Finite Group Databasebeta

← Group #13150717

Character table — Group #13150717

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order122222344666466121212123366666666661212121236666666661212121212121212121212121212224444442244444466661212121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-111-1-11-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-11-1-11-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1111-111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-11-1-111111-1-1-1-11111-1-1-1-1-111-1
χ61111111-1-1111-111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11-11111-1-1-1-1-1-1-1-111111-1-11
χ71111111-1-1111-111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-11-1-1-1-1-1-111111111-1-1-1-11-1-11
χ81111111-1-1111-111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-11111-1-1-1-11111-111-1
χ91111-1-1111111-1-1-111-1-1111-1-1-1-11111111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-11-11-11-111-1-111-1-111-1-111-1-1-11-11
χ101111-1-1111111-1-1-111-1-1111-1-1-1-11111111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-11-11-1-1-1111-1-111-1-1-1-111-1-1111-11-1
χ111111-1-1111111-1-1-111-1-1111-1-1-1-11111111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1111-1-111-1-11111-1-111-1-11-11-1
χ121111-1-1111111-1-1-111-1-1111-1-1-1-11111111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-11111-1-1-1-111-1-111-1-111-1-111-11-11
χ131111-1-11-1-11111-1-1-1-111111-1-1-1-111111-1-1-1-11-1-111-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-1-11-1111-1-111-1-1-1-11111-1-1-1-11111-1-1
χ141111-1-11-1-11111-1-1-1-111111-1-1-1-111111-1-1-1-11-1-111-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-111-1-11-1-111111-1-1-1-111-1-11111-1-1-1-111
χ151111-1-11-1-11111-1-1-1-111111-1-1-1-111111-1-1-1-11-1-111-1-1-1-11-1-11111-1-1-1-11111-1-11111-1-11-111-1-1-11-1-11111-1-111-1-1-1-111-1-111
χ161111-1-11-1-11111-1-1-1-111111-1-1-1-111111-1-1-1-11-1-111-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1111111-1-11-11-1-1-11111-1-1-1-11111-1-111-1-1
χ1722222222222222222222-1-1-1-1-1-12-122-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12200220020000200-1-1-1-1-1-1-1-1000000000000
χ1822222222222222222222-1-1-1-1-1-12-122-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-200-2-200-20000-20011111111000000000000
χ192222222222222222222-1222222-12-1-12-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1002200220002002000000000-1-1-1-1-1-1-1-10000
χ202222222222222222222-1222222-12-1-12-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-100-2-200-2-2000-200-2000000000111111110000
χ212222222-2-2222-222-2-2-2-22-1-1-1-1-1-12-122-1-2-2-2-2-122-1-1-1-1-1-1-111-2-211111111112200-2-20020000-200-1-1-1-11111000000000000
χ222222222-2-2222-222-2-2-2-22-1-1-1-1-1-12-122-1-2-2-2-2-122-1-1-1-1-1-1-111-2-21111111111-2-2002200-200002001111-1-1-1-1000000000000
