Finite Group Databasebeta

← Group #13161375

Character table — Group #13161375

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138
size111122222222222222222222224444444444444444444444444444666688888888888888888888888888888888881212121212121212121212121212121212121818181824242424242424242727272736363636363654547272108108
order124423333346666612121212121212121212233334666666666121212121212121212121212128888666666666666666661212121212121212121212121212121212242424242424242424242424242424242444446666121212128888881212121288242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ511111111111111111111111111-11111-111111111111111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1
χ611111111111111111111111111-11111-111111111111111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ711111111111111111111111111-11111-11111111111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111
χ811111111111111111111111111-11111-11111111111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1
χ911-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11111-11-1-1-1-1-1-1-1-1111111-1-111111-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1ii−i−i1111-1-1-1-1ii−i−ii−iii−i−ii−ii−ii−i
χ1011-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11111-11-1-1-1-1-1-1-1-1111111-1-111111-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1−i−iii1111-1-1-1-1−i−iii−ii−i−iii−ii−ii−ii
χ1111-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11111-11-1-1-1-1-1-1-1-11111-1-11111111-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111ii−i−i-1-1-1-11111−i−iiii−iii−i−i−iii−i−ii
χ1211-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11111-11-1-1-1-1-1-1-1-11111-1-11111111-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111−i−iii-1-1-1-11111ii−i−i−ii−i−iiii−i−iii−i
χ1311-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1111111111-1-1-1-1-1-1-1-1ii−i−i-1-1-1-11111ii−i−i−iiii−i−ii−i−ii−ii
χ1411-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1111111111-1-1-1-1-1-1-1-1−i−iii-1-1-1-11111−i−iiii−i−i−iii−iii−ii−i
χ1511-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-11-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-111111111ii−i−i1111-1-1-1-1−i−iii−iiii−i−i−ii−iii−i
χ1611-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-11-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-111111111−i−iii1111-1-1-1-1ii−i−ii−i−i−iiii−ii−i−ii
χ172222222-1-1-1222-1-1-122-1-1-1-1-1-12222-1-1-122-1-1-12-1-1-12222-1-1-1-1-1-12-1-1-1222222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-12-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-100002-1-1-12-1-1-10000000000000000
χ182222222-1-1-1222-1-1-122-1-1-1-1-1-12222-1-1-122-1-1-12-1-1-12222-1-1-1-1-1-12-1-1-1-2-2-2-222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-12-1-1-122-1-1-1-1-1-1-2-2-2-2111111-2-21111110000-2111-21110000000000000000
