Finite Group Databasebeta

← Group #13161364

Character table — Group #13161364

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size1111222222222222222222222244444444444444444444444444448888888888888888888888888888888888121212121212121212121212121212121212121224242424242424243636363636363636545454547272108108
order1244233333466666121212121212121212122333346666666661212121212121212121212121266666666666666666121212121212121212121212121212121244881212121212121212121212121212121224242424242424244488121212122244242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111111111111-11111-11111111111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1
χ611111111111111111111111111-11111-11111111111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ711111111111111111111111111-11111-11111111111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ811111111111111111111111111-11111-11111111111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ911-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1i−ii−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−ii−ii−iii−i−i1-11-1i−i1-1
χ1011-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1i−ii−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i−ii−ii−i−iii-11-11−ii-11
χ1111-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1−ii−ii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiiii−ii−iii−i−i-11-11i−i-11
χ1211-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1−ii−ii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−ii−ii−i−iii1-11-1−ii1-1
χ1311-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111i−i−iiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiii−i−iiii−i−i1-11-1−ii-11
χ1411-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111i−i−iiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii−iii−i−i−iii-11-11i−i1-1
χ1511-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111−iii−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−ii−i−iiii−i−i-11-11−ii1-1
χ1611-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111−iii−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−iii−i−i−iii1-11-1i−i-11
χ17222222222-122222-122222222-1-12-1-1-1-12-1-1-1-12222-12222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000002222-1-1-1-10000-1-100
χ18222222222-122222-122222222-1-12-1-1-1-12-1-1-1-12222-12222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000-2-2-2-2111100001100
χ19222222222-122222-122222222-1-1-2-1-1-1-1-2-1-1-1-12222-12222-1-1-1-1-1-1-1-1-1-2-2-2-21-1-1-1-111111111-2-2-2-21-1-1-1-111111111000000000000000000000000000022-2-2-1-1-1-100001100
χ20222222222-122222-122222222-1-1-2-1-1-1-1-2-1-1-1-12222-12222-1-1-1-1-1-1-1-1-1-2-2-2-21-1-1-1-111111111-2-2-2-21-1-1-1-1111111110000000000000000000000000000-2-22211110000-1-100
χ21222222-1-1-1222-1-1-1222-1-1-1-1-1-12222-1-1-122-1-1-12-1-1-122-1-1-1222-1-1-1-1-1-12-1-1-122-1-1-122-1-1-1-1-1-12-1-1-122-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-122-1-1-1-1-1-12-1-1-12-1-1-10000000000000000
