Finite Group Databasebeta

← Group #10698609

Character table — Group #10698609

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order12222222344444444666666612121212121212124488888888121212121212121224242424242424242424242424242424224466668888121212122424242424242424444488884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-111
χ9222222222222-2-2-22-2222222222222222-2-200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000022-2-200000000
χ10222222222222-2-2-22-2222222222222222-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-22200000000
χ11222222222-2-2-2222-222222222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000022-2-222220000-2-2-2-200000000000000000000
χ12222222222-2-2-2222-222222222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000-2-222-2-2-2-20000222200000000000000000000
χ13222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-22222000000000000000000000000000000000000000000000000002-2
χ14222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-2222200000000000000000000000000000000000000000000000000-22
χ1522222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ1622222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2111111111111000000000000
χ1722222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-1-1-1-1-2-2-2-2-1-1-1-111111111000000000000
χ1822222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2111122221111-1-1-1-1-1-1-1-1000000000000
χ1922222222-1-2-2-2222-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-1111133333333−3−3−3−3−3−3−3−322-2-2-1-1-1-1000011113333−3−3−3−3000000000000
χ2022222222-1-2-2-2222-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-1111133333333−3−3−3−3−3−3−3−3-2-22211110000-1-1-1-1−3−3−3−33333000000000000
χ2122222222-1-2-2-2222-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-11111−3−3−3−3−3−3−3−33333333322-2-2-1-1-1-100001111−3−3−3−33333000000000000
χ2222222222-1-2-2-2222-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-11111−3−3−3−3−3−3−3−333333333-2-22211110000-1-1-1-13333−3−3−3−3000000000000
χ2322-222-2-2-222-2-20002022-2-2-2-2222-2-2-2-222002222−2−2−2−2000000002222−2−2−2−22222−2−2−2−2000000000000000000000000002i−2i−i2−i2i2i20000
χ2422-222-2-2-222-2-20002022-2-2-2-2222-2-2-2-222002222−2−2−2−2000000002222−2−2−2−22222−2−2−2−200000000000000000000000000−2i2ii2i2−i2−i20000
χ2522-222-2-2-222-2-20002022-2-2-2-2222-2-2-2-22200−2−2−2−2222200000000−2−2−2−22222−2−2−2−22222000000000000000000000000002i−2ii2i2−i2−i20000
χ2622-222-2-2-222-2-20002022-2-2-2-2222-2-2-2-22200−2−2−2−2222200000000−2−2−2−22222−2−2−2−2222200000000000000000000000000−2i2i−i2−i2i2i20000
χ2722-2-2-2-222200022-20-22-22-22-2-2000000000022−2−222−2−222-2-2000022−2−222−2−222−2−222−2−2002i−2i0000−i2−i2i2i22i2i−2i−2i−i2−i2i2i2−i2−i2i2i2000000000000
χ2822-2-2-2-222200022-20-22-22-22-2-2000000000022−2−222−2−222-2-2000022−2−222−2−222−2−222−2−200−2i2i0000i2i2−i2−i2−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2000000000000
χ2922-2-2-2-222200022-20-22-22-22-2-20000000000−2−222−2−22222-2-20000−2−222−2−222−2−222−2−222002i−2i0000i2i2−i2−i22i2i−2i−2ii2i2−i2−i2i2i2−i2−i2000000000000
χ3022-2-2-2-222200022-20-22-22-22-2-20000000000−2−222−2−22222-2-20000−2−222−2−222−2−222−2−22200−2i2i0000−i2−i2i2i2−2i−2i2i2i−i2−i2i2i2−i2−i2i2i2000000000000
χ3122-2-2-2-222-100022-20-2-11-11-1113−333−3−33−30022−2−222−2−2-1-1113−33−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23002i−2i−i3−i3i3i3−i2−i2i2i2−i−iiiζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000000000
χ3222-2-2-2-222-100022-20-2-11-11-1113−333−3−33−30022−2−222−2−2-1-1113−33−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300−2i2ii3i3−i3−i3i2i2−i2−i2ii−i−i−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000000000
χ3322-2-2-2-222-100022-20-2-11-11-1113−333−3−33−300−2−222−2−222-1-1113−33−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23002i−2i−i3−i3i3i3i2i2−i2−i2−i−iii−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000000000
χ3422-2-2-2-222-100022-20-2-11-11-1113−333−3−33−300−2−222−2−222-1-1113−33−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300−2i2ii3i3−i3−i3−i2−i2i2i2ii−i−iζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000000000
χ3522-2-2-2-222-100022-20-2-11-11-111−33−3−333−330022−2−222−2−2-1-111−33−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7002i−2ii3i3−i3−i3−i2−i2i2i2−i−iiiζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000000000
χ3622-2-2-2-222-100022-20-2-11-11-111−33−3−333−330022−2−222−2−2-1-111−33−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700−2i2i−i3−i3i3i3i2i2−i2−i2ii−i−i−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000000000
χ3722-2-2-2-222-100022-20-2-11-11-111−33−3−333−3300−2−222−2−222-1-111−33−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7002i−2ii3i3−i3−i3i2i2−i2−i2−i−iii−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000000000
