281111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1
χ2911-111111-1-11-1-111-1-1-1-111-1-1111-111111-1-11-1-111-1-1-1-111-1-1111-111111-1-11-1-111-1-1-1-111-1-1111-111111-1-11-1-111-1-1-1-111-1-11-1-11-1-1-1-1-111-111-1-11111-1-111-1-1-11-1-1-1-1-111-111-1-11111-1-111-1
χ3011-111111-1-11-1-11-1-11111-1-11-111-111111-1-11-1-11-1-11111-1-11-111-111111-1-11-1-11-1-11111-1-11-111-111111-1-11-1-11-1-11111-1-11-1-1-11-1-1-1-1-111-111-111-1-1-1-111-11-1-11-1-1-1-1-111-111-111-1-1-1-111-11
χ3111-111111-1-11-1-1-111-111-111-1-111-111111-1-11-1-1-111-111-111-1-111-111111-1-11-1-1-111-111-111-1-111-111111-1-11-1-1-111-111-111-1-1-1-11-1-1-1-1-111-1111-1-11-1-11-1-111-1-11-1-1-1-1-111-1111-1-11-1-11-1-111
χ3211-111111-1-11-1-1-1-111-1-1-1-111111-111111-1-11-1-1-1-111-1-1-1-111111-111111-1-11-1-1-1-111-1-1-1-111111-111111-1-11-1-1-1-111-1-1-1-1111-1-11-1-1-1-1-111-11111-1-11111-1-1-1-1-11-1-1-1-1-111-11111-1-11111-1-1-1
χ332222-12-1-12-1-1-1-10202000-10-102222-12-1-12-1-1-1-10202000-10-102222-12-1-12-1-1-1-10202000-10-102222-12-1-12-1-1-1-10202000-10-10-2-2-2-21-211-211110-20-20001010-2-2-2-21-211-211110-20-20001010
χ342222-12-1-12-1-1-1-10-20-200010102222-12-1-12-1-1-1-10-20-200010102222-12-1-12-1-1-1-10-20-200010102222-12-1-12-1-1-1-10-20-20001010-2-2-2-21-211-211110202000-10-10-2-2-2-21-211-211110202000-10-10
χ35222-12-12-1-12-1-1-1202000-10-100222-12-12-1-12-1-1-1202000-10-100222-12-12-1-12-1-1-1202000-10-100222-12-12-1-12-1-1-1202000-10-100-2-2-21-21-211-2111-20-200010100-2-2-21-21-211-2111-20-200010100
χ36222-12-12-1-12-1-1-1-20-200010100222-12-12-1-12-1-1-1-20-200010100222-12-12-1-12-1-1-1-20-200010100222-12-12-1-12-1-1-1-20-200010100-2-2-21-21-211-2111202000-10-100-2-2-21-21-211-2111202000-10-100
χ3722-22-12-1-1-21-111020-2000-101022-22-12-1-1-21-111020-2000-101022-22-12-1-1-21-111020-2000-101022-22-12-1-1-21-111020-2000-1010-2-22-21-2112-11-1-10-20200010-10-2-22-21-2112-11-1-10-20200010-10
χ3822-22-12-1-1-21-1110-20200010-1022-22-12-1-1-21-1110-20200010-1022-22-12-1-1-21-1110-20200010-1022-22-12-1-1-21-1110-20200010-10-2-22-21-2112-11-1-1020-2000-1010-2-22-21-2112-11-1-1020-2000-1010
χ3922-2-12-12-11-2-11120-2000-1010022-2-12-12-11-2-11120-2000-1010022-2-12-12-11-2-11120-2000-1010022-2-12-12-11-2-11120-2000-10100-2-221-21-21-121-1-1-20200010-100-2-221-21-21-121-1-1-20200010-100
χ4022-2-12-12-11-2-111-20200010-10022-2-12-12-11-2-111-20200010-10022-2-12-12-11-2-111-20200010-10022-2-12-12-11-2-111-20200010-100-2-221-21-21-121-1-120-2000-10100-2-221-21-21-121-1-120-2000-10100
χ412-2022-2-2200-20000002i−2i000002-2022-2-2200-20000002i−2i000002-2022-2-2200-20000002i−2i000002-2022-2-2200-20000002i−2i00000-220-2-222-2002000000−2i2i00000-220-2-222-2002000000−2i2i00000
χ422-2022-2-2200-2000000−2i2i000002-2022-2-2200-2000000−2i2i000002-2022-2-2200-2000000−2i2i000002-2022-2-2200-2000000−2i2i00000-220-2-222-20020000002i−2i00000-220-2-222-20020000002i−2i00000
