Finite Group Databasebeta

← Group #13150834

Character table — Group #13150834

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222222222444444666666666666666666669999121212121212121212121212121212121212121212121818181818181818181818181818181818181818181836363636363636367272727272727272
order1222223444466666121212123366666666661212121212121212444436666666661212121212121212121212122222446666666612121212121212122244444466121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111-1-1-1-111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-11-11-11-11-11-11-1
χ61111111-1-1-1-111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-11-11-11-11-11-11-11
χ71111111-1-1-1-111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11-11-1-11-111-11-1-11-11
χ81111111-1-1-1-111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-11-111-11-1-11-111-11-1
χ91111-1-1111-1-1111-1-111-1-111111-1-1-1-11111111-1-1-1-111111-1-111-1-1-1-1111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111
χ101111-1-1111-1-1111-1-111-1-111111-1-1-1-11111111-1-1-1-111111-1-111-1-1-1-1111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ111111-1-1111-1-1111-1-111-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11-1-111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-111-1-1
χ121111-1-1111-1-1111-1-111-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11-1-111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111-1-111
χ131111-1-11-1-111111-1-1-1-11111111-1-1-1-1111-1-1-1-1111111111-1-111-1-1-1-11-1-111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-11-1-11-111-11-1-11-111-1
χ141111-1-11-1-111111-1-1-1-11111111-1-1-1-1111-1-1-1-1111111111-1-111-1-1-1-11-1-111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-111-11-1-11-111-11-1-11
χ151111-1-11-1-111111-1-1-1-11111111-1-1-1-1111-1-1-1-11111-1-1-1-11-1-111-1-1-1-11-1-111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-111111-1-111-1-111-1-111-1-11
χ161111-1-11-1-111111-1-1-1-11111111-1-1-1-1111-1-1-1-11111-1-1-1-11-1-111-1-1-1-11-1-111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-111-1-111-1-111-1-111-1
χ17222222222222222222222-12-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ18222222222222222222222-12-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-2-2-2-2-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111111111110000000000000000
χ1922222222222222222222-12-1222222-1-12222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000022220000-1-1-1-1
χ2022222222222222222222-12-1222222-1-12222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000-2-2-2-200001111
χ212222222-2-2-2-222222-2-2-2-22-12-1-1-1-1-1-122-1111111112222-122-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-22211111111-1-1-1-1-1-1-1-10000000000000000
χ222222222-2-2-2-222222-2-2-2-22-12-1-1-1-1-1-122-111111111-2-2-2-2-122-1-1-1-1-1-1-1-2-2-2-2111111112222-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ232222222-2-2-2-222222-2-2-2-2-12-1222222-1-12-2-2-2-2-2-2-2-20000-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000002-22-20000-11-11
