Finite Group Databasebeta

← Group #10690915

Character table — Group #10690915

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11111111222222222222222222222222222222224444444444444444444444444444448888888888888888888888881212121212121212121212121212121248484848
order122222222222344444444444466666661212121212121212222244666666666666121212121212121212121212888888882424242424242424242424242424242444444444444444444444
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
χ51111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ61111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ71111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ81111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1
χ911111111-1-1-1-111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1
χ1011111111-1-1-1-111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-11
χ1111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-11
χ1211111111-1-1-1-111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-1
χ1311111111-1-1-1-11-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-11
χ1411111111-1-1-1-11-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-111-1
χ1511111111-1-1-1-11-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-111-1
χ1611111111-1-1-1-11-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11
χ17222222222222222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
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
χ21222222222222-122222222-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-2-1-1-1-1111111111111-1-1-1-1-1-1-1-10000000033−3−333−3−333−3−333−3−300000000000000000000
χ22222222222222-122222222-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-2-1-1-1-1111111111111-1-1-1-1-1-1-1-100000000−3−333−3−333−3−333−3−33300000000000000000000
χ23222222222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-1-1-1-111111111-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000000000
χ24222222222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-1-1-1-111111111-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000000000000000
χ25222222222222-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111110000000033−3−333−3−3−3−333−3−33300000000000000000000
χ26222222222222-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111100000000−3−333−3−33333−3−333−3−300000000000000000000
χ2722222222-2-2-2-222222-2-2-2-22222222222222222222-2-222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000000000000000
χ2822222222-2-2-2-22-2-2-2-22222222222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ2922222222-2-2-2-2-12222-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-211111111-1-1-1-11111-1-1-1-1111100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ3022222222-2-2-2-2-12222-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-211111111-1-1-1-11111-1-1-1-1111100000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ3122222222-2-2-2-2-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-2221111-1-1-1-11111-1-1-1-1-1-1-1-111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii00000000000000000000
χ3222222222-2-2-2-2-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-2221111-1-1-1-11111-1-1-1-1-1-1-1-11111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i00000000000000000000
χ3322222222-2-2-2-2-1-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-21111-1-1-1-1111111111111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ3422222222-2-2-2-2-1-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-21111-1-1-1-1111111111111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ3522222222-2-2-2-2-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-111111111-2-2222211111111-1-1-1-1-1-1-1-11111-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000
χ3622222222-2-2-2-2-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-111111111-2-2222211111111-1-1-1-1-1-1-1-11111-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii00000000000000000000
χ3722-2-222-2-20000200002i2i−2i−2i2i2i−2i−2i222-2-2-2-22i2i2i2i−2i−2i−2i−2i2-20000000022-2-20000000000002i2i−2i−2i0000000000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000
χ3822-2-222-2-20000200002i2i−2i−2i2i2i−2i−2i222-2-2-2-22i2i2i2i−2i−2i−2i−2i2-20000000022-2-20000000000002i2i−2i−2i000000000000000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000
χ3922-2-222-2-20000200002i2i−2i−2i−2i−2i2i2i222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2200000000-2-2220000000000002i2i−2i−2i0000000000000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000