χ3822-2-2-2-222-100022-20-2-11-11-111−33−3−333−3300−2−222−2−222-1-111−33−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700−2i2i−i3−i3i3i3−i2−i2i2i2ii−i−iζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000000000
χ392-222-2-2-22222-22-22-2-2-2-2-2-2222222-22-2-2-2-22000000002-22-2-2-222000000000000000000000000000000000000000000002i−2i2i−2i0000
χ402-222-2-2-22222-22-22-2-2-2-2-2-2222222-22-2-2-2-22000000002-22-2-2-22200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ412-222-2-2-22222-2-22-2-22-2-2-2-2222222-22-2-2-22-22i−2i2i−2i2i−2i2i−2i-22-2222-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ422-222-2-2-22222-2-22-2-22-2-2-2-2222222-22-2-2-22-2−2i2i−2i2i−2i2i−2i2i-22-2222-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ432-222-2-2-222-2-222-222-2-2-2-2-2222-2-2-22-22222-2000000002-22-222-2-20000000000000000000000000000000000000000000000002i−2i00
χ442-222-2-2-222-2-222-222-2-2-2-2-2222-2-2-22-22222-2000000002-22-222-2-2000000000000000000000000000000000000000000000000−2i2i00
χ452-222-2-2-222-2-22-22-222-2-2-2-2222-2-2-22-2222-2200000000-22-22-2-2220000000000000000000000002-22-200002-22-22-22-2000000000000
χ462-222-2-2-222-2-22-22-222-2-2-2-2222-2-2-22-2222-2200000000-22-22-2-222000000000000000000000000-22-220000-22-22-22-22000000000000
χ472-222-2-2-22-122-2-22-2-221111-1-1-1-1-1-11-11112-22i−2i2i−2i2i−2i2i−2i1-11-1-1-111−ii−ii−ii−ii−ii−ii−ii−ii0000−i3i3−i3i30000−i3i3−i3i33−33−3−33−33000000000000
χ482-222-2-2-22-122-2-22-2-221111-1-1-1-1-1-11-11112-22i−2i2i−2i2i−2i2i−2i1-11-1-1-111−ii−ii−ii−ii−ii−ii−ii−ii0000i3−i3i3−i30000i3−i3i3−i3−33−333−33−3000000000000
χ492-222-2-2-22-122-2-22-2-221111-1-1-1-1-1-11-11112-2−2i2i−2i2i−2i2i−2i2i1-11-1-1-111i−ii−ii−ii−ii−ii−ii−ii−i0000−i3i3−i3i30000−i3i3−i3i3−33−333−33−3000000000000
χ502-222-2-2-22-122-2-22-2-221111-1-1-1-1-1-11-11112-2−2i2i−2i2i−2i2i−2i2i1-11-1-1-111i−ii−ii−ii−ii−ii−ii−ii−i0000i3−i3i3−i30000i3−i3i3−i33−33−3−33−33000000000000
χ512-222-2-2-22-1-2-22-22-2221111-1-1-1111-11-1-1-1-22000000001-11-111-1-1−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i30000−i3i3−i3i32-22-2i3−i3i3−i3-11-11-11-11000000000000
χ522-222-2-2-22-1-2-22-22-2221111-1-1-1111-11-1-1-1-22000000001-11-111-1-1−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i30000i3−i3i3−i3-22-22−i3i3−i3i31-11-11-11-1000000000000
χ532-222-2-2-22-1-2-22-22-2221111-1-1-1111-11-1-1-1-22000000001-11-111-1-1i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i30000−i3i3−i3i3-22-22i3−i3i3−i31-11-11-11-1000000000000
χ542-222-2-2-22-1-2-22-22-2221111-1-1-1111-11-1-1-1-22000000001-11-111-1-1i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i30000i3−i3i3−i32-22-2−i3i3−i3i3-11-11-11-11000000000000
χ552-2-22-222-222-22000-20-2-222-2-2222-22-22-2-200−i2i2−i2i2i2−i2i2−i200000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000000000002i−2i002−2−220000
χ562-2-22-222-222-22000-20-2-222-2-2222-22-22-2-200−i2i2−i2i2i2−i2i2−i200000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000000000000000−2i2i00−222−20000
χ572-2-22-222-222-22000-20-2-222-2-2222-22-22-2-200i2−i2i2−i2−i2i2−i2i200000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000000000002i−2i00−222−20000
χ582-2-22-222-222-22000-20-2-222-2-2222-22-22-2-200i2−i2i2−i2−i2i2−i2i200000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000000000000000−2i2i002−2−220000
χ592-2-2-222-222000-2220-2-22-222-2-20000000000−i2i2i2−i2−i2i2i2−i2-222-20000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i22-2002-2-22i2−i2−i2i20000i2−i2−i2i2i2−i2−i2i2000000000000
χ602-2-2-222-222000-2220-2-22-222-2-20000000000−i2i2i2−i2−i2i2i2−i2-222-20000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2-2200-222-2−i2i2i2−i20000−i2i2i2−i2−i2i2i2−i2000000000000
χ612-2-2-222-222000-2220-2-22-222-2-20000000000i2−i2−i2i2i2−i2−i2i2-222-20000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i22-2002-2-22−i2i2i2−i20000−i2i2i2−i2−i2i2i2−i2000000000000
χ622-2-2-222-222000-2220-2-22-222-2-20000000000i2−i2−i2i2i2−i2−i2i2-222-20000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2-2200-222-2i2−i2−i2i20000i2−i2−i2i2i2−i2−i2i2000000000000
χ632-2-2-222-22-1000-2220-21-11-1-1113−33−3−33−3300−i2i2i2−i2−i2i2i2−i21-1-113−3−33ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ72-200-111-1i2−i2−i2i23−3−33−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ642-2-2-222-22-1000-2220-21-11-1-1113−33−3−33−3300−i2i2i2−i2−i2i2i2−i21-1-113−3−33ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7-22001-1-11−i2i2i2−i2−333−3ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ652-2-2-222-22-1000-2220-21-11-1-1113−33−3−33−3300i2−i2−i2i2i2−i2−i2i21-1-113−3−33−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ72-200-111-1−i2i2i2−i23−3−33ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.