Finite Group Databasebeta

← Group #13147294

Character table — Group #13147294

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11112222222222666666666666121212121212121212121212121212121212121212121212181818182424242424242424242424242424242424242424545454547272727272727272
order12223446661212121222344666121212123366666666666666121212121212121244443366666612121212121212121212121244441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111111111−1−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+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111-1-1-1-1−1−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−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111111111−1+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−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111-1-1-1-1−1+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
χ711111-1-1111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ811111-1-1111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ911111-1-1111-1-1-1-1-1-1111111-1-1-1-1−1−i32−1+i32-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111111-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−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+i32-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111-1-111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−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−i32-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111111-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+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−i32-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111-1-111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ1311-1-111-1-1-1111-1-11-111-1-1-1111-1-1111-1111-1-1-1-1-111-1-11-1111-1-1-1i−ii−i11-1-1-1-1111-11-111-1-111-1-1i−ii−ii−ii−ii−ii−i
χ1411-1-111-1-1-1111-1-11-111-1-1-1111-1-1111-1111-1-1-1-1-111-1-11-1111-1-1-1−ii−ii11-1-1-1-1111-11-111-1-111-1-1−ii−ii−ii−ii−ii−ii
χ1511-1-111-1-1-1111-1-11-111-1-1-1111-1-1−1−i32−1+i321-1111-1-1-11+i321−i32−1−i32−1+i321+i321−i321-1111-1-1-1i−ii−i−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32i−ii−iζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7
χ1611-1-111-1-1-1111-1-11-111-1-1-1111-1-1−1−i32−1+i321-1111-1-1-11+i321−i32−1−i32−1+i321+i321−i321-1111-1-1-1−ii−ii−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−ii−ii−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7
χ1711-1-111-1-1-1111-1-11-111-1-1-1111-1-1−1+i32−1−i321-1111-1-1-11−i321+i32−1+i32−1−i321−i321+i321-1111-1-1-1i−ii−i−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32i−ii−iζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11
χ1811-1-111-1-1-1111-1-11-111-1-1-1111-1-1−1+i32−1−i321-1111-1-1-11−i321+i32−1+i32−1−i321−i321+i321-1111-1-1-1−ii−ii−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−ii−ii−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11
χ1911-1-11-11-1-11-1-111-1111-1-1-11-1-11111-11-1-1-1111-1-111-1-11-1111-1-1-1i−i−ii11-1-1-1-111-11-11-1-111-1-111i−i−iii−i−iii−i−ii
χ2011-1-11-11-1-11-1-111-1111-1-1-11-1-11111-11-1-1-1111-1-111-1-11-1111-1-1-1−iii−i11-1-1-1-111-11-11-1-111-1-111−iii−i−iii−i−iii−i
χ2111-1-11-11-1-11-1-111-1111-1-1-11-1-111−1−i32−1+i32-11-1-1-11111+i321−i32−1−i32−1+i321+i321−i321-1111-1-1-1i−i−ii−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i32−1−i321−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32i−i−iiζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7
χ2211-1-11-11-1-11-1-111-1111-1-1-11-1-111−1−i32−1+i32-11-1-1-11111+i321−i32−1−i32−1+i321+i321−i321-1111-1-1-1−iii−i−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i32−1−i321−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−iii−i−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ7
χ2311-1-11-11-1-11-1-111-1111-1-1-11-1-111−1+i32−1−i32-11-1-1-11111−i321+i32−1+i32−1−i321−i321+i321-1111-1-1-1i−i−ii−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i32−1+i321+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32i−i−iiζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11
χ2411-1-11-11-1-11-1-111-1111-1-1-11-1-111−1+i32−1−i32-11-1-1-11111−i321+i32−1+i32−1−i321−i321+i321-1111-1-1-1−iii−i−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i32−1+i321+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−iii−i−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ11
