Finite Group Databasebeta

← Group #11711768

Character table — Group #11711768

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size11111111333333334444448888888812121212121216161616161616161616161624242424242424242424242424242424
order1222222222222222444444366666664444441212121212121212121212122244444444444444
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
χ51111111111111111-1-111-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111
χ61111111111111111-1-111-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ71111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ81111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
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
χ132222-2-2-2-2222-2-22-2-20000002222-2-2-2-20000000000000000002-20000002-2000000
χ142222-2-2-2-2222-2-22-2-20000002222-2-2-2-2000000000000000000-22000000-22000000
χ1522-2-222-2-22-2-2222-2-200000022-2-2-222-2000000000000000000002i−2i0000002i−2i0000
χ1622-2-222-2-22-2-2222-2-200000022-2-2-222-200000000000000000000−2i2i000000−2i2i0000
χ1722-2-2-2-2222-2-2-2-222200002-222-2-22-2-2200002-20000000022-2-20000000000000000
χ1822-2-2-2-2222-2-2-2-222200002-2-1-111-111-100002-233−3−333−3−3-1-1110000000000000000
χ1922-2-2-2-2222-2-2-2-222200002-2-1-111-111-100002-2−3−333−3−333-1-1110000000000000000
χ2022-2-2-2-2222-2-2-2-22220000-2222-2-22-2-220000-2200000000-2-2220000000000000000
χ2122-2-2-2-2222-2-2-2-22220000-22-1-111-111-10000-2233−3−3−3−33311-1-10000000000000000
χ2222-2-2-2-2222-2-2-2-22220000-22-1-111-111-10000-22−3−33333−3−311-1-10000000000000000
χ232-22-22-22-2-22-22-222-2002i−2i002-22-222-2-2002i−2i0000002i−2i2i−2i00000000000000000000
χ242-22-22-22-2-22-22-222-2002i−2i00-11-11-1-111002i−2i00−i3i3−i3i3−ii−ii3−33−30000000000000000
χ252-22-22-22-2-22-22-222-2002i−2i00-11-11-1-111002i−2i00i3−i3i3−i3−ii−ii−33−330000000000000000
χ262-22-22-22-2-22-22-222-200−2i2i002-22-222-2-200−2i2i000000−2i2i−2i2i00000000000000000000
χ272-22-22-22-2-22-22-222-200−2i2i00-11-11-1-11100−2i2i00−i3i3−i3i3i−ii−i−33−330000000000000000
χ282-22-22-22-2-22-22-222-200−2i2i00-11-11-1-11100−2i2i00i3−i3i3−i3i−ii−i3−33−30000000000000000
χ292-22-2-22-22-22-2-222-220000002-22-2-2-2220000000000000000000000002-20000002-2
χ302-22-2-22-22-22-2-222-220000002-22-2-2-222000000000000000000000000-22000000-22
χ312-2-222-2-22-2-222-22-220000002-2-22-22-2200000000000000000000002-20000002-200
χ322-2-222-2-22-2-222-22-220000002-2-22-22-220000000000000000000000-22000000-2200
χ332-2-22-222-2-2-22-2222-22i−2i00002-2-222-22-22i−2i00002i−2i−2i2i000000000000000000000000
χ342-2-22-222-2-2-22-2222-22i−2i0000-111-1-11-112i−2i0000−iii−i−i3i3i3−i3−333−30000000000000000
χ352-2-22-222-2-2-22-2222-22i−2i0000-111-1-11-112i−2i0000−iii−ii3−i3−i3i33−3−330000000000000000
χ362-2-22-222-2-2-22-2222-2−2i2i00002-2-222-22-2−2i2i0000−2i2i2i−2i000000000000000000000000
χ372-2-22-222-2-2-22-2222-2−2i2i0000-111-1-11-11−2i2i0000i−i−ii−i3i3i3−i33−3−330000000000000000
χ382-2-22-222-2-2-22-2222-2−2i2i0000-111-1-11-11−2i2i0000i−i−iii3−i3−i3i3−333−30000000000000000
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
χ4333333333-1-1-1-1-1-1-1-1-3-333-3-30000000011-1-11100000000000011-1-1-1-111-1-11111-1-1
χ4433333333-1-1-1-1-1-1-1-1-3-333-3-30000000011-1-111000000000000-1-11111-1-111-1-1-1-111
χ4533333333-1-1-1-1-1-1-1-1-3-3-3-333000000001111-1-10000000000001111-1-1-1-1-1-1-1-11111
χ4633333333-1-1-1-1-1-1-1-1-3-3-3-333000000001111-1-1000000000000-1-1-1-111111111-1-1-1-1
χ474444-4-4-4-4444-4-44-4-4000000-2-2-2-222220000000000000000000000000000000000
χ4844-4-444-4-44-4-4444-4-4000000-2-2222-2-220000000000000000000000000000000000
χ494-44-4-44-44-44-4-444-44000000-22-2222-2-20000000000000000000000000000000000
χ504-4-444-4-44-4-444-44-44000000-222-22-22-20000000000000000000000000000000000
χ516666-6-6-6-6-2-2-222-222000000000000000000000000000000002-2000000-22000000
χ526666-6-6-6-6-2-2-222-22200000000000000000000000000000000-220000002-2000000
χ5366-6-666-6-6-222-2-2-22200000000000000000000000000000000002i−2i000000−2i2i0000
χ5466-6-666-6-6-222-2-2-2220000000000000000000000000000000000−2i2i0000002i−2i0000
χ5566-6-6-6-666-22222-2-2-200006-6000000000000-220000000000000000000000000000
χ5666-6-6-6-666-22222-2-2-20000-660000000000002-20000000000000000000000000000
χ576-66-66-66-62-22-22-2-22006i−6i000000000000−2i2i000000000000000000000000000000
χ586-66-66-66-62-22-22-2-2200−6i6i0000000000002i−2i000000000000000000000000000000
χ596-66-6-66-662-222-2-22-2000000000000000000000000000000000000002-2000000-22
χ606-66-6-66-662-222-2-22-200000000000000000000000000000000000000-220000002-2
χ616-6-666-6-6622-2-22-22-20000000000000000000000000000000000002-2000000-2200
χ626-6-666-6-6622-2-22-22-2000000000000000000000000000000000000-220000002-200
χ636-6-66-666-622-22-2-2-226i−6i000000000000−2i2i00000000000000000000000000000000
χ646-6-66-666-622-22-2-2-22−6i6i0000000000002i−2i00000000000000000000000000000000

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