χ192222222-1-1-1222-1-1-122-1-1-1-1-1-122-22-1-1-1-22-1-1-12-1-1-12222-1-1-1-1-1-12-1-1-12222-2-21112-1-1-1-2-2111111-2-21112-1-1-1-2-2111111-2-222-1-1-1-1-1-122-1-1-1-1-1-10000-2111-21110000000000000000
χ202222222-1-1-1222-1-1-122-1-1-1-1-1-122-22-1-1-1-22-1-1-12-1-1-12222-1-1-1-1-1-12-1-1-1-2-2-2-2-2-21112-1-1-1-2-2111111-2-21112-1-1-1-2-211111122-2-2111111-2-211111100002-1-1-12-1-1-10000000000000000
χ21222222-12-1-122-12-1-1-1-122-1-1-1-1222-12-1-12-12-1-1-12-1-122-1-122-1-1-1-1-12-1-122222-12-1-1-12-1-1-1-122-1-1-1-12-12-1-1-12-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-10000-12-1-1-12-1-10000000000000000
χ22222222-12-1-122-12-1-1-1-122-1-1-1-1222-12-1-12-12-1-1-12-1-122-1-122-1-1-1-1-12-1-1-2-2-2-22-12-1-1-12-1-1-1-122-1-1-1-12-12-1-1-12-1-1-1-122-1-1-1-1-2-211-2-2111111-2-2111100001-2111-2110000000000000000
χ23222222-12-1-122-12-1-1-1-122-1-1-1-122-2-12-1-1-2-12-1-1-12-1-122-1-122-1-1-1-1-12-1-12222-21-211-12-1-111-2-21111-21-211-12-1-111-2-21111-2-2-1-122-1-1-1-1-1-122-1-1-1-100001-2111-2110000000000000000
χ24222222-12-1-122-12-1-1-1-122-1-1-1-122-2-12-1-1-2-12-1-1-12-1-122-1-122-1-1-1-1-12-1-1-2-2-2-2-21-211-12-1-111-2-21111-21-211-12-1-111-2-211112211-2-2111111-2-211110000-12-1-1-12-1-10000000000000000
χ25222222-1-12-122-1-12-1-1-1-1-122-1-1222-1-12-12-1-12-1-1-12-122-1-1-1-122-1-1-1-12-122222-1-12-1-1-12-1-1-1-1-122-1-12-1-12-1-1-12-1-1-1-1-122-1-122-1-1-1-122-1-1-1-1-1-122-1-10000-1-12-1-1-12-10000000000000000
χ26222222-1-12-122-1-12-1-1-1-1-122-1-1222-1-12-12-1-12-1-1-12-122-1-1-1-122-1-1-1-12-1-2-2-2-22-1-12-1-1-12-1-1-1-1-122-1-12-1-12-1-1-12-1-1-1-1-122-1-1-2-21111-2-2111111-2-211000011-2111-210000000000000000
χ27222222-1-12-122-1-12-1-1-1-1-122-1-122-2-1-12-1-2-1-12-1-1-12-122-1-1-1-122-1-1-1-12-12222-211-21-1-12-11111-2-211-211-21-1-12-11111-2-211-2-2-1-1-1-122-1-1-1-1-1-122-1-1000011-2111-210000000000000000
χ28222222-1-12-122-1-12-1-1-1-1-122-1-122-2-1-12-1-2-1-12-1-1-12-122-1-1-1-122-1-1-1-12-1-2-2-2-2-211-21-1-12-11111-2-211-211-21-1-12-11111-2-211221111-2-2111111-2-2110000-1-12-1-1-12-10000000000000000
χ29222222-1-1-1222-1-1-12-1-1-1-1-1-122222-1-1-122-1-1-12-1-1-1222-1-1-1-1-1-122-1-1-1222222-1-1-12-1-1-12-1-1-1-1-1-1222-1-1-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1220000-1-1-12-1-1-120000000000000000
χ30222222-1-1-1222-1-1-12-1-1-1-1-1-122222-1-1-122-1-1-12-1-1-1222-1-1-1-1-1-122-1-1-12-2-2-2-22-1-1-12-1-1-12-1-1-1-1-1-1222-1-1-12-1-1-12-1-1-1-1-1-122-2-2111111-2-2111111-2-20000111-2111-20000000000000000
χ31222222-1-1-1222-1-1-12-1-1-1-1-1-12222-2-1-1-12-2-1-1-12-1-1-1222-1-1-1-1-1-122-1-1-122222-2111-2-1-1-12111111-2-2-2111-2-1-1-12111111-2-2-2-2-1-1-1-1-1-122-1-1-1-1-1-1220000111-2111-20000000000000000
χ32222222-1-1-1222-1-1-12-1-1-1-1-1-12222-2-1-1-12-2-1-1-12-1-1-1222-1-1-1-1-1-122-1-1-12-2-2-2-2-2111-2-1-1-12111111-2-2-2111-2-1-1-12111111-2-222111111-2-2111111-2-20000-1-1-12-1-1-120000000000000000