χ252222222222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-122222222-1-1-1-1-1-10000-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ262222222222222222-122-1-1-1-1-1-1-1−1−i3−1+i322-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322-1-1-1-1-1-100001+i321−i321+i321+i321−i321−i321+i321−i32−1−i3−1−i3−1+i3−1+i31+i321+i321+i321+i321−i321−i321−i321−i32000000000000
χ272222222222222222-122-1-1-1-1-1-1-1−1+i3−1−i322-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322-1-1-1-1-1-100001−i321+i321−i321−i321+i321+i321−i321+i32−1+i3−1+i3−1−i3−1−i31−i321−i321−i321−i321+i321+i321+i321+i32000000000000
χ2822222-2-2222-2-2-2-2-2-2-122-1-1-1111122-2-211111122222222-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ2922222-2-2222-2-2-2-2-2-2-122-1-1-11111−1−i3−1+i3-2-2111111−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322-1-1-1-1-1-100001+i321−i321+i321+i321−i321−i321+i321−i321+i31+i31−i31−i3−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32000000000000
χ3022222-2-2222-2-2-2-2-2-2-122-1-1-11111−1+i3−1−i3-2-2111111−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322-1-1-1-1-1-100001−i321+i321−i321−i321+i321+i321−i321+i321−i31−i31+i31+i3−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32000000000000
χ3122-2-222-2-2-2222-2-22-2-12-211-1-1-111222-2-1-1-1111-2-222-2-22-2-1-1-11110000-1-11111-1-12-22-2-1-111-1-111000000000000
χ3222-2-222-2-2-2222-2-22-2-12-211-1-1-111−1−i3−1+i32-2-1-1-11111+i31−i3−1−i3−1+i31+i31−i32-2-1-1-111100001+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i31+i3−1+i31−i31+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32000000000000
χ3322-2-222-2-2-2222-2-22-2-12-211-1-1-111−1+i3−1−i32-2-1-1-11111−i31+i3−1+i3−1−i31−i31+i32-2-1-1-111100001−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i31−i3−1−i31+i31−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32000000000000
χ3422-2-22-22-2-22-2-222-22-12-211-111-1-122-22111-1-1-1-2-222-2-22-2-1-1-11110000-1-11111-1-1-22-2211-1-111-1-1000000000000
χ3522-2-22-22-2-22-2-222-22-12-211-111-1-1−1−i3−1+i3-22111-1-1-11+i31−i3−1−i3−1+i31+i31−i32-2-1-1-111100001+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i3−1−i31−i3−1+i3−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32000000000000
χ3622-2-22-22-2-22-2-222-22-12-211-111-1-1−1+i3−1−i3-22111-1-1-11−i31+i3−1+i3−1−i31−i31+i32-2-1-1-111100001−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i3−1+i31+i3−1−i3−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32000000000000
χ3733333333333333-1-13-1-1333333300-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1333300000000000000000000-1-1-1-100000000
χ3833333333333333-1-13-1-1333333300-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1-3-3-3-300000000000000000000111100000000
χ3933333-3-3333-3-3-3-3113-1-1333-3-3-3-30011111111000000-1-1-1-1-1-1-1-133-3-300000000000000000000-1-11100000000
χ4033333-3-3333-3-3-3-3113-1-1333-3-3-3-30011111111000000-1-1-1-1-1-1-1-1-3-3330000000000000000000011-1-100000000
χ4133-3-333-3-3-3333-3-3-113-11-3-3333-3-300-11-1-1-1111000000-11-1-1-11113i−3i3i−3i00000000000000000000−ii−ii00000000
χ4233-3-333-3-3-3333-3-3-113-11-3-3333-3-300-11-1-1-1111000000-11-1-1-1111−3i3i−3i3i00000000000000000000i−ii−i00000000
χ4333-3-33-33-3-33-3-3331-13-11-3-33-3-333001-1111-1-1-1000000-11-1-1-11113i−3i−3i3i00000000000000000000−iii−i00000000
χ4433-3-33-33-3-33-3-3331-13-11-3-33-3-333001-1111-1-1-1000000-11-1-1-1111−3i3i3i−3i00000000000000000000i−i−ii00000000
χ454-44-44004-4-40000004004-4-40000-2-2000000002222-2-2000000000000-2-22-22-222000000000000000000000000
χ464-44-44004-4-40000004004-4-400001+i31−i300000000−1−i3−1+i3−1−i3−1+i31+i31−i30000000000001+i31−i3−1−i31+i3−1+i31−i3−1−i3−1+i3000000000000000000000000
χ474-44-44004-4-40000004004-4-400001−i31+i300000000−1+i3−1−i3−1+i3−1−i31−i31+i30000000000001−i31+i3−1+i31−i3−1−i31+i3−1+i3−1−i3000000000000000000000000
χ484-44-44004-4-4000000-200-22223−2323−23-2-2000000002222-2-200000000000011-11-11-1-100003−33−33−33−3000000000000
χ494-44-44004-4-4000000-200-22223−2323−231+i31−i300000000−1−i3−1+i3−1−i3−1+i31+i31−i3000000000000−1−i32−1+i321+i32−1−i321−i32−1+i321+i321−i3200002ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11000000000000
χ504-44-44004-4-4000000-200-22223−2323−231−i31+i300000000−1+i3−1−i3−1+i3−1−i31−i31+i3000000000000−1+i32−1−i321−i32−1+i321+i32−1−i321−i321+i320000−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ11000000000000
χ514-44-44004-4-4000000-200-222−2323−2323-2-2000000002222-2-200000000000011-11-11-1-10000−33−33−33−33000000000000
χ524-44-44004-4-4000000-200-222−2323−23231+i31−i300000000−1−i3−1+i3−1−i3−1+i31+i31−i3000000000000−1−i32−1+i321+i32−1−i321−i32−1+i321+i321−i320000−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11000000000000