χ242222222-2-2-2-222222-2-2-2-2-12-1222222-1-12-2-2-2-2-2-2-2-20000-1-1-1-1-1-1-1-1-1-111111111111100000000000000000000000000-22-2200001-11-1
χ252222-2-2222-2-2222-2-222-2-22-12-1-1111122-1-1-1-1-111112222-1-2-2-1-11111-122-2-2-1-1-1-1111122-2-2-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ262222-2-2222-2-2222-2-222-2-22-12-1-1111122-1-1-1-1-11111-2-2-2-2-1-2-2-1-11111-122-2-2-1-1-1-11111-2-222221111-1-1-1-11111-1-1-1-10000000000000000
χ272222-2-2222-2-2222-2-222-2-2-12-122-2-2-2-2-1-122222-2-2-2-20000-111-1-11111-1-1-111-1-1-1-111110000000000000000000000000022-2-20000-1-111
χ282222-2-2222-2-2222-2-222-2-2-12-122-2-2-2-2-1-122222-2-2-2-20000-111-1-11111-1-1-111-1-1-1-1111100000000000000000000000000-2-222000011-1-1
χ292222-2-22-2-222222-2-2-2-2222-12-1-1111122-11111-1-1-1-12222-1-2-2-1-11111-1-2-2221111-1-1-1-1-2-222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ302222-2-22-2-222222-2-2-2-2222-12-1-1111122-11111-1-1-1-1-2-2-2-2-1-2-2-1-11111-1-2-2221111-1-1-1-122-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ312222-2-22-2-222222-2-2-2-222-12-122-2-2-2-2-1-12-2-2-2-222220000-111-1-11111-111-1-11111-1-1-1-1000000000000000000000000002-2-220000-111-1
χ322222-2-22-2-222222-2-2-2-222-12-122-2-2-2-2-1-12-2-2-2-222220000-111-1-11111-111-1-11111-1-1-1-100000000000000000000000000-222-200001-1-11
χ3322-2-2002002i−2i2-2-200002i−2i22-22-200002-2-200002i2i−2i−2i2i2i−2i−2i2002-20000-2002i−2i00002i2i−2i−2i002-200000022-2-22i2i−2i−2i00000000000000000000
χ3422-2-2002002i−2i2-2-200002i−2i22-22-200002-2-200002i2i−2i−2i−2i−2i2i2i2002-20000-2002i−2i00002i2i−2i−2i00-22000000-2-222−2i−2i2i2i00000000000000000000
χ3522-2-2002002i−2i2-2-200002i−2i2-1-2-11−i3−i3i3i32-2133−3−3−i−iii2i2i−2i−2i-100-11−i3−i3i3i31002i−2i33−3−3−i−iii002-200−i3−i3i3i3-1-111−i−iii33−3−30000000000000000
χ3622-2-2002002i−2i2-2-200002i−2i2-1-2-11−i3−i3i3i32-2133−3−3−i−iii−2i−2i2i2i-100-11−i3−i3i3i31002i−2i33−3−3−i−iii00-2200i3i3−i3−i311-1-1ii−i−i−3−3330000000000000000
χ3722-2-2002002i−2i2-2-200002i−2i2-1-2-11i3i3−i3−i32-21−3−333−i−iii2i2i−2i−2i-100-11i3i3−i3−i31002i−2i−3−333−i−iii002-200i3i3−i3−i3-1-111−i−iii−3−3330000000000000000
χ3822-2-2002002i−2i2-2-200002i−2i2-1-2-11i3i3−i3−i32-21−3−333−i−iii−2i−2i2i2i-100-11i3i3−i3−i31002i−2i−3−333−i−iii00-2200−i3−i3i3i311-1-1ii−i−i33−3−30000000000000000
χ3922-2-200200−2i2i2-2-20000−2i2i22-22-200002-2-20000−2i−2i2i2i2i2i−2i−2i2002-20000-200−2i2i0000−2i−2i2i2i00-22000000-2-2222i2i−2i−2i00000000000000000000
χ4022-2-200200−2i2i2-2-20000−2i2i22-22-200002-2-20000−2i−2i2i2i−2i−2i2i2i2002-20000-200−2i2i0000−2i−2i2i2i002-200000022-2-2−2i−2i2i2i00000000000000000000
χ4122-2-200200−2i2i2-2-20000−2i2i2-1-2-11−i3−i3i3i32-21−3−333ii−i−i2i2i−2i−2i-100-11−i3−i3i3i3100−2i2i−3−333ii−i−i00-2200i3i3−i3−i311-1-1−i−iii33−3−30000000000000000