χ43444-2-2-2-21-2-211100000000000444-2-2-2-21-2-211100000000000444-2-2-2-21-2-211100000000000444-2-2-2-21-2-211100000000000-4-4-42222-122-1-1-100000000000-4-4-42222-122-1-1-100000000000
χ4444-4-2-2-2-21221-1-10000000000044-4-2-2-2-21221-1-10000000000044-4-2-2-2-21221-1-10000000000044-4-2-2-2-21221-1-100000000000-4-442222-1-2-2-11100000000000-4-442222-1-2-2-11100000000000
χ454-404-2-42-200200000000000004-404-2-42-200200000000000004-404-2-42-200200000000000004-404-2-42-20020000000000000-440-424-2200-20000000000000-440-424-2200-20000000000000
χ464-40-242-4-200200000000000004-40-242-4-200200000000000004-40-242-4-200200000000000004-40-242-4-20020000000000000-4402-4-24200-20000000000000-4402-4-24200-20000000000000
χ474-40-2-222100-13-3000000000004-40-2-222100-13-3000000000004-40-2-222100-13-3000000000004-40-2-222100-13-300000000000-44022-2-2-1001-3300000000000-44022-2-2-1001-3300000000000
χ484-40-2-222100-1-33000000000004-40-2-222100-1-33000000000004-40-2-222100-1-33000000000004-40-2-222100-1-3300000000000-44022-2-2-10013-300000000000-44022-2-2-10013-300000000000
χ49111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ5011111111111111-11-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-11-11111111111111111-11-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-11-111iiiiiiiiiiiiii−ii−i−i−ii−ii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−ii−iiii−ii−iii
χ511111111111111-11-11-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1111-11-111111111111111-11-11-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1111-11-11iiiiiiiiiiiii−ii−ii−i−i−ii−ii−i−i−i−i−i−i−i−i−i−i−i−i−i−ii−ii−iiii−ii−ii
χ521111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-11111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1iiiiiiiiiiiii−i−i−i−iii−i−i−i−ii−i−i−i−i−i−i−i−i−i−i−i−i−iiiii−i−iiiii−i
χ5311-111111-1-11-1-111-1-1-1-111-1-11-1-11-1-1-1-1-111-111-1-11111-1-111-111-111111-1-11-1-111-1-1-1-111-1-11-1-11-1-1-1-1-111-111-1-11111-1-111-1ii−iiiiii−i−ii−i−iii−i−i−i−iii−i−ii−i−ii−i−i−i−i−iii−iii−i−iiiii−i−iii−i
χ5411-111111-1-11-1-11-1-11111-1-11-1-1-11-1-1-1-1-111-111-111-1-1-1-111-1111-111111-1-11-1-11-1-11111-1-11-1-1-11-1-1-1-1-111-111-111-1-1-1-111-11ii−iiiiii−i−ii−i−ii−i−iiiii−i−ii−i−i−ii−i−i−i−i−iii−iii−iii−i−i−i−iii−ii
χ5511-111111-1-11-1-1-111-111-111-1-1-1-11-1-1-1-1-111-1111-1-11-1-11-1-11111-111111-1-11-1-1-111-111-111-1-1-1-11-1-1-1-1-111-1111-1-11-1-11-1-111ii−iiiiii−i−ii−i−i−iii−iii−iii−i−i−i−ii−i−i−i−i−iii−iiii−i−ii−i−ii−i−iii
χ5611-111111-1-11-1-1-1-111-1-1-1-1111-1-11-1-1-1-1-111-11111-1-11111-1-1-111-111111-1-11-1-1-1-111-1-1-1-1111-1-11-1-1-1-1-111-11111-1-11111-1-1-1ii−iiiiii−i−ii−i−i−i−iii−i−i−i−iiii−i−ii−i−i−i−i−iii−iiiii−i−iiiii−i−i−i
χ572222-12-1-12-1-1-1-10202000-10-10-2-2-2-21-211-211110-20-200010102222-12-1-12-1-1-1-10202000-10-10-2-2-2-21-211-211110-20-200010102i2i2i2i−i2i−i−i2i−i−i−i−i02i02i000−i0−i0−2i−2i−2i−2ii−2iii−2iiiii0−2i0−2i000i0i0