χ232222222-2-2222-222-2-2-2-2-1222222-12-1-121111-1-1-1-1-1-1-1-1-1-1-2-211-2-21111111100220022000-200-2000000000-1-1-1-111110000
χ242222222-2-2222-222-2-2-2-2-1222222-12-1-121111-1-1-1-1-1-1-1-1-1-1-2-211-2-21111111100-2-200-2-200020020000000001111-1-1-1-10000
χ252222-2-2222222-2-2-222-2-22-1-111112-122-12222-1-2-2-1-11111-1-1-1-2-211-1-1-1-1111122002200-20000-200-1-111-1-111000000000000
χ262222-2-2222222-2-2-222-2-22-1-111112-122-12222-1-2-2-1-11111-1-1-1-2-211-1-1-1-11111-2-200-2-2002000020011-1-111-1-1000000000000
χ272222-2-2222222-2-2-222-2-2-122-2-2-2-2-12-1-12-1-1-1-1-111-1-11111-12211-2-2-1-1-1-11111002200-2-2000-2002000000000-1-111-1-1110000
χ282222-2-2222222-2-2-222-2-2-122-2-2-2-2-12-1-12-1-1-1-1-111-1-11111-12211-2-2-1-1-1-1111100-2-20022000200-200000000011-1-111-1-10000
χ292222-2-22-2-22222-2-2-2-2222-1-111112-122-1-2-2-2-2-1-2-2-1-11111-11122-1-11111-1-1-1-12200-2-200-20000200-1-11111-1-1000000000000
χ302222-2-22-2-22222-2-2-2-2222-1-111112-122-1-2-2-2-2-1-2-2-1-11111-11122-1-11111-1-1-1-1-2-200220020000-20011-1-1-1-111000000000000
χ312222-2-22-2-22222-2-2-2-222-122-2-2-2-2-12-1-121111-111-1-11111-1-2-2-1-1221111-1-1-1-1002200-2-2000200-2000000000-1-11111-1-10000
χ322222-2-22-2-22222-2-2-2-222-122-2-2-2-2-12-1-121111-111-1-11111-1-2-2-1-1221111-1-1-1-100-2-20022000-200200000000011-1-1-1-1110000
χ3322-2-22-2200-2-2202-2000022-222-2-222-2-2-2000022-2-2-222-2-2200000000000000002i−2i002i−2i00000000000000002i−2i2i−2i00000000
χ3422-2-22-2200-2-2202-2000022-222-2-222-2-2-2000022-2-2-222-2-220000000000000000−2i2i00−2i2i0000000000000000−2i2i−2i2i00000000
χ3522-2-22-2200-2-2202-20000-12-222-2-2-1211-2−i3−i3i3i3-1-1111-1-111-100−i3i300−i3−i3i3i3−i3−i3i3i3002i−2i002i−2i0000000000000000−ii−ii3−33−30000
χ3622-2-22-2200-2-2202-20000-12-222-2-2-1211-2−i3−i3i3i3-1-1111-1-111-100−i3i300−i3−i3i3i3−i3−i3i3i300−2i2i00−2i2i0000000000000000i−ii−i−33−330000
χ3722-2-22-2200-2-2202-20000-12-222-2-2-1211-2i3i3−i3−i3-1-1111-1-111-100i3−i300i3i3−i3−i3i3i3−i3−i3002i−2i002i−2i0000000000000000−ii−ii−33−330000
χ3822-2-22-2200-2-2202-20000-12-222-2-2-1211-2i3i3−i3−i3-1-1111-1-111-100i3−i300i3i3−i3−i3i3i3−i3−i300−2i2i00−2i2i0000000000000000i−ii−i3−33−30000
χ3922-2-2-22200-2-220-22000022-2-2-22222-2-2-200002-22-2-2-2-222200000000000000002i−2i00−2i2i00000000000000002i−2i−2i2i00000000
χ4022-2-2-22200-2-220-22000022-2-2-22222-2-2-200002-22-2-2-2-22220000000000000000−2i2i002i−2i0000000000000000−2i2i2i−2i00000000
χ4122-2-2-22200-2-220-220000-12-2-2-222-1211-2−i3−i3i3i3-11-11111-1-1-100i3−i300−i3−i3i3i3i3i3−i3−i3002i−2i00−2i2i0000000000000000−iii−i3−3−330000
χ4222-2-2-22200-2-220-220000-12-2-2-222-1211-2−i3−i3i3i3-11-11111-1-1-100i3−i300−i3−i3i3i3i3i3−i3−i300−2i2i002i−2i0000000000000000i−i−ii−333−30000