χ4222-2-200200−2i2i2-2-20000−2i2i2-1-2-11−i3−i3i3i32-21−3−333ii−i−i−2i−2i2i2i-100-11−i3−i3i3i3100−2i2i−3−333ii−i−i002-200−i3−i3i3i3-1-111ii−i−i−3−3330000000000000000
χ4322-2-200200−2i2i2-2-20000−2i2i2-1-2-11i3i3−i3−i32-2133−3−3ii−i−i2i2i−2i−2i-100-11i3i3−i3−i3100−2i2i33−3−3ii−i−i00-2200−i3−i3i3i311-1-1−i−iii−3−3330000000000000000
χ4422-2-200200−2i2i2-2-20000−2i2i2-1-2-11i3i3−i3−i32-2133−3−3ii−i−i−2i−2i2i2i-100-11i3i3−i3−i3100−2i2i33−3−3ii−i−i002-200i3i3−i3−i3-1-111ii−i−i33−3−30000000000000000
χ452-22-22-220000-2-222-20000222-222-22-2-2-2-2000000002i−2i2i−2i22-2-222-22-2-200000000000000002i−2i000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ462-22-22-220000-2-222-20000222-222-22-2-2-2-200000000−2i2i−2i2i22-2-222-22-2-20000000000000000−2i2i00000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ472-22-22-220000-2-222-200002-121-1-11-11-2-213−33−33−33−32i−2i2i−2i-12-21-1-11-11100003−33−33−33−300002i−2i−i3i3−i3i3−i3i3−i3i3−ii−ii−ii−ii0000000000000000
χ482-22-22-220000-2-222-200002-121-1-11-11-2-213−33−33−33−3−2i2i−2i2i-12-21-1-11-11100003−33−33−33−30000−2i2ii3−i3i3−i3i3−i3i3−i3i−ii−ii−ii−i0000000000000000
χ492-22-22-220000-2-222-200002-121-1-11-11-2-21−33−33−33−332i−2i2i−2i-12-21-1-11-1110000−33−33−33−3300002i−2ii3−i3i3−i3i3−i3i3−i3−ii−ii−ii−ii0000000000000000
χ502-22-22-220000-2-222-200002-121-1-11-11-2-21−33−33−33−33−2i2i−2i2i-12-21-1-11-1110000−33−33−33−330000−2i2i−i3i3−i3i3−i3i3−i3i3i−ii−ii−ii−i0000000000000000
χ512-22-2-2220000-2-22-220000222-22-22-22-2-2-2000000002i−2i2i−2i2-22-22-22-22-20000000000000000−2i2i000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ522-22-2-2220000-2-22-220000222-22-22-22-2-2-200000000−2i2i−2i2i2-22-22-22-22-200000000000000002i−2i00000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ532-22-2-2220000-2-22-2200002-121-11-11-1-2-213−33−3−33−332i−2i2i−2i-1-221-11-11-1100003−33−3−33−330000−2i2i−i3i3−i3i3i3−i3i3−i3−ii−iii−ii−i0000000000000000
χ542-22-2-2220000-2-22-2200002-121-11-11-1-2-213−33−3−33−33−2i2i−2i2i-1-221-11-11-1100003−33−3−33−3300002i−2ii3−i3i3−i3−i3i3−i3i3i−ii−i−ii−ii0000000000000000
χ552-22-2-2220000-2-22-2200002-121-11-11-1-2-21−33−333−33−32i−2i2i−2i-1-221-11-11-110000−33−333−33−30000−2i2ii3−i3i3−i3−i3i3−i3i3−ii−iii−ii−i0000000000000000
χ562-22-2-2220000-2-22-2200002-121-11-11-1-2-21−33−333−33−3−2i2i−2i2i-1-221-11-11-110000−33−333−33−300002i−2i−i3i3−i3i3i3−i3i3−i3i−ii−i−ii−ii0000000000000000
χ572-2-220022-200-22-2002-20022-2-2-20000-2222-2-2200002-2-22200-2-2000022-2002-2-2200002-200002-2-2200002-2-2200000000000000000000
χ582-2-220022-200-22-2002-20022-2-2-20000-2222-2-220000-222-2200-2-2000022-2002-2-220000-220000-222-20000-222-200000000000000000000
χ592-2-220022-200-22-2002-2002-1-211−i3i3i3−i3-22-1-111-1−i3i3i3−i32-2-22-10011−i3i3i3−i3-12-200-111-1−i3i3i3−i32-20000-111-1−i3i3i3−i3-111-1−i3i3i3−i30000000000000000
χ602-2-220022-200-22-2002-2002-1-211−i3i3i3−i3-22-1-111-1−i3i3i3−i3-222-2-10011−i3i3i3−i3-12-200-111-1−i3i3i3−i3-2200001-1-11i3−i3−i3i31-1-11i3−i3−i3i30000000000000000