χ3322222-122222-1222222222222-1-12-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000-12222-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000222200000000000022-1-1-1-100-1-100
χ3422222-122222-1222222222222-1-12-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000-12222-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2-2-2000000000000-2-21111001100
χ3522222-122222-1222222222222-1-1-2-1-1-1-1-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200001-2-2-2-2-1-1-1-1111111111-2-2-2-2-1-1-1-1111111110000000000000000002222000000000000-2-2-1-1-1-1001100
χ3622222-122222-1222222222222-1-1-2-1-1-1-1-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200001-2-2-2-2-1-1-1-1111111111-2-2-2-2-1-1-1-111111111000000000000000000-2-2-2-200000000000022111100-1-100
χ372222-222222-2222222222222222022220-2-2-2-22222-2-222222222-2-2-2-2000000000-2-2-2-20000000000000-2-2-2-2000000000000000000000000000000000000002222000000-2-20000
χ382222-222222-2222222222222222022220-2-2-2-22222-2-222222222-2-2-2-2000000000-2-2-2-20000000000000-2-2-2-200000000000000000000000000000000000000-2-2-2-2000000220000
χ3922-2-2222222-222222-2-2-2-2-2-2-2-2-2-2022220222222222-2-2-2-2-2-2-2-2-2-2-2-2-200000000022220000000000000-2-2-2-2000000000000000000000000000000000000002i2i−2i−2i000000−2i2i0000
χ4022-2-2222222-222222-2-2-2-2-2-2-2-2-2-2022220222222222-2-2-2-2-2-2-2-2-2-2-2-2-200000000022220000000000000-2-2-2-200000000000000000000000000000000000000−2i−2i2i2i0000002i−2i0000
χ4122-2-2-222-1-1-1222-1-1-1-2-2111111-2-222-1-1-1-2-21112-1-1-1-22-2-21111112-1-1-122-2-222-1-1-1-211122-1-1-1-1-1-1-2-21112-1-1-1-2-21111112-222-1-1-1-1-1-1-2-211111100002-1-1-1-21110000000000000000
χ4222-2-2-222-1-1-1222-1-1-1-2-2111111-2-222-1-1-1-2-21112-1-1-1-22-2-21111112-1-1-1-2-22222-1-1-1-211122-1-1-1-1-1-1-2-21112-1-1-1-2-2111111-22-2-211111122-1-1-1-1-1-10000-21112-1-1-10000000000000000
χ4322-2-2-222-1-1-1222-1-1-1-2-2111111-2-2-22-1-1-12-21112-1-1-1-22-2-21111112-1-1-122-2-2-2-2111-2111-2-211111122-1-1-12-1-1-122-1-1-1-1-1-1-2222-1-1-1-1-1-1-2-21111110000-21112-1-1-10000000000000000
χ4422-2-2-222-1-1-1222-1-1-1-2-2111111-2-2-22-1-1-12-21112-1-1-1-22-2-21111112-1-1-1-2-222-2-2111-2111-2-211111122-1-1-12-1-1-122-1-1-1-1-1-12-2-2-211111122-1-1-1-1-1-100002-1-1-1-21110000000000000000
χ4522-2-2-22-12-1-122-12-1-111-2-21111-2-22-12-1-1-21-211-12-1-1-2211-2-21111-12-1-122-2-22-12-1-11-211-1-122-1-1-1-1-21-211-12-1-111-2-211112-2-1-122-1-1-1-111-2-211110000-12-1-11-2110000000000000000
χ4622-2-2-22-12-1-122-12-1-111-2-21111-2-22-12-1-1-21-211-12-1-1-2211-2-21111-12-1-1-2-2222-12-1-11-211-1-122-1-1-1-1-21-211-12-1-111-2-21111-2211-2-21111-1-122-1-1-1-100001-211-12-1-10000000000000000
χ4722-2-2-22-12-1-122-12-1-111-2-21111-2-2-2-12-1-121-211-12-1-1-2211-2-21111-12-1-122-2-2-21-2111-21111-2-211112-12-1-1-12-1-1-1-122-1-1-1-1-22-1-122-1-1-1-111-2-2111100001-211-12-1-10000000000000000
