Finite Group Databasebeta

← Group #10690780

Character table — Group #10690780

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11111111222222222222222222222222222222224444444444444444444444444444448888888888888888888888881212121212121212121212121212121248484848
order12222222222234444444444446666666121212121212121244444466661212121212121212121212121212121212121212888888882424242424242424242424242424242488888888888888882444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-1
χ61111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-111
χ71111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-111
χ81111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-1
χ911111111-1-1-1-111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1
χ1011111111-1-1-1-111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-11
χ1111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-11
χ1211111111-1-1-1-111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-1
χ1311111111-1-1-1-11-1-1-1-111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11
χ1411111111-1-1-1-11-1-1-1-111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1
χ1511111111-1-1-1-11-1-1-1-111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1
χ1611111111-1-1-1-11-1-1-1-111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11
χ172222222222222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000000000000000
χ182222222222222-2-2-2-2-2-22222-2-222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000000000000000
χ19222222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ20222222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000000000000000
χ21222222222222-1222222-2-2-2-222-1-1-1-1-1-1-111111111-2-2-2-2-2-2-1-1-1-111111111-1-1-1-11111-1-1-1-10000000033−3−333−3−333−3−333−3−300000000000000000000
χ22222222222222-1222222-2-2-2-222-1-1-1-1-1-1-111111111-2-2-2-2-2-2-1-1-1-111111111-1-1-1-11111-1-1-1-100000000−3−333−3−333−3−333−3−33300000000000000000000
χ23222222222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1111111111111-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ24222222222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1111111111111-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ25222222222222-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-22222-1-1-1-1-1-1-1-1-1-1-1-11111111111112i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii00000000000000000000
χ26222222222222-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-22222-1-1-1-1-1-1-1-1-1-1-1-1111111111111−2i−2i−2i−2i2i2i2i2iiiiiiiii−i−i−i−i−i−i−i−i00000000000000000000
χ2722222222-2-2-2-222222-2-22222-2-2222222222222222-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ2822222222-2-2-2-22-2-2-2-222-2-2-2-2222222222-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-22222-2-2-2-22222222200000000000000000000000000000000000000000000
χ2922222222-2-2-2-2-12222-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22211111111-1-1-1-1-1-1-1-11111111100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ3022222222-2-2-2-2-12222-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22211111111-1-1-1-1-1-1-1-11111111100000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ3122222222-2-2-2-2-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii00000000000000000000
χ3222222222-2-2-2-2-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-11111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i00000000000000000000
χ3322222222-2-2-2-2-1-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-1111111111111-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-100000000000000000000
χ3422222222-2-2-2-2-1-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-1111111111111-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-1111100000000000000000000
χ3522222222-2-2-2-2-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-11111111122-2-22211111111-1-1-1-11111-1-1-1-1-1-1-1-10000000033−3−3−3−333−3−33333−3−300000000000000000000
χ3622222222-2-2-2-2-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-11111111122-2-22211111111-1-1-1-11111-1-1-1-1-1-1-1-100000000−3−33333−3−333−3−3−3−33300000000000000000000