χ4022-2-222-2-20000200002i2i−2i−2i−2i−2i2i2i222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2200000000-2-2220000000000002i2i−2i−2i000000000000000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000
χ4122-2-222-2-2000020000−2i−2i2i2i2i2i−2i−2i222-2-2-2-22i2i2i2i−2i−2i−2i−2i-2200000000-2-222000000000000−2i−2i2i2i0000000000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000
χ4222-2-222-2-2000020000−2i−2i2i2i2i2i−2i−2i222-2-2-2-22i2i2i2i−2i−2i−2i−2i-2200000000-2-222000000000000−2i−2i2i2i000000000000000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000
χ4322-2-222-2-2000020000−2i−2i2i2i−2i−2i2i2i222-2-2-2-2−2i−2i−2i−2i2i2i2i2i2-20000000022-2-2000000000000−2i−2i2i2i0000000000000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000
χ4422-2-222-2-2000020000−2i−2i2i2i−2i−2i2i2i222-2-2-2-2−2i−2i−2i−2i2i2i2i2i2-20000000022-2-2000000000000−2i−2i2i2i000000000000000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000
χ452-22-22-22-2000022i2i−2i−2i00002i−2i2i−2i2-2-222-2-22i2i−2i−2i2i2i−2i−2i002-2000000000022-2-200002i2i−2i−2i00000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ462-22-22-22-2000022i2i−2i−2i00002i−2i2i−2i2-2-222-2-22i2i−2i−2i2i2i−2i−2i002-2000000000022-2-200002i2i−2i−2i0000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ472-22-22-22-2000022i2i−2i−2i0000−2i2i−2i2i2-2-222-2-2−2i−2i2i2i−2i−2i2i2i00-220000000000-2-22200002i2i−2i−2i00000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ482-22-22-22-2000022i2i−2i−2i0000−2i2i−2i2i2-2-222-2-2−2i−2i2i2i−2i−2i2i2i00-220000000000-2-22200002i2i−2i−2i0000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ492-22-22-22-200002−2i−2i2i2i00002i−2i2i−2i2-2-222-2-22i2i−2i−2i2i2i−2i−2i00-220000000000-2-2220000−2i−2i2i2i00000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ502-22-22-22-200002−2i−2i2i2i00002i−2i2i−2i2-2-222-2-22i2i−2i−2i2i2i−2i−2i00-220000000000-2-2220000−2i−2i2i2i0000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ512-22-22-22-200002−2i−2i2i2i0000−2i2i−2i2i2-2-222-2-2−2i−2i2i2i−2i−2i2i2i002-2000000000022-2-20000−2i−2i2i2i00000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ522-22-22-22-200002−2i−2i2i2i0000−2i2i−2i2i2-2-222-2-2−2i−2i2i2i−2i−2i2i2i002-2000000000022-2-20000−2i−2i2i2i0000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ532-2-222-2-2222-2-22000000002-2-222-2-2-2-22222-2-2-2-22200002-222-2-20000000022-2-2000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ542-2-222-2-2222-2-22000000002-2-222-2-2-2-22222-2-2-2-22200002-222-2-20000000022-2-200000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ552-2-222-2-2222-2-2200000000-222-22-2-2-2-222-2-22222-2-20000-2222-2-200000000-2-22200000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000
χ562-2-222-2-2222-2-2200000000-222-22-2-2-2-222-2-22222-2-20000-2222-2-200000000-2-2220000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000
χ572-2-222-2-22-2-2222000000002-2-222-2-2-2-22222-2-2-2-2220000-22-2-22200000000-2-22200000000000000000000000000000000000000002-2-222-2-220000
χ582-2-222-2-22-2-2222000000002-2-222-2-2-2-22222-2-2-2-2220000-22-2-22200000000-2-2220000000000000000000000000000000000000000-222-2-222-20000
χ592-2-222-2-22-2-222200000000-222-22-2-2-2-222-2-22222-2-200002-2-2-2220000000022-2-2000000000000000000000000000000002-2-222-2-22000000000000
χ602-2-222-2-22-2-222200000000-222-22-2-2-2-222-2-22222-2-200002-2-2-2220000000022-2-200000000000000000000000000000000-222-2-222-2000000000000
χ612-2-22-222-22-22-222i−2i2i−2i2i−2i2i−2i0000-22-22-22-2000000000000002-22-20000000000002i−2i2i−2i2i−2i2i−2i2−22−2−i2i2−i2i22−22−22−22−2−i2i2−i2i2−i2i2−i2i200000000000000000000
χ622-2-22-222-22-22-222i−2i2i−2i2i−2i2i−2i0000-22-22-22-2000000000000002-22-20000000000002i−2i2i−2i2i−2i2i−2i−22−22i2−i2i2−i2−22−22−22−22i2−i2i2−i2i2−i2i2−i200000000000000000000
χ632-2-22-222-22-22-22−2i2i−2i2i−2i2i−2i2i0000-22-22-22-2000000000000002-22-2000000000000−2i2i−2i2i−2i2i−2i2i2−22−2i2−i2i2−i22−22−22−22−2i2−i2i2−i2i2−i2i2−i200000000000000000000
χ642-2-22-222-22-22-22−2i2i−2i2i−2i2i−2i2i0000-22-22-22-2000000000000002-22-2000000000000−2i2i−2i2i−2i2i−2i2i−22−22−i2i2−i2i2−22−22−22−22−i2i2−i2i2−i2i2−i2i200000000000000000000
χ652-2-22-222-22-22-2-12i−2i2i−2i2i−2i2i−2i00001-11-11-113−33−33−33−3000000-11-11−i3i3−i3i3−i3i3−i3i33−33−3−ii−ii−ii−ii2−22−2−i2i2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.