χ4322-2-2-22200-2-220-220000-12-2-2-222-1211-2i3i3−i3−i3-11-11111-1-1-100−i3i300i3i3−i3−i3−i3−i3i3i3002i−2i00−2i2i0000000000000000−iii−i−333−30000
χ4422-2-2-22200-2-220-220000-12-2-2-222-1211-2i3i3−i3−i3-11-11111-1-1-100−i3i300i3i3−i3−i3−i3−i3i3i300−2i2i002i−2i0000000000000000i−i−ii3−3−330000
χ452-22-20022i−2i2-2-20002i−2i002220000-2-22-2-22i−2i2i−2i2002-20000-22i−2i00002i−2i2i−2i00002-2002i−2i00000000002-2002i−2i00000000000000
χ462-22-20022i−2i2-2-20002i−2i002220000-2-22-2-22i−2i2i−2i2002-20000-22i−2i00002i−2i2i−2i0000-2200−2i2i0000000000-2200−2i2i00000000000000
χ472-22-20022i−2i2-2-20002i−2i002-1-1−i3i3−i3i3-212-212i−2i2i−2i-100-11−i3i3−i3i31−ii003−3−ii−ii3−33−32-2002i−2i0000000000-11−i3i3−ii3−3000000000000
χ482-22-20022i−2i2-2-20002i−2i002-1-1−i3i3−i3i3-212-212i−2i2i−2i-100-11−i3i3−i3i31−ii003−3−ii−ii3−33−3-2200−2i2i00000000001-1i3−i3i−i−33000000000000
χ492-22-20022i−2i2-2-20002i−2i002-1-1i3−i3i3−i3-212-212i−2i2i−2i-100-11i3−i3i3−i31−ii00−33−ii−ii−33−332-2002i−2i0000000000-11i3−i3−ii−33000000000000
χ502-22-20022i−2i2-2-20002i−2i002-1-1i3−i3i3−i3-212-212i−2i2i−2i-100-11i3−i3i3−i31−ii00−33−ii−ii−33−33-2200−2i2i00000000001-1−i3i3i−i3−3000000000000
χ512-22-2002−2i2i2-2-2000−2i2i002220000-2-22-2-2−2i2i−2i2i2002-20000-2−2i2i0000−2i2i−2i2i00002-200−2i2i00000000002-200−2i2i00000000000000
χ522-22-2002−2i2i2-2-2000−2i2i002220000-2-22-2-2−2i2i−2i2i2002-20000-2−2i2i0000−2i2i−2i2i0000-22002i−2i0000000000-22002i−2i00000000000000
χ532-22-2002−2i2i2-2-2000−2i2i002-1-1−i3i3−i3i3-212-21−2i2i−2i2i-100-11−i3i3−i3i31i−i00−33i−ii−i−33−332-200−2i2i0000000000-11−i3i3i−i−33000000000000
χ542-22-2002−2i2i2-2-2000−2i2i002-1-1−i3i3−i3i3-212-21−2i2i−2i2i-100-11−i3i3−i3i31i−i00−33i−ii−i−33−33-22002i−2i00000000001-1i3−i3−ii3−3000000000000
χ552-22-2002−2i2i2-2-2000−2i2i002-1-1i3−i3i3−i3-212-21−2i2i−2i2i-100-11i3−i3i3−i31i−i003−3i−ii−i3−33−32-200−2i2i0000000000-11i3−i3i−i3−3000000000000
χ562-22-2002−2i2i2-2-2000−2i2i002-1-1i3−i3i3−i3-212-21−2i2i−2i2i-100-11i3−i3i3−i31i−i003−3i−ii−i3−33−3-22002i−2i00000000001-1−i3i3−ii−33000000000000
χ574444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000000000
χ584444444-4-4444-444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-222221-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ594444-4-4444444-4-4-444-4-4-2-2-22222-2-2-2-2-2-2-2-2-212211-1-1-1-11-2-222221111-1-1-1-1000000000000000000000000000000000000
χ604444-4-44-4-44444-4-4-4-444-2-2-22222-2-2-2-2-2222212211-1-1-1-1122-2-2-2-2-1-1-1-11111000000000000000000000000000000000000
χ6144-4-44-4400-4-4404-400004-22-2-2224-2-4-420000-24-422-2-222-200000000000000000000000000000000000000000000000000
χ6244-4-44-4400-4-4404-40000-2-22-2-222-2-2222−2i3−2i32i32i31-22-1-111-1-1100−2i32i300i3i3−i3−i3i3i3−i3−i3000000000000000000000000000000000000
χ6344-4-44-4400-4-4404-40000-2-22-2-222-2-22222i32i3−2i3−2i31-22-1-111-1-11002i3−2i300−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000000000