χ22222222-1-1-1222-1-1-1222-1-1-1-1-1-12222-1-1-122-1-1-12-1-1-122-1-1-1222-1-1-1-1-1-12-1-1-122-1-1-122-1-1-1-1-1-12-1-1-122-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2111111-2-2111111-2111-21110000000000000000
χ23222222-1-1-1222-1-1-1222-1-1-1-1-1-122-22-1-1-1-22-1-1-12-1-1-122-1-1-1222-1-1-1-1-1-1-2111-22-1-1-1-2-2111111-2111-22-1-1-1-2-211111122-2-222-1-1-1-1-1-122-1-1-1-1-1-1-2111-21110000000000000000
χ24222222-1-1-1222-1-1-1222-1-1-1-1-1-122-22-1-1-1-22-1-1-12-1-1-122-1-1-1222-1-1-1-1-1-1-2111-22-1-1-1-2-2111111-2111-22-1-1-1-2-2111111-2-222-2-2111111-2-21111112-1-1-12-1-1-10000000000000000
χ2522222-12-1-122-12-1-12-1-122-1-1-1-1222-12-1-12-12-1-1-12-1-12-12-1-12-1-122-1-1-1-1-12-1-12-12-1-1-1-122-1-1-1-1-12-1-12-12-1-1-1-122-1-1-1-12222-1-122-1-1-1-1-1-122-1-1-1-1-12-1-1-12-1-10000000000000000
χ2622222-12-1-122-12-1-12-1-122-1-1-1-1222-12-1-12-12-1-1-12-1-12-12-1-12-1-122-1-1-1-1-12-1-12-12-1-1-1-122-1-1-1-1-12-1-12-12-1-1-1-122-1-1-1-1-2-2-2-211-2-2111111-2-211111-2111-2110000000000000000
χ2722222-12-1-122-12-1-12-1-122-1-1-1-122-2-12-1-1-2-12-1-1-12-1-12-12-1-12-1-122-1-1-1-11-211-2-12-1-111-2-211111-211-2-12-1-111-2-2111122-2-2-1-122-1-1-1-1-1-122-1-1-1-11-2111-2110000000000000000
χ2822222-12-1-122-12-1-12-1-122-1-1-1-122-2-12-1-1-2-12-1-1-12-1-12-12-1-12-1-122-1-1-1-11-211-2-12-1-111-2-211111-211-2-12-1-111-2-21111-2-22211-2-2111111-2-21111-12-1-1-12-1-10000000000000000
χ2922222-1-12-122-1-12-12-1-1-1-122-1-1222-1-12-12-1-12-1-1-12-12-1-12-12-1-1-1-122-1-1-1-12-12-1-12-1-1-1-1-122-1-1-1-12-12-1-12-1-1-1-1-122-1-12222-1-1-1-122-1-1-1-1-1-122-1-1-1-12-1-1-12-10000000000000000
χ3022222-1-12-122-1-12-12-1-1-1-122-1-1222-1-12-12-1-12-1-1-12-12-1-12-12-1-1-1-122-1-1-1-12-12-1-12-1-1-1-1-122-1-1-1-12-12-1-12-1-1-1-1-122-1-1-2-2-2-21111-2-2111111-2-21111-2111-210000000000000000
χ3122222-1-12-122-1-12-12-1-1-1-122-1-122-2-1-12-1-2-1-12-1-1-12-12-1-12-12-1-1-1-122-1-111-21-2-1-12-11111-2-21111-21-2-1-12-11111-2-21122-2-2-1-1-1-122-1-1-1-1-1-122-1-111-2111-210000000000000000
χ3222222-1-12-122-1-12-12-1-1-1-122-1-122-2-1-12-1-2-1-12-1-1-12-12-1-12-12-1-1-1-122-1-111-21-2-1-12-11111-2-21111-21-2-1-12-11111-2-211-2-2221111-2-2111111-2-211-1-12-1-1-12-10000000000000000
χ3322222-1-1-1222-1-1-122-1-1-1-1-1-122222-1-1-122-1-1-12-1-1-122-1-1-122-1-1-1-1-1-122-1-1-122-1-1-12-1-1-1-1-1-122-1-1-122-1-1-12-1-1-1-1-1-1222222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-12-1-1-120000000000000000
χ3422222-1-1-1222-1-1-122-1-1-1-1-1-122222-1-1-122-1-1-12-1-1-122-1-1-122-1-1-1-1-1-122-1-1-122-1-1-12-1-1-1-1-1-122-1-1-122-1-1-12-1-1-1-1-1-122-2-2-2-2111111-2-2111111-2-2111-2111-20000000000000000
χ3522222-1-1-1222-1-1-122-1-1-1-1-1-12222-2-1-1-12-2-1-1-12-1-1-122-1-1-122-1-1-1-1-1-122111-2-2-1-1-12111111-2-2111-2-2-1-1-12111111-2-222-2-2-1-1-1-1-1-122-1-1-1-1-1-122111-2111-20000000000000000
