Finite Group Databasebeta

← Group #13161366

Character table — Group #13161366

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138
size1111222222222222222222222244444444444444444444444444444444888888888888888888888888888888881212121212121212121212121212121212121212181818181818181824242424242424243636363636363636108108108108
order12442333334666661212121212121212121223333466666666666121212121212121212121212121212666666666666666612121212121212121212121212121212248824242424242424242424242424242424888824242424666612121212882424242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-11111-11-1-1111111111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-111
χ611111111111111111111111111-11111-11-1-1111111111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1
χ711111111111111111111111111-11111-11-1-1111111111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ811111111111111111111111111-11111-11-1-1111111111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111
χ911-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11-11-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i1111-1-1-1-1i−ii−iii−i−ii−ii−i
χ1011-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11-11-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii1111-1-1-1-1−ii−ii−i−iii−ii−ii
χ1111-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-111111111ii−i−iii−i−i-1-1-1-11111i−ii−iii−i−i−ii−ii
χ1211-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-111111111−i−iii−i−iii-1-1-1-11111−ii−ii−i−iiii−ii−i
χ1311-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-11-1-1-1-1-1-1-1-111111111ii−i−iii−i−i1111-1-1-1-1−iii−i−i−iii−iii−i
χ1411-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-11-1-1-1-1-1-1-1-111111111−i−iii−i−iii1111-1-1-1-1i−i−iiii−i−ii−i−ii
χ1511-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-111-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-1-1-11111−iii−i−i−iiii−i−ii
χ1611-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-111-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii-1-1-1-11111i−i−iiii−i−i−iii−i
χ172222222-1-1-1222-1-1-122-1-1-1-1-1-12222-1-1-122222-1-1-12-1-1-122222-1-1-1-1-1-12-1-1-12-1-1-12-1-1-122-1-1-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-122-1-1-1-1-1-1000000002-1-1-12-1-1-1000000000000
χ182222222-1-1-1222-1-1-122-1-1-1-1-1-12222-1-1-122222-1-1-12-1-1-122222-1-1-1-1-1-12-1-1-12-1-1-12-1-1-122-1-1-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2111111-2-211111100000000-2111-2111000000000000
χ192222222-1-1-1222-1-1-122-1-1-1-1-1-122-22-1-1-1-22-2-22-1-1-12-1-1-12-2-222-1-1-1-1-1-12-1-1-1-21112-1-1-1-2-2111111-21112-1-1-1-2-211111122-2-2-2-2111111-2-2111111000000002-1-1-12-1-1-1000000000000
χ202222222-1-1-1222-1-1-122-1-1-1-1-1-122-22-1-1-1-22-2-22-1-1-12-1-1-12-2-222-1-1-1-1-1-12-1-1-1-21112-1-1-1-2-2111111-21112-1-1-1-2-2111111-2-22222-1-1-1-1-1-122-1-1-1-1-1-100000000-2111-2111000000000000
