Finite Group Databasebeta

← Group #11711776

Character table — Group #11711776

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size11111111333333334444448888888812121212121216161616161616161616161624242424242424242424242424242424
order1222222222222222444444366666664444441212121212121212121212124444444444444444
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ4111111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ51111111111111111-1-111-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-111-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ81111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ92222222222222222222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ10222222222222222222-2-2-2-2-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1111111110000000000000000
χ112222222222222222-2-222-2-2-1-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-111110000000000000000
χ122222222222222222-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-22211111111-1-1-1-10000000000000000
χ132222-2-2-2-22222-2-2-2-22-20000222-2-2-22-22-2000022-2-2000000000000000000000000
χ142222-2-2-2-22222-2-2-2-22-20000-1-1-1111-112-20000-1-11133−3−333−3−30000000000000000
χ152222-2-2-2-22222-2-2-2-22-20000-1-1-1111-112-20000-1-111−3−333−3−3330000000000000000
χ162222-2-2-2-22222-2-2-2-2-220000222-2-2-22-2-220000-2-222000000000000000000000000
χ172222-2-2-2-22222-2-2-2-2-220000-1-1-1111-11-22000011-1-133−3−3−3−3330000000000000000
χ182222-2-2-2-22222-2-2-2-2-220000-1-1-1111-11-22000011-1-1−3−33333−3−30000000000000000
χ1922-2-22-22-222-2-222-2-200000022-22-2-2-2200000000000000000000002i−2i0000002i−2i00
χ2022-2-22-22-222-2-222-2-200000022-22-2-2-220000000000000000000000−2i2i000000−2i2i00
χ2122-2-2-22-2222-2-2-2-22200000022-2-222-2-20000000000000000002i−2i0000002i−2i000000
χ2222-2-2-22-2222-2-2-2-22200000022-2-222-2-2000000000000000000−2i2i000000−2i2i000000
χ232-22-22-2-222-22-2-22-220000002-2222-2-2-2000000000000000000002i−2i0000002i−2i0000
χ242-22-22-2-222-22-2-22-220000002-2222-2-2-200000000000000000000−2i2i000000−2i2i0000
χ252-22-2-222-22-22-22-22-20000002-22-2-22-220000000000000000000000002i−2i0000002i−2i
χ262-22-2-222-22-22-22-22-20000002-22-2-22-22000000000000000000000000−2i2i000000−2i2i
χ272-2-2222-2-22-2-22-222-200002i−2i2-2-22-222-200002i−2i000000002i−2i2i−2i0000000000000000
χ282-2-2222-2-22-2-22-222-200002i−2i-111-11-1-1100002i−2i−i3i3−i3i33−33−3−ii−ii0000000000000000
χ292-2-2222-2-22-2-22-222-200002i−2i-111-11-1-1100002i−2ii3−i3i3−i3−33−33−ii−ii0000000000000000
χ302-2-2222-2-22-2-22-222-20000−2i2i2-2-22-222-20000−2i2i00000000−2i2i−2i2i0000000000000000
χ312-2-2222-2-22-2-22-222-20000−2i2i-111-11-1-110000−2i2i−i3i3−i3i3−33−33i−ii−i0000000000000000
χ322-2-2222-2-22-2-22-222-20000−2i2i-111-11-1-110000−2i2ii3−i3i3−i33−33−3i−ii−i0000000000000000
χ332-2-22-2-2222-2-222-2-22002-2002-2-2-22-222002-20000002-2-2200000000000000000000
χ342-2-22-2-2222-2-222-2-22002-200-1111-11-1-1002-200−i3i3i3−i3-111-1−i3i3i3−i30000000000000000
χ352-2-22-2-2222-2-222-2-22002-200-1111-11-1-1002-200i3−i3−i3i3-111-1i3−i3−i3i30000000000000000
χ362-2-22-2-2222-2-222-2-2200-22002-2-2-22-22200-22000000-222-200000000000000000000
χ372-2-22-2-2222-2-222-2-2200-2200-1111-11-1-100-2200−i3i3i3−i31-1-11i3−i3−i3i30000000000000000
χ382-2-22-2-2222-2-222-2-2200-2200-1111-11-1-100-2200i3−i3−i3i31-1-11−i3i3i3−i30000000000000000
χ3933333333-1-1-1-1-1-1-1-133333300000000-1-1-1-1-1-100000000000011111111-1-1-1-1-1-1-1-1
χ4033333333-1-1-1-1-1-1-1-133333300000000-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-111111111
χ4133333333-1-1-1-1-1-1-1-133-3-3-3-300000000-1-1111100000000000011-1-111-1-1-1-111-1-111
χ4233333333-1-1-1-1-1-1-1-133-3-3-3-300000000-1-11111000000000000-1-111-1-11111-1-111-1-1
χ4333333333-1-1-1-1-1-1-1-1-3-333-3-30000000011-1-1110000000000001111-1-1-1-1-1-1-1-11111
χ4433333333-1-1-1-1-1-1-1-1-3-333-3-30000000011-1-111000000000000-1-1-1-111111111-1-1-1-1
χ4533333333-1-1-1-1-1-1-1-1-3-3-3-333000000001111-1-100000000000011-1-1-1-111-1-11111-1-1
χ4633333333-1-1-1-1-1-1-1-1-3-3-3-333000000001111-1-1000000000000-1-11111-1-111-1-1-1-111
χ4744-4-44-44-444-4-444-4-4000000-2-22-2222-20000000000000000000000000000000000
χ4844-4-4-44-4444-4-4-4-444000000-2-222-2-2220000000000000000000000000000000000
χ494-44-44-4-444-44-4-44-44000000-22-2-2-22220000000000000000000000000000000000
χ504-44-4-444-44-44-44-44-4000000-22-222-22-20000000000000000000000000000000000
χ516666-6-6-6-6-2-2-2-222226-6000000000000-2200000000000000000000000000000000
χ526666-6-6-6-6-2-2-2-22222-660000000000002-200000000000000000000000000000000
χ5366-6-66-66-6-2-222-2-2220000000000000000000000000000000000002i−2i000000−2i2i00
χ5466-6-66-66-6-2-222-2-222000000000000000000000000000000000000−2i2i0000002i−2i00
χ5566-6-6-66-66-2-22222-2-2000000000000000000000000000000002i−2i000000−2i2i000000
χ5666-6-6-66-66-2-22222-2-200000000000000000000000000000000−2i2i0000002i−2i000000
χ576-66-66-6-66-22-222-22-200000000000000000000000000000000002i−2i000000−2i2i0000
χ586-66-66-6-66-22-222-22-20000000000000000000000000000000000−2i2i0000002i−2i0000
χ596-66-6-666-6-22-22-22-22000000000000000000000000000000000000002i−2i000000−2i2i
χ606-66-6-666-6-22-22-22-2200000000000000000000000000000000000000−2i2i0000002i−2i
χ616-6-6666-6-6-222-22-2-2200006i−6i000000000000−2i2i0000000000000000000000000000
χ626-6-6666-6-6-222-22-2-220000−6i6i0000000000002i−2i0000000000000000000000000000
χ636-6-66-6-666-222-2-222-2006-6000000000000-22000000000000000000000000000000
χ646-6-66-6-666-222-2-222-200-660000000000002-2000000000000000000000000000000

Here i is the imaginary unit (i² = −1).