Finite Group Databasebeta

← Group #13147183

Character table — Group #13147183

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11112222222222666666666666121212121212121212121212121212121212121212121212181818182424242424242424242424242424242424242424545454547272727272727272
order12223446661212121222449181818363636363366666666121218181818181836363636363644449912121212181818181818363636363636363644441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ411111111111111111111111111−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111111111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32
χ511111111111111111111111111−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ611111111111111111111111111−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111111111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32
χ711111-1-1111-1-1-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ811111-1-1111-1-1-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1-1-1111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ911111-1-1111-1-1-1-1-1-1111111-1-1-1-1−1−i32−1+i32-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-1-1-111111111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ1011111-1-1111-1-1-1-1-1-1111111-1-1-1-1−1−i32−1+i32-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-1-1-1111111-1-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ1111111-1-1111-1-1-1-1-1-1111111-1-1-1-1−1+i32−1−i32-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-1-1-111111111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ1211111-1-1111-1-1-1-1-1-1111111-1-1-1-1−1+i32−1−i32-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-1-1-1111111-1-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ1311-1-111-1-1-1111-1-11-11-11-1-1111-1-1111-1-1-111-1-11-1111-1-1-1111-1-1-1i−ii−i111-11-1-1-1-1-11111-1-111-1-1i−ii−ii−ii−ii−ii−i
χ1411-1-111-1-1-1111-1-11-11-11-1-1111-1-1111-1-1-111-1-11-1111-1-1-1111-1-1-1−ii−ii111-11-1-1-1-1-11111-1-111-1-1−ii−ii−ii−ii−ii−ii
χ1511-1-111-1-1-1111-1-11-11-11-1-1111-1-1−1−i32−1+i321-11+i321−i32−1−i32−1+i321+i321−i321-1111-1-1-1111-1-1-1i−ii−i−1−i32−1+i32−1−i321+i32−1+i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32i−ii−i−ζ15ζ15−ζ15ζ15−ζ3ζ3−ζ3ζ3
χ1611-1-111-1-1-1111-1-11-11-11-1-1111-1-1−1−i32−1+i321-11+i321−i32−1−i32−1+i321+i321−i321-1111-1-1-1111-1-1-1−ii−ii−1−i32−1+i32−1−i321+i32−1+i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−ii−iiζ15−ζ15ζ15−ζ15ζ3−ζ3ζ3−ζ3
χ1711-1-111-1-1-1111-1-11-11-11-1-1111-1-1−1+i32−1−i321-11−i321+i32−1+i32−1−i321−i321+i321-1111-1-1-1111-1-1-1i−ii−i−1+i32−1−i32−1+i321−i32−1−i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32i−ii−i−ζ3ζ3−ζ3ζ3−ζ15ζ15−ζ15ζ15
χ1811-1-111-1-1-1111-1-11-11-11-1-1111-1-1−1+i32−1−i321-11−i321+i32−1+i32−1−i321−i321+i321-1111-1-1-1111-1-1-1−ii−ii−1+i32−1−i32−1+i321−i32−1−i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−ii−iiζ3−ζ3ζ3−ζ3ζ15−ζ15ζ15−ζ15
χ1911-1-11-11-1-11-1-111-111-11-1-11-1-11111-11-1-111-1-11-1-1-1-1111111-1-1-1i−i−ii11-11-11-1-1-1-111-1-111-1-111i−i−iii−i−iii−i−ii
χ2011-1-11-11-1-11-1-111-111-11-1-11-1-11111-11-1-111-1-11-1-1-1-1111111-1-1-1−iii−i11-11-11-1-1-1-111-1-111-1-111−iii−i−iii−i−iii−i
χ2111-1-11-11-1-11-1-111-111-11-1-11-1-111−1−i32−1+i32-111+i321−i32−1−i32−1+i321+i321−i321-1-1-1-1111111-1-1-1i−i−ii−1−i32−1+i321+i32−1−i321−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32i−i−ii−ζ15ζ15ζ15−ζ15−ζ3ζ3ζ3−ζ3
χ2211-1-11-11-1-11-1-111-111-11-1-11-1-111−1−i32−1+i32-111+i321−i32−1−i32−1+i321+i321−i321-1-1-1-1111111-1-1-1−iii−i−1−i32−1+i321+i32−1−i321−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−iii−iζ15−ζ15−ζ15ζ15ζ3−ζ3−ζ3ζ3