χ612-2-220022-200-22-2002-2002-1-211i3−i3−i3i3-22-1-111-1i3−i3−i3i32-2-22-10011i3−i3−i3i3-12-200-111-1i3−i3−i3i32-20000-111-1i3−i3−i3i3-111-1i3−i3−i3i30000000000000000
χ622-2-220022-200-22-2002-2002-1-211i3−i3−i3i3-22-1-111-1i3−i3−i3i3-222-2-10011i3−i3−i3i3-12-200-111-1i3−i3−i3i3-2200001-1-11−i3i3i3−i31-1-11−i3i3i3−i30000000000000000
χ632-2-22002-2200-22-200-220022-2-2-20000-222-222-200002-2-22200-2-200002-2200-222-20000-220000-222-200002-2-2200000000000000000000
χ642-2-22002-2200-22-200-220022-2-2-20000-222-222-20000-222-2200-2-200002-2200-222-200002-200002-2-220000-222-200000000000000000000
χ652-2-22002-2200-22-200-22002-1-211−i3i3i3−i3-22-11-1-11i3−i3−i3i32-2-22-10011−i3i3i3−i3-1-22001-1-11i3−i3−i3i3-2200001-1-11i3−i3−i3i3-111-1−i3i3i3−i30000000000000000
χ662-2-22002-2200-22-200-22002-1-211−i3i3i3−i3-22-11-1-11i3−i3−i3i3-222-2-10011−i3i3i3−i3-1-22001-1-11i3−i3−i3i32-20000-111-1−i3i3i3−i31-1-11i3−i3−i3i30000000000000000
χ672-2-22002-2200-22-200-22002-1-211i3−i3−i3i3-22-11-1-11−i3i3i3−i32-2-22-10011i3−i3−i3i3-1-22001-1-11−i3i3i3−i3-2200001-1-11−i3i3i3−i3-111-1i3−i3−i3i30000000000000000
χ682-2-22002-2200-22-200-22002-1-211i3−i3−i3i3-22-11-1-11−i3i3i3−i3-222-2-10011i3−i3−i3i3-1-22001-1-11−i3i3i3−i32-20000-111-1i3−i3−i3i31-1-11−i3i3i3−i30000000000000000
χ6944444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200001-2-21111111-2-2-2-21111111100000000000000000000000000000000000000
χ704444444-4-4-4-444444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-22222222200001-2-211111112222-1-1-1-1-1-1-1-100000000000000000000000000000000000000
χ714444-4-4444-4-4444-4-444-4-4-2-2-2-2-22222-2-2-2-2-2-2-22222000012211-1-1-1-11-2-2221111-1-1-1-100000000000000000000000000000000000000
χ724444-4-44-4-444444-4-4-4-444-2-2-2-2-22222-2-2-22222-2-2-2-2000012211-1-1-1-1122-2-2-1-1-1-1111100000000000000000000000000000000000000
χ7344-4-4004004i−4i4-4-400004i−4i-2424-40000-22-400004i4i−4i−4i0000-200-220000200−2i2i0000−2i−2i2i2i00000000000000000000000000000000000000
χ7444-4-4004004i−4i4-4-400004i−4i-2-22-22−2i3−2i32i32i3-2222323−23−23−2i−2i2i2i00001001-1i3i3−i3−i3-100−2i2i−3−333ii−i−i00000000000000000000000000000000000000
χ7544-4-4004004i−4i4-4-400004i−4i-2-22-222i32i3−2i3−2i3-222−23−232323−2i−2i2i2i00001001-1−i3−i3i3i3-100−2i2i33−3−3ii−i−i00000000000000000000000000000000000000
χ7644-4-400400−4i4i4-4-40000−4i4i-2424-40000-22-40000−4i−4i4i4i0000-200-2200002002i−2i00002i2i−2i−2i00000000000000000000000000000000000000
χ7744-4-400400−4i4i4-4-40000−4i4i-2-22-22−2i3−2i32i32i3-222−23−2323232i2i−2i−2i00001001-1i3i3−i3−i3-1002i−2i33−3−3−i−iii00000000000000000000000000000000000000
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χ794-44-44-440000-4-444-40000-24-2-444-44-422-4000000000000-2-222-2-22-22200000000000000000000000000000000000000000000000000
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χ814-44-44-440000-4-444-40000-2-2-22-2-22-22222−2323−2323−2323−232300001-22-111-11-1-100003−33−33−33−300000000000000000000000000000000000000