χ21222222-12-1-122-12-1-1-1-122-1-1-1-1222-12-1-12222-12-1-1-12-1-1222-1-122-1-1-1-1-12-1-1-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-12222-1-122-1-1-1-1-1-122-1-1-1-100000000-12-1-1-12-1-1000000000000
χ22222222-12-1-122-12-1-1-1-122-1-1-1-1222-12-1-12222-12-1-1-12-1-1222-1-122-1-1-1-1-12-1-1-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-1-2-2-2-211-2-2111111-2-21111000000001-2111-211000000000000
χ23222222-12-1-122-12-1-1-1-122-1-1-1-122-2-12-1-1-22-2-2-12-1-1-12-1-12-2-2-1-122-1-1-1-1-12-1-11-211-12-1-111-2-211111-211-12-1-111-2-2111122-2-211-2-2111111-2-2111100000000-12-1-1-12-1-1000000000000
χ24222222-12-1-122-12-1-1-1-122-1-1-1-122-2-12-1-1-22-2-2-12-1-1-12-1-12-2-2-1-122-1-1-1-1-12-1-11-211-12-1-111-2-211111-211-12-1-111-2-21111-2-222-1-122-1-1-1-1-1-122-1-1-1-1000000001-2111-211000000000000
χ25222222-1-12-122-1-12-1-1-1-1-122-1-1222-1-12-12222-1-12-1-1-12-1222-1-1-1-122-1-1-1-12-1-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1-1-12-1-1-1-1-122-1-12222-1-1-1-122-1-1-1-1-1-122-1-100000000-1-12-1-1-12-1000000000000
χ26222222-1-12-122-1-12-1-1-1-1-122-1-1222-1-12-12222-1-12-1-1-12-1222-1-1-1-122-1-1-1-12-1-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1-1-12-1-1-1-1-122-1-1-2-2-2-21111-2-2111111-2-2110000000011-2111-21000000000000
χ27222222-1-12-122-1-12-1-1-1-1-122-1-122-2-1-12-1-22-2-2-1-12-1-1-12-12-2-2-1-1-1-122-1-1-1-12-111-21-1-12-11111-2-21111-21-1-12-11111-2-21122-2-21111-2-2111111-2-21100000000-1-12-1-1-12-1000000000000
χ28222222-1-12-122-1-12-1-1-1-1-122-1-122-2-1-12-1-22-2-2-1-12-1-1-12-12-2-2-1-1-1-122-1-1-1-12-111-21-1-12-11111-2-21111-21-1-12-11111-2-211-2-222-1-1-1-122-1-1-1-1-1-122-1-10000000011-2111-21000000000000
χ29222222-1-1-1222-1-1-12-1-1-1-1-1-122222-1-1-122222-1-1-12-1-1-12222-1-1-1-1-1-122-1-1-12-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12-1-1-1-1-1-1222222-1-1-1-1-1-122-1-1-1-1-1-12200000000-1-1-12-1-1-12000000000000
χ30222222-1-1-1222-1-1-12-1-1-1-1-1-122222-1-1-122222-1-1-12-1-1-12222-1-1-1-1-1-122-1-1-12-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12-1-1-1-1-1-122-2-2-2-2111111-2-2111111-2-200000000111-2111-2000000000000
χ31222222-1-1-1222-1-1-12-1-1-1-1-1-12222-2-1-1-12-22-2-2-1-1-12-1-1-122-2-2-1-1-1-1-1-122-1-1-12111-2-1-1-12111111-2-2111-2-1-1-12111111-2-222-2-2111111-2-2111111-2-200000000-1-1-12-1-1-12000000000000
χ32222222-1-1-1222-1-1-12-1-1-1-1-1-12222-2-1-1-12-22-2-2-1-1-12-1-1-122-2-2-1-1-1-1-1-122-1-1-12111-2-1-1-12111111-2-2111-2-1-1-12111111-2-2-2-222-1-1-1-1-1-122-1-1-1-1-1-12200000000111-2111-2000000000000
χ3322222-122222-1222222222222-1-12-1-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000002222-1-1-1-10000000022-1-1-1-1-1-10000
χ3422222-122222-1222222222222-1-12-1-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000-2-2-2-2111100000000-2-21111110000
χ3522222-122222-1222222222222-1-1-2-1-1-1-1-2-1112222-1-1-1-1-111-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-2-2-2-2-1-1-1-111111111000000000000000000002222-1-1-1-100000000-2-2-1-111110000