χ582222-12-1-12-1-1-1-10-20-20001010-2-2-2-21-211-211110202000-10-102222-12-1-12-1-1-1-10-20-20001010-2-2-2-21-211-211110202000-10-102i2i2i2i−i2i−i−i2i−i−i−i−i0−2i0−2i000i0i0−2i−2i−2i−2ii−2iii−2iiiii02i02i000−i0−i0
χ59222-12-12-1-12-1-1-1202000-10-100-2-2-21-21-211-2111-20-200010100222-12-12-1-12-1-1-1202000-10-100-2-2-21-21-211-2111-20-2000101002i2i2i−i2i−i2i−i−i2i−i−i−i2i02i000−i0−i00−2i−2i−2ii−2ii−2iii−2iiii−2i0−2i000i0i00
χ60222-12-12-1-12-1-1-1-20-200010100-2-2-21-21-211-2111202000-10-100222-12-12-1-12-1-1-1-20-200010100-2-2-21-21-211-2111202000-10-1002i2i2i−i2i−i2i−i−i2i−i−i−i−2i0−2i000i0i00−2i−2i−2ii−2ii−2iii−2iiii2i02i000−i0−i00
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χ13344-44-24-2-2-42-222040-4000-2020-4-44-42-4224-22-2-20-40400020-20-2-22-21-2112-11-1-10-20200010-1022-22-12-1-1-21-111020-2000-1010000000000000000000000000000000000000000000000000
χ13444-44-24-2-2-42-2220-40400020-20-4-44-42-4224-22-2-2040-4000-2020-2-22-21-2112-11-1-1020-2000-101022-22-12-1-1-21-1110-20200010-10000000000000000000000000000000000000000000000000
χ13544-4-24-24-22-4-22240-4000-20200-4-442-42-42-242-2-2-40400020-200-2-221-21-21-121-1-1-20200010-10022-2-12-12-11-2-11120-2000-10100000000000000000000000000000000000000000000000000
χ13644-4-24-24-22-4-222-40400020-200-4-442-42-42-242-2-240-4000-20200-2-221-21-21-121-1-120-2000-1010022-2-12-12-11-2-111-20200010-100000000000000000000000000000000000000000000000000
χ1374-4044-4-4400-40000004i−4i00000-440-4-444-4004000000−4i4i00000-220-2-222-2002000000−2i2i000002-2022-2-2200-20000002i−2i00000000000000000000000000000000000000000000000000000
χ1384-4044-4-4400-4000000−4i4i00000-440-4-444-40040000004i−4i00000-220-2-222-20020000002i−2i000002-2022-2-2200-2000000−2i2i00000000000000000000000000000000000000000000000000000
χ139888-4-4-4-42-4-422200000000000-8-8-84444-244-2-2-200000000000-4-4-42222-122-1-1-100000000000444-2-2-2-21-2-211100000000000000000000000000000000000000000000000000000000000
χ14088-8-4-4-4-42442-2-200000000000-8-884444-2-4-4-22200000000000-4-442222-1-2-2-1110000000000044-4-2-2-2-21221-1-100000000000000000000000000000000000000000000000000000000000
χ1418-808-4-84-40040000000000000-880-848-4400-40000000000000-440-424-2200-200000000000004-404-2-42-20020000000000000000000000000000000000000000000000000000000000000
χ1428-80-484-8-40040000000000000-8804-8-48400-40000000000000-4402-4-24200-200000000000004-40-242-4-20020000000000000000000000000000000000000000000000000000000000000
χ1438-80-4-444200-26-600000000000-88044-4-4-2002-6600000000000-44022-2-2-1001-33000000000004-40-2-222100-13-300000000000000000000000000000000000000000000000000000000000
χ1448-80-4-444200-2-6600000000000-88044-4-4-20026-600000000000-44022-2-2-10013-3000000000004-40-2-222100-1-3300000000000000000000000000000000000000000000000000000000000

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