χ3622222-1-1-1222-1-1-122-1-1-1-1-1-12222-2-1-1-12-2-1-1-12-1-1-122-1-1-122-1-1-1-1-1-122111-2-2-1-1-12111111-2-2111-2-2-1-1-12111111-2-2-2-222111111-2-2111111-2-2-1-1-12-1-1-120000000000000000
χ372222-222222-22222222222222220222202222-2-2-2-2-2-2-2-2-2-22222222200000-2-2-2-20000000000000-2-2-2-2000000000000000000000000000000000000000000002-2-220000
χ382222-222222-22222222222222220222202222-2-2-2-2-2-2-2-2-2-22222222200000-2-2-2-20000000000000-2-2-2-200000000000000000000000000000000000000000000-222-20000
χ3922-2-2222222-222222-2-2-2-2-2-2-2-2-2-2022220222222222-2-2-2-2-2-2-2-2-2-2-2-2-20000022220000000000000-2-2-2-20000000000000000000000000000000000000000000022-2-20000
χ4022-2-2222222-222222-2-2-2-2-2-2-2-2-2-2022220222222222-2-2-2-2-2-2-2-2-2-2-2-2-20000022220000000000000-2-2-2-200000000000000000000000000000000000000000000-2-2220000
χ4122-2-2-22222-122222-1-2-2-2-2-2-2-2-2112-1-1-1-1-2-1-1-1-1-2-2-2-212222-1111111112222-11111-1-1-1-1-1-1-1-1-2-2-2-21-1-1-1-11111111100000000000000000000000000002i−2i2i−2i−i−iii0000−ii00
χ4222-2-2-22222-122222-1-2-2-2-2-2-2-2-2112-1-1-1-1-2-1-1-1-1-2-2-2-212222-1111111112222-11111-1-1-1-1-1-1-1-1-2-2-2-21-1-1-1-1111111110000000000000000000000000000−2i2i−2i2iii−i−i0000i−i00
χ4322-2-2-22222-122222-1-2-2-2-2-2-2-2-211-2-1-1-1-12-1-1-1-1-2-2-2-212222-111111111-2-2-2-211111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000002i−2i−2i2i−i−iii0000i−i00
χ4422-2-2-22222-122222-1-2-2-2-2-2-2-2-211-2-1-1-1-12-1-1-1-1-2-2-2-212222-111111111-2-2-2-211111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000−2i2i2i−2iii−i−i0000−ii00
χ4522-2-2-22-1-1-1222-1-1-12-2-2111111-2-222-1-1-1-22-1-1-1-2111-22-1-1-12-2-21111112-1-1-12-211122-1-1-1-1-1-1-2111-22-1-1-1-2-21111112i−2i2i−2i2i2i−i−i−i−i−i−i−2i−2iiiiiii2i−i−i−i−2iiii0000000000000000
χ4622-2-2-22-1-1-1222-1-1-12-2-2111111-2-222-1-1-1-22-1-1-1-2111-22-1-1-12-2-21111112-1-1-12-211122-1-1-1-1-1-1-2111-22-1-1-1-2-2111111−2i2i−2i2i−2i−2iiiiiii2i2i−i−i−i−i−i−i−2iiii2i−i−i−i0000000000000000
χ4722-2-2-22-1-1-1222-1-1-12-2-2111111-2-2-22-1-1-122-1-1-1-2111-22-1-1-12-2-2111111-2111-2-2111-2-21111112-1-1-122-1-1-122-1-1-1-1-1-12i−2i−2i2i2i2i−i−i−i−i−i−i−2i−2iiiiiii−2iiii2i−i−i−i0000000000000000
χ4822-2-2-22-1-1-1222-1-1-12-2-2111111-2-2-22-1-1-122-1-1-1-2111-22-1-1-12-2-2111111-2111-2-2111-2-21111112-1-1-122-1-1-122-1-1-1-1-1-1−2i2i2i−2i−2i−2iiiiiii2i2i−i−i−i−i−i−i2i−i−i−i−2iiii0000000000000000
χ4922-2-2-2-12-1-122-12-1-1211-2-21111-2-22-12-1-1-2-12-1-11-211-2-12-1-1211-2-21111-12-1-121-211-1-122-1-1-1-11-211-2-12-1-111-2-211112i−2i2i−2i−i−i2i2i−i−i−i−iii−2i−2iiiii−i2i−i−ii−2iii0000000000000000
χ5022-2-2-2-12-1-122-12-1-1211-2-21111-2-22-12-1-1-2-12-1-11-211-2-12-1-1211-2-21111-12-1-121-211-1-122-1-1-1-11-211-2-12-1-111-2-21111−2i2i−2i2iii−2i−2iiiii−i−i2i2i−i−i−i−ii−2iii−i2i−i−i0000000000000000
χ5122-2-2-2-12-1-122-12-1-1211-2-21111-2-2-2-12-1-12-12-1-11-211-2-12-1-1211-2-211111-211-21-21111-2-21111-12-1-12-12-1-1-1-122-1-1-1-12i−2i−2i2i−i−i2i2i−i−i−i−iii−2i−2iiiiii−2iii−i2i−i−i0000000000000000
