Finite Group Databasebeta

← Group #13144758

Character table — Group #13144758

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122
size111111111111222222444444444444444444666666666666666612121212121212121212121212121212121212121212121218181818181818181818181824242424242424242424242424242424363636363636363636363636363636363636
order122233666666441212121244448812121212121212122424242433336666666666661212121212121212242424242424242424242424242424244444121212121212121212121212121212121212121212121212444488121212121212121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ5111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-11111
χ7111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1
χ911-1-11111-1-1-1-11-111-1-11-11-11-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1i−ii−ii−iii−i−iii−i−iii−i−i
χ1011-1-11111-1-1-1-11-111-1-11-11-11-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−ii−ii−ii−i−iii−i−iii−i−iii
χ1111-1-11111-1-1-1-11-111-1-11-1-11-1111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111ii−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111i−i−ii−iiii−i−i−i−iii−i−iii
χ1211-1-11111-1-1-1-11-111-1-11-1-11-1111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−iii−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−iii−ii−i−i−iiiii−i−iii−i−i
χ1311-1-11111-1-1-1-11-111-1-1-111-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111ii−i−iiiii−i−i−i−i-1-1-1-111111111-1-1-1-1−iii−i−ii−i−iiiii−i−i−i−iii
χ1411-1-11111-1-1-1-11-111-1-1-111-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−iii−i−i−i−iiiii-1-1-1-111111111-1-1-1-1i−i−iii−iii−i−i−i−iiiii−i−i
χ1511-1-11111-1-1-1-11-111-1-1-11-111-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−ii−iii−i−i−iii−i−iiiii−i−i
χ1611-1-11111-1-1-1-11-111-1-1-11-111-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111i−ii−i−iiii−i−iii−i−i−i−iii
χ172222222222222222222222222222222222222-1-1-122-1-1-1-1-1-12-1-1-12-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000000000002-1-1-12-1-1-12-1-1-12-1-1-1000000000000000000
χ18222222222222222222222222222222222222-12-1-1-1-122-1-1-1-1-12-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000-12-1-1-12-1-1-12-1-1-12-1-1000000000000000000
χ19222222222222222222222222222222222222-1-12-1-1-1-1-122-1-1-1-12-1-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1000000000000-1-12-1-1-12-1-1-12-1-1-12-1000000000000000000
χ20222222222222222222222222222222222222-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122000000000000-1-1-12-1-1-12-1-1-12-1-1-12000000000000000000
χ2122222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-12-1-1-12-1-1-1-2-2111111-2-21111110000000000002-1-1-12-1-1-1-2111-2111000000000000000000
χ2222222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-1-12-1-1-12-1-111-2-2111111-2-21111000000000000-12-1-1-12-1-11-2111-211000000000000000000
χ2322222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-1-1-12-1-1-12-11111-2-2111111-2-211000000000000-1-12-1-1-12-111-2111-21000000000000000000
χ2422222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12-1-1-12111111-2-2111111-2-2000000000000-1-1-12-1-1-12111-2111-2000000000000000000
χ25222222222222222222-2-222-2-2-2-2-2-22222-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-12-1-1-12-1-1-1-2-2111111-2-2111111000000000000-2111-21112-1-1-12-1-1-1000000000000000000
χ26222222222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-1-12-1-1-12-1-111-2-2111111-2-211110000000000001-2111-211-12-1-1-12-1-1000000000000000000
χ27222222222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-1-1-12-1-1-12-11111-2-2111111-2-21100000000000011-2111-21-1-12-1-1-12-1000000000000000000
χ28222222222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12-1-1-12111111-2-2111111-2-2000000000000111-2111-2-1-1-12-1-1-12000000000000000000
χ29222222222222222222-2-2-2-222-2-2-2-2-2-2-2-222222-1-1-122-1-1-1-1-1-12-1-1-12-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000-2111-2111-2111-2111000000000000000000
χ30222222222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-12-1-1-1-122-1-1-1-1-12-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-10000000000001-2111-2111-2111-211000000000000000000
χ31222222222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-1-12-1-1-1-1-122-1-1-1-12-1-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-100000000000011-2111-2111-2111-21000000000000000000
χ32222222222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122000000000000111-2111-2111-2111-2000000000000000000
χ33222222222222-2-2-2-2-2-20000000000000000002222222222222222-2-2-2-2-2-2-2-200000000000000002-22-222-2-222-2-20000000000000000000000000000000000