χ824-44-4-4440000-4-44-440000-24-2-44-44-4422-4000000000000-22-22-22-22-2200000000000000000000000000000000000000000000000000
χ834-44-4-4440000-4-44-440000-2-2-22-22-22-222223−2323−23−2323−2323000012-2-11-11-11-10000−33−333−33−300000000000000000000000000000000000000
χ844-44-4-4440000-4-44-440000-2-2-22-22-22-2222−2323−232323−2323−23000012-2-11-11-11-100003−33−3−33−3300000000000000000000000000000000000000
χ854-4-440044-400-44-4004-400-242-4-400002-244-4-4400000000-200220000-2-2200-222-2000000000000000000000000000000000000000000
χ864-4-440044-400-44-4004-400-2-2222−2i32i32i3−2i32-2-2-222-2−2i32i32i3−2i30000100-1-1i3−i3−i3i31-22001-1-11i3−i3−i3i300000000000000000000000000000000000000
χ874-4-440044-400-44-4004-400-2-22222i3−2i3−2i32i32-2-2-222-22i3−2i3−2i32i30000100-1-1−i3i3i3−i31-22001-1-11−i3i3i3−i300000000000000000000000000000000000000
χ884-4-44004-4400-44-400-4400-242-4-400002-24-444-400000000-200220000-22-2002-2-22000000000000000000000000000000000000000000
χ894-4-44004-4400-44-400-4400-2-2222−2i32i32i3−2i32-2-22-2-222i3−2i3−2i32i30000100-1-1i3−i3−i3i312-200-111-1−i3i3i3−i300000000000000000000000000000000000000
χ904-4-44004-4400-44-400-4400-2-22222i3−2i3−2i32i32-2-22-2-22−2i32i32i3−2i30000100-1-1−i3i3i3−i312-200-111-1i3−i3−i3i300000000000000000000000000000000000000
χ91666666-36666-3-3-3-3-3-3-3-3-30000000000000000000000000000000000000000000000000000000000000000000022220000-1-1-1-10000
χ92666666-36666-3-3-3-3-3-3-3-3-300000000000000000000000000000000000000000000000000000000000000000000-2-2-2-2000011110000
χ93666666-3-6-6-6-6-3-3-3-3-33333000000000000000000000000000000000000000000000000000000000000000000002-22-20000-11-110000
χ94666666-3-6-6-6-6-3-3-3-3-3333300000000000000000000000000000000000000000000000000000000000000000000-22-2200001-11-10000
χ956666-6-6-366-6-6-3-3-333-3-3330000000000000000000000000000000000000000000000000000000000000000000022-2-20000-1-1110000
χ966666-6-6-366-6-6-3-3-333-3-33300000000000000000000000000000000000000000000000000000000000000000000-2-222000011-1-10000
χ976666-6-6-3-6-666-3-3-33333-3-3000000000000000000000000000000000000000000000000000000000000000000002-2-220000-111-10000
χ986666-6-6-3-6-666-3-3-33333-3-300000000000000000000000000000000000000000000000000000000000000000000-222-200001-1-110000
χ991212-12-1200-60012i−12i-6660000−6i6i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1001212-12-1200-600−12i12i-66600006i−6i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10112-1212-1212-12-6000066-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10212-1212-12-1212-6000066-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-12-121200-612-12006-6600-6600000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-121200-6-1212006-66006-600000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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