χ534-44-44004-4-4000000-200-222−2323−23231−i31+i300000000−1+i3−1−i3−1+i3−1−i31−i31+i3000000000000−1+i32−1−i321−i32−1+i321+i32−1−i321−i321+i320000ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11000000000000
χ544-4-44400-44-4000000400-44-40000-2-200000000-2-22222000000000000-2-2-22-2222000000000000000000000000
χ554-4-44400-44-4000000400-44-400001+i31−i3000000001+i31−i3−1−i3−1+i3−1−i3−1+i30000000000001+i31−i31+i3−1−i31−i3−1+i3−1−i3−1+i3000000000000000000000000
χ564-4-44400-44-4000000400-44-400001−i31+i3000000001−i31+i3−1+i3−1−i3−1+i3−1−i30000000000001−i31+i31−i3−1+i31+i3−1−i3−1+i3−1−i3000000000000000000000000
χ574-4-44400-44-4000000-2002-2223−23−2323-2-200000000-2-22222000000000000111-11-1-1-100003−3−333−3−33000000000000
χ584-4-44400-44-4000000-2002-2223−23−23231+i31−i3000000001+i31−i3−1−i3−1+i3−1−i3−1+i3000000000000−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i3200002ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ11−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ11000000000000
χ594-4-44400-44-4000000-2002-2223−23−23231−i31+i3000000001−i31+i3−1+i3−1−i3−1+i3−1−i3000000000000−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i320000−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ112ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ11000000000000
χ604-4-44400-44-4000000-2002-22−232323−23-2-200000000-2-22222000000000000111-11-1-1-10000−333−3−333−3000000000000
χ614-4-44400-44-4000000-2002-22−232323−231+i31−i3000000001+i31−i3−1−i3−1+i3−1−i3−1+i3000000000000−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i320000−2ζ7−ζ112ζ7+ζ112ζ7+ζ11−2ζ7−ζ11ζ7+2ζ11−ζ7−2ζ11−ζ7−2ζ11ζ7+2ζ11000000000000
χ624-4-44400-44-4000000-2002-22−232323−231−i31+i3000000001−i31+i3−1+i3−1−i3−1+i3−1−i3000000000000−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i320000ζ7+2ζ11−ζ7−2ζ11−ζ7−2ζ11ζ7+2ζ11−2ζ7−ζ112ζ7+ζ112ζ7+ζ11−2ζ7−ζ11000000000000
χ6366666666666666-2-2-3-2-2-3-3-3-3-3-3-300-2-2111111000000-2-2111111000000000000000000000000000000000000
χ6466666-6-6666-6-6-6-622-3-2-2-3-3-333330022-1-1-1-1-1-1000000-2-2111111000000000000000000000000000000000000
χ656666-366-3-3-3-3-3-3-366066000000000-3-3000000000000-3-3000000000000000000000000000000000000000000
χ666666-366-3-3-3-3-3-3-3-2-20-2-2000000000114-2-24-2-2000000114-2-24-2-2000000000000000000000000000000000000
χ676666-366-3-3-3-3-3-3-3-2-20-2-200000000011-24-2-24-200000011-24-2-24-2000000000000000000000000000000000000
χ686666-366-3-3-3-3-3-3-3-2-20-2-200000000011-2-24-2-2400000011-2-24-2-24000000000000000000000000000000000000
χ696666-3-6-6-3-3-33333220-2-2000000000-1-122-422-400000011-2-24-2-24000000000000000000000000000000000000
χ706666-3-6-6-3-3-33333220-2-2000000000-1-12-422-4200000011-24-2-24-2000000000000000000000000000000000000
χ716666-3-6-6-3-3-33333220-2-2000000000-1-1-422-422000000114-2-24-2-2000000000000000000000000000000000000
χ726666-3-6-6-3-3-33333-6-606600000000033000000000000-3-3000000000000000000000000000000000000000000
χ7366-6-666-6-6-6666-6-6-22-3-2233-3-3-33300-22111-1-1-1000000-22111-1-1-1000000000000000000000000000000000000
χ7466-6-66-66-6-66-6-6662-2-3-2233-333-3-3002-2-1-1-1111000000-22111-1-1-1000000000000000000000000000000000000
χ7566-6-6-36-633-3-3-3336-606-6000000000-33000000000000-33000000000000000000000000000000000000000000
χ7666-6-6-36-633-3-3-333-220-220000000001-14-2-2-4220000001-14-2-2-422000000000000000000000000000000000000
χ7766-6-6-36-633-3-3-333-220-220000000001-1-24-22-420000001-1-24-22-42000000000000000000000000000000000000
χ7866-6-6-36-633-3-3-333-220-220000000001-1-2-2422-40000001-1-2-2422-4000000000000000000000000000000000000
χ7966-6-6-3-6633-333-3-32-20-22000000000-1122-4-2-240000001-1-2-2422-4000000000000000000000000000000000000
χ8066-6-6-3-6633-333-3-32-20-22000000000-112-42-24-20000001-1-24-22-42000000000000000000000000000000000000
χ8166-6-6-3-6633-333-3-32-20-22000000000-11-4224-2-20000001-14-2-2-422000000000000000000000000000000000000
χ8266-6-6-3-6633-333-3-3-6606-60000000003-3000000000000-33000000000000000000000000000000000000000000
χ8312-1212-12-600-66663−6363−63000000000000000000000000000000000000000000000000000000000000000000000000
χ8412-1212-12-600-666−6363−6363000000000000000000000000000000000000000000000000000000000000000000000000
χ8512-12-1212-6006-6663−63−6363000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-12-1212-6006-66−636363−63000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.