χ5222-2-2-2-12-1-122-12-1-1211-2-21111-2-2-2-12-1-12-12-1-11-211-2-12-1-1211-2-211111-211-21-21111-2-21111-12-1-12-12-1-1-1-122-1-1-1-1−2i2i2i−2iii−2i−2iiiii−i−i2i2i−i−i−i−i−i2i−i−ii−2iii0000000000000000
χ5322-2-2-2-1-12-122-1-12-121111-2-211-2-22-1-12-1-2-1-12-111-21-2-1-12-121111-2-211-1-12-1211-21-1-1-1-122-1-111-21-2-1-12-11111-2-2112i−2i2i−2i−i−i−i−i2i2i−i−iiiii−2i−2iii−i−i2i−iii−2ii0000000000000000
χ5422-2-2-2-1-12-122-1-12-121111-2-211-2-22-1-12-1-2-1-12-111-21-2-1-12-121111-2-211-1-12-1211-21-1-1-1-122-1-111-21-2-1-12-11111-2-211−2i2i−2i2iiiii−2i−2iii−i−i−i−i2i2i−i−iii−2ii−i−i2i−i0000000000000000
χ5522-2-2-2-1-12-122-1-12-121111-2-211-2-2-2-1-12-12-1-12-111-21-2-1-12-121111-2-21111-21-211-211111-2-211-1-12-12-1-12-1-1-1-1-122-1-12i−2i−2i2i−i−i−i−i2i2i−i−iiiii−2i−2iiiii−2ii−i−i2i−i0000000000000000
χ5622-2-2-2-1-12-122-1-12-121111-2-211-2-2-2-1-12-12-1-12-111-21-2-1-12-121111-2-21111-21-211-211111-2-211-1-12-12-1-12-1-1-1-1-122-1-1−2i2i2i−2iiiii−2i−2iii−i−i−i−i2i2i−i−i−i−i2i−iii−2ii0000000000000000
χ5722-2-2-2-1-1-1222-1-1-122111111-2-2-2-22-1-1-12-2-1-1-12111-2-2-1-1-122111111-2-2-1-1-122111-2-1-1-1-1-1-122111-2-2-1-1-12111111-2-22i−2i2i−2i−i−i−i−i−i−i2i2iiiiiii−2i−2i−i−i−i2iiii−2i0000000000000000
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χ1234-4−4i4i0-2-2-2440222-4-42i−2i2i−2i2i−2i−4i4i−4i4i0-2-2-240222-400000000002i−2i2i−2i2i−2i−4i4i00000000000000000000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000000000000000000000
χ1244-4−4i4i0-2-2-2440222-4-42i−2i2i−2i2i−2i−4i4i−4i4i0-2-2-240222-400000000002i−2i2i−2i2i−2i−4i4i00000000000000000000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000000000000000000000
χ1258-88i−8i08-4-4-4-40-844448i−8i−4i4i−4i4i−4i4i−4i4i0-422204-2-2-20000000000−4i4i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1268-88i−8i0-48-4-4-404-8444−4i4i8i−8i−4i4i−4i4i−4i4i02-4220-24-2-200000000002i−2i−4i4i2i−2i2i−2i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1278-88i−8i0-4-48-4-4044-844−4i4i−4i4i8i−8i−4i4i−4i4i022-420-2-24-200000000002i−2i2i−2i−4i4i2i−2i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1288-88i−8i0-4-4-48-40444-84−4i4i−4i4i−4i4i8i−8i−4i4i0222-40-2-2-2400000000002i−2i2i−2i2i−2i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1298-8−8i8i08-4-4-4-40-84444−8i8i4i−4i4i−4i4i−4i4i−4i0-422204-2-2-200000000004i−4i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1308-8−8i8i0-48-4-4-404-84444i−4i−8i8i4i−4i4i−4i4i−4i02-4220-24-2-20000000000−2i2i4i−4i−2i2i−2i2i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1318-8−8i8i0-4-48-4-4044-8444i−4i4i−4i−8i8i4i−4i4i−4i022-420-2-24-20000000000−2i2i−2i2i4i−4i−2i2i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1328-8−8i8i0-4-4-48-40444-844i−4i4i−4i4i−4i−8i8i4i−4i0222-40-2-2-240000000000−2i2i−2i2i−2i2i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000000

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