χ2311-1-11-11-1-11-1-111-111-11-1-11-1-111−1+i32−1−i32-111−i321+i32−1+i32−1−i321−i321+i321-1-1-1-1111111-1-1-1i−i−ii−1+i32−1−i321−i32−1+i321+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32i−i−ii−ζ3ζ3ζ3−ζ3−ζ15ζ15ζ15−ζ15
χ2411-1-11-11-1-11-1-111-111-11-1-11-1-111−1+i32−1−i32-111−i321+i32−1+i32−1−i321−i321+i321-1-1-1-1111111-1-1-1−iii−i−1+i32−1−i321−i32−1+i321+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−iii−iζ3−ζ3−ζ3ζ3ζ15−ζ15−ζ15ζ15
χ25222222222222222222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-10000-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ26222222222222222222-1-1-1-1-1-1-1-1−1−i3−1+i322−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322-1-1-1-1-1-1-1-1-1-1-1-100001+i321−i32−1−i3−1−i3−1+i3−1+i31+i321+i321−i321−i321+i321−i321+i321+i321+i321+i321−i321−i321−i321−i32000000000000
χ27222222222222222222-1-1-1-1-1-1-1-1−1+i3−1−i322−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322-1-1-1-1-1-1-1-1-1-1-1-100001−i321+i32−1+i3−1+i3−1−i3−1−i31−i321−i321+i321+i321−i321+i321−i321−i321−i321−i321+i321+i321+i321+i32000000000000
χ2822222-2-2222-2-2-2-2-2-222-1-1-1-1111122-2-222222222111111-1-1-1-1-1-10000-1-1-2-2-2-2-1-1-1-1-1-111111111000000000000
χ2922222-2-2222-2-2-2-2-2-222-1-1-1-11111−1−i3−1+i3-2-2−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322111111-1-1-1-1-1-100001+i321−i321+i31+i31−i31−i31+i321+i321−i321−i321+i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32000000000000
χ3022222-2-2222-2-2-2-2-2-222-1-1-1-11111−1+i3−1−i3-2-2−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322111111-1-1-1-1-1-100001−i321+i321−i31−i31+i31+i31−i321−i321+i321+i321−i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32000000000000
χ3122-2-222-2-2-2222-2-22-22-2-111-1-1-111222-2-2-222-2-22-2-1-1-1111-1-1-11110000-1-12-22-21111-1-1-1-111-1-111000000000000
χ3222-2-222-2-2-2222-2-22-22-2-111-1-1-111−1−i3−1+i32-21+i31−i3−1−i3−1+i31+i31−i32-2-1-1-1111-1-1-111100001+i321−i32−1−i31+i3−1+i31−i3−1−i32−1−i32−1+i32−1+i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32000000000000
χ3322-2-222-2-2-2222-2-22-22-2-111-1-1-111−1+i3−1−i32-21−i31+i3−1+i3−1−i31−i31+i32-2-1-1-1111-1-1-111100001−i321+i32−1+i31−i3−1−i31+i3−1+i32−1+i32−1−i32−1−i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32000000000000
χ3422-2-22-22-2-22-2-222-222-2-111-111-1-122-22-2-222-2-22-2111-1-1-1-1-1-11110000-1-1-22-221111-1-111-1-111-1-1000000000000
χ3522-2-22-22-2-22-2-222-222-2-111-111-1-1−1−i3−1+i3-221+i31−i3−1−i3−1+i31+i31−i32-2111-1-1-1-1-1-111100001+i321−i321+i3−1−i31−i3−1+i3−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32000000000000
χ3622-2-22-22-2-22-2-222-222-2-111-111-1-1−1+i3−1−i3-221−i31+i3−1+i3−1−i31−i31+i32-2111-1-1-1-1-1-111100001−i321+i321−i3−1+i31+i3−1−i3−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32000000000000
χ3733333333333333-1-1-1-13333333300-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1333300000000000000000000-1-1-1-100000000
χ3833333333333333-1-1-1-13333333300-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-300000000000000000000111100000000
χ3933333-3-3333-3-3-3-311-1-13333-3-3-3-30011000000-1-1111111-1-1-1-1-1-133-3-300000000000000000000-1-11100000000
χ4033333-3-3333-3-3-3-311-1-13333-3-3-3-30011000000-1-1111111-1-1-1-1-1-1-3-3330000000000000000000011-1-100000000
χ4133-3-333-3-3-3333-3-3-11-113-3-3333-3-300-11000000-11-1-1-1111-1-1-11113i−3i3i−3i00000000000000000000−ii−ii00000000