χ3622222-122222-1222222222222-1-1-2-1-1-1-1-2-1112222-1-1-1-1-111-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-2-2-2-2-1-1-1-11111111100000000000000000000-2-2-2-21111000000002211-1-1-1-10000
χ372222-222222-2222222222222222022220-200-2-2-2-22222-20022222222-2-2-2-20000-2-2-2-2000000000000-2-2-2-200000000000000000000000000002-22-222220000000000-2-200000000
χ382222-222222-2222222222222222022220-200-2-2-2-22222-20022222222-2-2-2-20000-2-2-2-2000000000000-2-2-2-20000000000000000000000000000-22-22-2-2-2-200000000002200000000
χ392222-2-12222-2-1222222222222-1-10-1-1-1-101−i3i3-2-2-2-2-1-1-1-11−i3i3-1-1-1-1-1-1-1-1-2-2-2-200001111−i3i3−i3i3−i3i3−i3i300001111−i3i3−i3i3−i3i3−i3i3000000000000000000002-22-2-1-1-1-1000000000011−i3i3−i3i30000
χ402222-2-12222-2-1222222222222-1-10-1-1-1-101−i3i3-2-2-2-2-1-1-1-11−i3i3-1-1-1-1-1-1-1-1-2-2-2-200001111−i3i3−i3i3−i3i3−i3i300001111−i3i3−i3i3−i3i3−i3i300000000000000000000-22-2211110000000000-1-1i3−i3i3−i30000
χ412222-2-12222-2-1222222222222-1-10-1-1-1-101i3−i3-2-2-2-2-1-1-1-11i3−i3-1-1-1-1-1-1-1-1-2-2-2-200001111i3−i3i3−i3i3−i3i3−i300001111i3−i3i3−i3i3−i3i3−i3000000000000000000002-22-2-1-1-1-1000000000011i3−i3i3−i30000
χ422222-2-12222-2-1222222222222-1-10-1-1-1-101i3−i3-2-2-2-2-1-1-1-11i3−i3-1-1-1-1-1-1-1-1-2-2-2-200001111i3−i3i3−i3i3−i3i3−i300001111i3−i3i3−i3i3−i3i3−i300000000000000000000-22-2211110000000000-1-1−i3i3−i3i30000
χ4322-2-2222222-222222-2-2-2-2-2-2-2-2-2-202222020022222222-200-2-2-2-2-2-2-2-2-2-2-2-200002222000000000000-2-2-2-200000000000000000000000000002i−2i−2i2i2i2i−2i−2i0000000000−2i2i00000000
χ4422-2-2222222-222222-2-2-2-2-2-2-2-2-2-202222020022222222-200-2-2-2-2-2-2-2-2-2-2-2-200002222000000000000-2-2-2-20000000000000000000000000000−2i2i2i−2i−2i−2i2i2i00000000002i−2i00000000
χ4522-2-22-12222-2-12222-2-2-2-2-2-2-2-2110-1-1-1-10-1−i3i32222-1-1-1-11i3−i311111111-2-2-2-20000-1-1-1-1−i3i3−i3i3−i3i3−i3i300001111i3−i3i3−i3i3−i3i3−i3000000000000000000002i−2i−2i2i−i−iii0000000000i−i3−3−330000
χ4622-2-22-12222-2-12222-2-2-2-2-2-2-2-2110-1-1-1-10-1−i3i32222-1-1-1-11i3−i311111111-2-2-2-20000-1-1-1-1−i3i3−i3i3−i3i3−i3i300001111i3−i3i3−i3i3−i3i3−i300000000000000000000−2i2i2i−2iii−i−i0000000000−ii−333−30000
χ4722-2-22-12222-2-12222-2-2-2-2-2-2-2-2110-1-1-1-10-1i3−i32222-1-1-1-11−i3i311111111-2-2-2-20000-1-1-1-1i3−i3i3−i3i3−i3i3−i300001111−i3i3−i3i3−i3i3−i3i3000000000000000000002i−2i−2i2i−i−iii0000000000i−i−333−30000
χ4822-2-22-12222-2-12222-2-2-2-2-2-2-2-2110-1-1-1-10-1i3−i32222-1-1-1-11−i3i311111111-2-2-2-20000-1-1-1-1i3−i3i3−i3i3−i3i3−i300001111−i3i3−i3i3−i3i3−i3i300000000000000000000−2i2i2i−2iii−i−i0000000000−ii3−3−330000
χ4922-2-2-222-1-1-1222-1-1-1-2-2111111-2-222-1-1-1-2-222-21112-1-1-12-2-2-2-21111112-1-1-12-1-1-1-211122-1-1-1-1-1-1-21112-1-1-1-2-21111112-22-222-1-1-1-1-1-1-2-2111111000000002-1-1-1-2111000000000000
χ5022-2-2-222-1-1-1222-1-1-1-2-2111111-2-222-1-1-1-2-222-21112-1-1-12-2-2-2-21111112-1-1-12-1-1-1-211122-1-1-1-1-1-1-21112-1-1-1-2-2111111-22-22-2-211111122-1-1-1-1-1-100000000-21112-1-1-1000000000000