χ4822-2-2-22-12-1-122-12-1-111-2-21111-2-2-2-12-1-121-211-12-1-1-2211-2-21111-12-1-1-2-222-21-2111-21111-2-211112-12-1-1-12-1-1-1-122-1-1-1-12-211-2-21111-1-122-1-1-1-10000-12-1-11-2110000000000000000
χ4922-2-2-22-1-12-122-1-12-11111-2-211-2-22-1-12-1-211-21-1-12-1-221111-2-211-1-12-122-2-22-1-12-111-21-1-1-1-122-1-1-211-21-1-12-11111-2-2112-2-1-1-1-122-1-11111-2-2110000-1-12-111-210000000000000000
χ5022-2-2-22-1-12-122-1-12-11111-2-211-2-22-1-12-1-211-21-1-12-1-221111-2-211-1-12-1-2-2222-1-12-111-21-1-1-1-122-1-1-211-21-1-12-11111-2-211-221111-2-211-1-1-1-122-1-1000011-21-1-12-10000000000000000
χ5122-2-2-22-1-12-122-1-12-11111-2-211-2-2-2-1-12-1211-21-1-12-1-221111-2-211-1-12-122-2-2-211-2111-211111-2-2112-1-12-1-1-12-1-1-1-1-122-1-1-22-1-1-1-122-1-11111-2-211000011-21-1-12-10000000000000000
χ5222-2-2-22-1-12-122-1-12-11111-2-211-2-2-2-1-12-1211-21-1-12-1-221111-2-211-1-12-1-2-222-211-2111-211111-2-2112-1-12-1-1-12-1-1-1-1-122-1-12-21111-2-211-1-1-1-122-1-10000-1-12-111-210000000000000000
χ5322-2-2-22-1-1-1222-1-1-12111111-2-2-2-22-1-1-12-2111-2-1-1-12-22111111-2-2-1-1-1222-2-22-1-1-12111-2-1-1-1-1-1-122-2111-2-1-1-12111111-2-22-2-1-1-1-1-1-122111111-2-20000-1-1-12111-20000000000000000
χ5422-2-2-22-1-1-1222-1-1-12111111-2-2-2-22-1-1-12-2111-2-1-1-12-22111111-2-2-1-1-12-2-2222-1-1-12111-2-1-1-1-1-1-122-2111-2-1-1-12111111-2-2-22111111-2-2-1-1-1-1-1-1220000111-2-1-1-120000000000000000
χ5522-2-2-22-1-1-1222-1-1-12111111-2-2-2-2-2-1-1-122111-2-1-1-12-22111111-2-2-1-1-1222-2-2-2111-2111-2111111-2-22-1-1-12-1-1-12-1-1-1-1-1-122-22-1-1-1-1-1-122111111-2-20000111-2-1-1-120000000000000000
χ5622-2-2-22-1-1-1222-1-1-12111111-2-2-2-2-2-1-1-122111-2-1-1-12-22111111-2-2-1-1-12-2-222-2111-2111-2111111-2-22-1-1-12-1-1-12-1-1-1-1-1-1222-2111111-2-2-1-1-1-1-1-1220000-1-1-12111-20000000000000000
χ5722-2-2-2-122222-12222-2-2-2-2-2-2-2-2112-1-1-1-1-2-2-2-2-2-1-1-1-11-11111111122220000-122221111-1-1-1-1-1-1-1-11-2-2-2-2-1-1-1-1111111110000000000000000002i2i−2i−2i0000000000002i−2i−i−iii00−ii00
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χ1338-88i−8i0-4-4-48-40444-84−4i4i−4i4i8i−8i−4i4i−4i4i022-4200000-2-24-2002i−2i2i−2i−4i4i2i−2i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1348-88i−8i0-4-4-4-4804444-8−4i4i−4i4i−4i4i8i−8i−4i4i0222-400000-2-2-24002i−2i2i−2i2i−2i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1358-8−8i8i0-48-4-4-404-8444−8i8i4i−4i4i−4i4i−4i4i−4i0-4222000004-2-2-2004i−4i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1368-8−8i8i0-4-48-4-4044-8444i−4i−8i8i4i−4i4i−4i4i−4i02-42200000-24-2-200−2i2i4i−4i−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1378-8−8i8i0-4-4-48-40444-844i−4i4i−4i−8i8i4i−4i4i−4i022-4200000-2-24-200−2i2i−2i2i4i−4i−2i2i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1388-8−8i8i0-4-4-4-4804444-84i−4i4i−4i4i−4i−8i8i4i−4i0222-400000-2-2-2400−2i2i−2i2i−2i2i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.