χ4233-3-333-3-3-3333-3-3-11-113-3-3333-3-300-11000000-11-1-1-1111-1-1-1111−3i3i−3i3i00000000000000000000i−ii−i00000000
χ4333-3-33-33-3-33-3-3331-1-113-3-33-3-333001-1000000-11111-1-1-1-1-1-11113i−3i−3i3i00000000000000000000−iii−i00000000
χ4433-3-33-33-3-33-3-3331-1-113-3-33-3-333001-1000000-11111-1-1-1-1-1-1111−3i3i3i−3i00000000000000000000i−i−ii00000000
χ454-44-44004-4-40000000044-4-40000-2-2002222-2-2000000000000000000-2-200002-22-22200000000000000000000
χ464-44-44004-4-40000000044-4-400001+i31−i300−1−i3−1+i3−1−i3−1+i31+i31−i30000000000000000001+i31−i30000−1−i31+i3−1+i31−i3−1−i3−1+i300000000000000000000
χ474-44-44004-4-40000000044-4-400001−i31+i300−1+i3−1−i3−1+i3−1−i31−i31+i30000000000000000001−i31+i30000−1+i31−i3−1−i31+i3−1+i3−1−i300000000000000000000
χ484-44-44004-4-400000000-2-22223−2323−23-2-2002222-2-2000000000000000000110000-11-11-1-13−33−33−33−3000000000000
χ494-44-44004-4-400000000-2-22223−2323−231+i31−i300−1−i3−1+i3−1−i3−1+i31+i31−i3000000000000000000−1−i32−1+i3200001+i32−1−i321−i32−1+i321+i321−i32−2ζ3−ζ152ζ3+ζ15−2ζ3−ζ152ζ3+ζ15ζ3+2ζ15−ζ3−2ζ15ζ3+2ζ15−ζ3−2ζ15000000000000
χ504-44-44004-4-400000000-2-22223−2323−231−i31+i300−1+i3−1−i3−1+i3−1−i31−i31+i3000000000000000000−1+i32−1−i3200001−i32−1+i321+i32−1−i321−i321+i32ζ3+2ζ15−ζ3−2ζ15ζ3+2ζ15−ζ3−2ζ15−2ζ3−ζ152ζ3+ζ15−2ζ3−ζ152ζ3+ζ15000000000000
χ514-44-44004-4-400000000-2-222−2323−2323-2-2002222-2-2000000000000000000110000-11-11-1-1−33−33−33−33000000000000
χ524-44-44004-4-400000000-2-222−2323−23231+i31−i300−1−i3−1+i3−1−i3−1+i31+i31−i3000000000000000000−1−i32−1+i3200001+i32−1−i321−i32−1+i321+i321−i322ζ3+ζ15−2ζ3−ζ152ζ3+ζ15−2ζ3−ζ15−ζ3−2ζ15ζ3+2ζ15−ζ3−2ζ15ζ3+2ζ15000000000000
χ534-44-44004-4-400000000-2-222−2323−23231−i31+i300−1+i3−1−i3−1+i3−1−i31−i31+i3000000000000000000−1+i32−1−i3200001−i32−1+i321+i32−1−i321−i321+i32−ζ3−2ζ15ζ3+2ζ15−ζ3−2ζ15ζ3+2ζ152ζ3+ζ15−2ζ3−ζ152ζ3+ζ15−2ζ3−ζ15000000000000
χ544-4-44400-44-4000000004-44-40000-2-200-2-22222000000000000000000-2-20000-22-222200000000000000000000
χ554-4-44400-44-4000000004-44-400001+i31−i3001+i31−i3−1−i3−1+i3−1−i3−1+i30000000000000000001+i31−i300001+i3−1−i31−i3−1+i3−1−i3−1+i300000000000000000000
χ564-4-44400-44-4000000004-44-400001−i31+i3001−i31+i3−1+i3−1−i3−1+i3−1−i30000000000000000001−i31+i300001−i3−1+i31+i3−1−i3−1+i3−1−i300000000000000000000
χ574-4-44400-44-400000000-22-2223−23−2323-2-200-2-222220000000000000000001100001-11-1-1-13−3−333−3−33000000000000
χ584-4-44400-44-400000000-22-2223−23−23231+i31−i3001+i31−i3−1−i3−1+i3−1−i3−1+i3000000000000000000−1−i32−1+i320000−1−i321+i32−1+i321−i321+i321−i32−2ζ3−ζ152ζ3+ζ152ζ3+ζ15−2ζ3−ζ15ζ3+2ζ15−ζ3−2ζ15−ζ3−2ζ15ζ3+2ζ15000000000000
χ594-4-44400-44-400000000-22-2223−23−23231−i31+i3001−i31+i3−1+i3−1−i3−1+i3−1−i3000000000000000000−1+i32−1−i320000−1+i321−i32−1−i321+i321−i321+i32ζ3+2ζ15−ζ3−2ζ15−ζ3−2ζ15ζ3+2ζ15−2ζ3−ζ152ζ3+ζ152ζ3+ζ15−2ζ3−ζ15000000000000
χ604-4-44400-44-400000000-22-22−232323−23-2-200-2-222220000000000000000001100001-11-1-1-1−333−3−333−3000000000000
χ614-4-44400-44-400000000-22-22−232323−231+i31−i3001+i31−i3−1−i3−1+i3−1−i3−1+i3000000000000000000−1−i32−1+i320000−1−i321+i32−1+i321−i321+i321−i322ζ3+ζ15−2ζ3−ζ15−2ζ3−ζ152ζ3+ζ15−ζ3−2ζ15ζ3+2ζ15ζ3+2ζ15−ζ3−2ζ15000000000000
χ624-4-44400-44-400000000-22-22−232323−231−i31+i3001−i31+i3−1+i3−1−i3−1+i3−1−i3000000000000000000−1+i32−1−i320000−1+i321−i32−1−i321+i321−i321+i32−ζ3−2ζ15ζ3+2ζ15ζ3+2ζ15−ζ3−2ζ152ζ3+ζ15−2ζ3−ζ15−2ζ3−ζ152ζ3+ζ15000000000000
χ6366666666666666-2-2-2-2-3-3-3-3-3-3-3-300-2-2000000-2-2111111111111000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 36 (ζ36 = 1); i = ζ9.