χ5122-2-2-222-1-1-1222-1-1-1-2-2111111-2-2-22-1-1-12-2-2-2-21112-1-1-1222-2-21111112-1-1-1-2111-2111-2-21111112-1-1-12-1-1-122-1-1-1-1-1-12-2-22-2-211111122-1-1-1-1-1-1000000002-1-1-1-2111000000000000
χ5222-2-2-222-1-1-1222-1-1-1-2-2111111-2-2-22-1-1-12-2-2-2-21112-1-1-1222-2-21111112-1-1-1-2111-2111-2-21111112-1-1-12-1-1-122-1-1-1-1-1-1-222-222-1-1-1-1-1-1-2-211111100000000-21112-1-1-1000000000000
χ5322-2-2-22-12-1-122-12-1-111-2-21111-2-22-12-1-1-2-2221-211-12-1-12-2-211-2-21111-12-1-1-12-1-11-211-1-122-1-1-1-11-211-12-1-111-2-211112-22-2-1-122-1-1-1-111-2-2111100000000-12-1-11-211000000000000
χ5422-2-2-22-12-1-122-12-1-111-2-21111-2-22-12-1-1-2-2221-211-12-1-12-2-211-2-21111-12-1-1-12-1-11-211-1-122-1-1-1-11-211-12-1-111-2-21111-22-2211-2-21111-1-122-1-1-1-1000000001-211-12-1-1000000000000
χ5522-2-2-22-12-1-122-12-1-111-2-21111-2-2-2-12-1-12-2-2-21-211-12-1-122211-2-21111-12-1-11-2111-21111-2-21111-12-1-1-12-1-1-1-122-1-1-1-12-2-2211-2-21111-1-122-1-1-1-100000000-12-1-11-211000000000000
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χ1284-4−4i4i04-2-2-240-4222-42i−2i2i−2i2i−2i−4i4i−4i4i0-2-2-2400000000222-40002i−2i2i−2i2i−2i−4i4i0000000000000000000000000000000000000000−i6i6−i6i6i6−i6006−66−6−66000000000000000000000000000000
χ1294-4−4i4i0-2444402-4-4-4-4−4i4i−4i4i−4i4i−4i4i2i−2i0-2-2-2-20000000022220002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000000000002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ2300000000000000000000
χ1304-4−4i4i0-2444402-4-4-4-4−4i4i−4i4i−4i4i−4i4i2i−2i0-2-2-2-20000000022220002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000000000000000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ2300000000000000000000
χ1318-88i−8i0-48-4-4-404-84448i−8i−4i4i−4i4i−4i4i−4i4i0-4222000000004-2-2-2000−4i4i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1328-88i−8i0-4-48-4-4044-844−4i4i8i−8i−4i4i−4i4i−4i4i02-42200000000-24-2-20002i−2i−4i4i2i−2i2i−2i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1338-88i−8i0-4-4-48-40444-84−4i4i−4i4i8i−8i−4i4i−4i4i022-4200000000-2-24-20002i−2i2i−2i−4i4i2i−2i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1348-88i−8i0-4-4-4-4804444-8−4i4i−4i4i−4i4i8i−8i−4i4i0222-400000000-2-2-240002i−2i2i−2i2i−2i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1358-8−8i8i0-48-4-4-404-8444−8i8i4i−4i4i−4i4i−4i4i−4i0-4222000000004-2-2-20004i−4i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1368-8−8i8i0-4-48-4-4044-8444i−4i−8i8i4i−4i4i−4i4i−4i02-42200000000-24-2-2000−2i2i4i−4i−2i2i−2i2i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1378-8−8i8i0-4-4-48-40444-844i−4i4i−4i−8i8i4i−4i4i−4i022-4200000000-2-24-2000−2i2i−2i2i4i−4i−2i2i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1388-8−8i8i0-4-4-4-4804444-84i−4i4i−4i4i−4i−8i8i4i−4i0222-400000000-2-2-24000−2i2i−2i2i−2i2i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.