χ34222222222222-2-2-2-2-2-20000000000000000002222222222222222-2-2-2-2-2-2-2-20000000000000000-22-22-2-222-2-2220000000000000000000000000000000000
χ3522-2-22222-2-2-2-22-222-2-22-22-22-222-2-222-2-222-2-22-1-1-1-2-21111112-1-1-1-21112-1-1-122-1-1-1-1-1-1-2-21111110000000000002-1-1-1-21112-1-1-1-2111000000000000000000
χ3622-2-22222-2-2-2-22-222-2-22-22-22-222-2-222-2-222-2-2-12-1-111-2-21111-12-1-11-211-12-1-1-1-122-1-1-1-111-2-21111000000000000-12-1-11-211-12-1-11-211000000000000000000
χ3722-2-22222-2-2-2-22-222-2-22-22-22-222-2-222-2-222-2-2-1-12-11111-2-211-1-12-111-21-1-12-1-1-1-1-122-1-11111-2-211000000000000-1-12-111-21-1-12-111-21000000000000000000
χ3822-2-22222-2-2-2-22-222-2-22-22-22-222-2-222-2-222-2-2-1-1-12111111-2-2-1-1-12111-2-1-1-12-1-1-1-1-1-122111111-2-2000000000000-1-1-12111-2-1-1-12111-2000000000000000000
χ3922-2-22222-2-2-2-22-222-2-22-2-22-2222-2-2-2-222-2-2222-1-1-1-2-21111112-1-1-1-21112-1-1-1-2-211111122-1-1-1-1-1-10000000000002-1-1-1-2111-21112-1-1-1000000000000000000
χ4022-2-22222-2-2-2-22-222-2-22-2-22-2222-2-2-2-222-2-222-12-1-111-2-21111-12-1-11-211-12-1-111-2-21111-1-122-1-1-1-1000000000000-12-1-11-2111-211-12-1-1000000000000000000
χ4122-2-22222-2-2-2-22-222-2-22-2-22-2222-2-2-2-222-2-222-1-12-11111-2-211-1-12-111-21-1-12-11111-2-211-1-1-1-122-1-1000000000000-1-12-111-2111-21-1-12-1000000000000000000
χ4222-2-22222-2-2-2-22-222-2-22-2-22-2222-2-2-2-222-2-222-1-1-12111111-2-2-1-1-12111-2-1-1-12111111-2-2-1-1-1-1-1-122000000000000-1-1-12111-2111-2-1-1-12000000000000000000
χ4322-2-22222-2-2-2-22-222-2-2-222-2-22-2-22222-2-2-2-2222-1-1-1-2-21111112-1-1-1-21112-1-1-1-2-211111122-1-1-1-1-1-1000000000000-21112-1-1-12-1-1-1-2111000000000000000000
χ4422-2-22222-2-2-2-22-222-2-2-222-2-22-2-22222-2-2-2-222-12-1-111-2-21111-12-1-11-211-12-1-111-2-21111-1-122-1-1-1-10000000000001-211-12-1-1-12-1-11-211000000000000000000
χ4522-2-22222-2-2-2-22-222-2-2-222-2-22-2-22222-2-2-2-222-1-12-11111-2-211-1-12-111-21-1-12-11111-2-211-1-1-1-122-1-100000000000011-21-1-12-1-1-12-111-21000000000000000000
χ4622-2-22222-2-2-2-22-222-2-2-222-2-22-2-22222-2-2-2-222-1-1-12111111-2-2-1-1-12111-2-1-1-12111111-2-2-1-1-1-1-1-122000000000000111-2-1-1-12-1-1-12111-2000000000000000000
χ4722-2-22222-2-2-2-22-222-2-2-22-222-2-2-222-2-22222-2-22-1-1-1-2-21111112-1-1-1-21112-1-1-122-1-1-1-1-1-1-2-2111111000000000000-21112-1-1-1-21112-1-1-1000000000000000000
χ4822-2-22222-2-2-2-22-222-2-2-22-222-2-2-222-2-22222-2-2-12-1-111-2-21111-12-1-11-211-12-1-1-1-122-1-1-1-111-2-211110000000000001-211-12-1-11-211-12-1-1000000000000000000
χ4922-2-22222-2-2-2-22-222-2-2-22-222-2-2-222-2-22222-2-2-1-12-11111-2-211-1-12-111-21-1-12-1-1-1-1-122-1-11111-2-21100000000000011-21-1-12-111-21-1-12-1000000000000000000
χ5022-2-22222-2-2-2-22-222-2-2-22-222-2-2-222-2-22222-2-2-1-1-12111111-2-2-1-1-12111-2-1-1-12-1-1-1-1-1-122111111-2-2000000000000111-2-1-1-12111-2-1-1-12000000000000000000
χ5122-2-22222-2-2-2-2-22-2-2220000000000000000002222-2-2-2-2-2-2-2-222222222-2-2-2-200000000000000002i−2i−2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000
χ5222-2-22222-2-2-2-2-22-2-2220000000000000000002222-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000
χ533333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ543333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i320000000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i320000000000000000-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32
χ553333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233-3-3-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i3200000000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32000000000000000011-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i32
χ563333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233-3-3-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i320000000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i320000000000000000-1-111111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ573333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-333-3-33+3i323−3i323+3i323−3i32−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i3200000000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000-1-111-1-11+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ583333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-333-3-33+3i323−3i323+3i323−3i32−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i320000000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32000000000000000011-1-111−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ593333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-3-3-3333+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000-1-1-1-1111+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.