χ3722-22-22-2-20000222-2-2002i2i−2i−2i0022-2-22-2-22i2i2i2i−2i−2i−2i−2i00002i−2i000000002i2i−2i−2i22-2-2000000000000000000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000
χ3822-22-22-2-20000222-2-2002i2i−2i−2i0022-2-22-2-22i2i2i2i−2i−2i−2i−2i00002i−2i000000002i2i−2i−2i22-2-200000000000000000000000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000
χ3922-22-22-2-20000222-2-200−2i−2i2i2i0022-2-22-2-2−2i−2i−2i−2i2i2i2i2i0000−2i2i00000000−2i−2i2i2i22-2-2000000000000000000000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000
χ4022-22-22-2-20000222-2-200−2i−2i2i2i0022-2-22-2-2−2i−2i−2i−2i2i2i2i2i0000−2i2i00000000−2i−2i2i2i22-2-200000000000000000000000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000
χ4122-22-22-2-200002-2-222002i2i−2i−2i0022-2-22-2-22i2i2i2i−2i−2i−2i−2i0000−2i2i00000000−2i−2i2i2i-2-222000000000000000000000000000000001+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i0000
χ4222-22-22-2-200002-2-222002i2i−2i−2i0022-2-22-2-22i2i2i2i−2i−2i−2i−2i0000−2i2i00000000−2i−2i2i2i-2-22200000000000000000000000000000000−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i0000
χ4322-22-22-2-200002-2-22200−2i−2i2i2i0022-2-22-2-2−2i−2i−2i−2i2i2i2i2i00002i−2i000000002i2i−2i−2i-2-222000000000000000000000000000000001−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i0000
χ4422-22-22-2-200002-2-22200−2i−2i2i2i0022-2-22-2-2−2i−2i−2i−2i2i2i2i2i00002i−2i000000002i2i−2i−2i-2-22200000000000000000000000000000000−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i0000
χ4522-2-22-22-222-2-222i−2i2i−2i2i−2i00002i−2i2-22-2-22-20000000000000022-2-2000000002i−2i2i−2i00002i2i−2i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i00000000000000000000
χ4622-2-22-22-222-2-222i−2i2i−2i2i−2i00002i−2i2-22-2-22-20000000000000022-2-2000000002i−2i2i−2i00002i2i−2i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i00000000000000000000
χ4722-2-22-22-222-2-22−2i2i−2i2i−2i2i0000−2i2i2-22-2-22-20000000000000022-2-200000000−2i2i−2i2i0000−2i−2i2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i00000000000000000000
χ4822-2-22-22-222-2-22−2i2i−2i2i−2i2i0000−2i2i2-22-2-22-20000000000000022-2-200000000−2i2i−2i2i0000−2i−2i2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i00000000000000000000
χ4922-2-22-22-222-2-2-12i−2i2i−2i2i−2i00002i−2i-11-111-11−i3−i3i3i3−i3−i3i3i3000000-1-11133−3−33−33−3−ii−ii−i3−i3i3i3−i−iii1+i−1−i1+i−1−i1−i−1+i1−i−1+i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ700000000000000000000
χ5022-2-22-22-222-2-2-12i−2i2i−2i2i−2i00002i−2i-11-111-11−i3−i3i3i3−i3−i3i3i3000000-1-11133−3−33−33−3−ii−ii−i3−i3i3i3−i−iii−1−i1+i−1−i1+i−1+i1−i−1+i1−iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ700000000000000000000
χ5122-2-22-22-222-2-2-12i−2i2i−2i2i−2i00002i−2i-11-111-11i3i3−i3−i3i3i3−i3−i3000000-1-111−3−333−33−33−ii−iii3i3−i3−i3−i−iii1+i−1−i1+i−1−i1−i−1+i1−i−1+i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ1100000000000000000000
χ5222-2-22-22-222-2-2-12i−2i2i−2i2i−2i00002i−2i-11-111-11i3i3−i3−i3i3i3−i3−i3000000-1-111−3−333−33−33−ii−iii3i3−i3−i3−i−iii−1−i1+i−1−i1+i−1+i1−i−1+i1−iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ1100000000000000000000
χ5322-2-22-22-222-2-2-1−2i2i−2i2i−2i2i0000−2i2i-11-111-11−i3−i3i3i3−i3−i3i3i3000000-1-111−3−333−33−33i−ii−i−i3−i3i3i3ii−i−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ700000000000000000000
χ5422-2-22-22-222-2-2-1−2i2i−2i2i−2i2i0000−2i2i-11-111-11−i3−i3i3i3−i3−i3i3i3000000-1-111−3−333−33−33i−ii−i−i3−i3i3i3ii−i−i−1+i1−i−1+i1−i−1−i1+i−1−i1+iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ700000000000000000000
χ5522-2-22-22-222-2-2-1−2i2i−2i2i−2i2i0000−2i2i-11-111-11i3i3−i3−i3i3i3−i3−i3000000-1-11133−3−33−33−3i−ii−ii3i3−i3−i3ii−i−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ1100000000000000000000
χ5622-2-22-22-222-2-2-1−2i2i−2i2i−2i2i0000−2i2i-11-111-11i3i3−i3−i3i3i3−i3−i3000000-1-11133−3−33−33−3i−ii−ii3i3−i3−i3ii−i−i−1+i1−i−1+i1−i−1−i1+i−1−i1+iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ1100000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.