χ6444-4-4-44400-4-440-4400004-2222-2-24-2-4-420000-2-442222-2-2-200000000000000000000000000000000000000000000000000
χ6544-4-4-44400-4-440-440000-2-2222-2-2-2-2222−2i3−2i32i32i312-2-1-1-1-1111002i3−2i300i3i3−i3−i3−i3−i3i3i3000000000000000000000000000000000000
χ6644-4-4-44400-4-440-440000-2-2222-2-2-2-22222i32i3−2i3−2i312-2-1-1-1-111100−2i32i300−i3−i3i3i3i3i3−i3−i3000000000000000000000000000000000000
χ674-44-40044i−4i4-4-40004i−4i00-24400002-4-22-4−2i2i−2i2i-200-22000024i−4i0000−2i2i−2i2i0000000000000000000000000000000000000000
χ684-44-40044i−4i4-4-40004i−4i00-2-2-2−2i32i3−2i32i322-222−2i2i−2i2i1001-1i3−i3i3−i3-1−2i2i0023−23i−ii−i−33−33000000000000000000000000000000000000
χ694-44-40044i−4i4-4-40004i−4i00-2-2-22i3−2i32i3−2i322-222−2i2i−2i2i1001-1−i3i3−i3i3-1−2i2i00−2323i−ii−i3−33−3000000000000000000000000000000000000
χ704-44-4004−4i4i4-4-4000−4i4i00-24400002-4-22-42i−2i2i−2i-200-2200002−4i4i00002i−2i2i−2i0000000000000000000000000000000000000000
χ714-44-4004−4i4i4-4-4000−4i4i00-2-2-2−2i32i3−2i32i322-2222i−2i2i−2i1001-1i3−i3i3−i3-12i−2i00−2323−ii−ii3−33−3000000000000000000000000000000000000
χ724-44-4004−4i4i4-4-4000−4i4i00-2-2-22i3−2i32i3−2i322-2222i−2i2i−2i1001-1−i3i3−i3i3-12i−2i0023−23−ii−ii−33−33000000000000000000000000000000000000
χ734-4-4400400-44-4000000044-40000-4-4-4440000400-440000-400000000000000000000000000000000000000000000000000
χ744-4-4400400-44-400000004-22−2i32i32i3−2i3-42-44-20000-2002-2−2i32i32i3−2i3200000000000000000000000000000000000000000000000000
χ754-4-4400400-44-400000004-222i3−2i3−2i32i3-42-44-20000-2002-22i3−2i3−2i32i3200000000000000000000000000000000000000000000000000
χ764-4-4400400-44-40000000-24-400002-42-2423−23−2323-2002-20000200000023−23−23230000000000000000000000000000000000000000
χ774-4-4400400-44-40000000-24-400002-42-24−232323−23-2002-200002000000−232323−230000000000000000000000000000000000000000
χ784-4-4400400-44-40000000-2-22−2i32i32i3−2i3222-2-223−23−2323100-11i3−i3−i3i3-1000000−333−3−3i3i3i−3i000000000000000000000000000000000000
χ794-4-4400400-44-40000000-2-22−2i32i32i3−2i3222-2-2−232323−23100-11i3−i3−i3i3-10000003−3−333i−3i−3i3i000000000000000000000000000000000000
χ804-4-4400400-44-40000000-2-222i3−2i3−2i32i3222-2-223−23−2323100-11−i3i3i3−i3-1000000−333−33i−3i−3i3i000000000000000000000000000000000000
χ814-4-4400400-44-40000000-2-222i3−2i3−2i32i3222-2-2−232323−23100-11−i3i3i3−i3-10000003−3−33−3i3i3i−3i000000000000000000000000000000000000
χ82666666-366-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000022020020000000000000000-1-1-1-1
χ83666666-366-3-3-36-3-3-3-3-3-30000000000000000000000000000000000000000000000000-2-20-200-200000000000000001111
χ84666666-3-6-6-3-3-3-6-3-333330000000000000000000000000000000000000000000000000220-200-20000000000000000-111-1
χ85666666-3-6-6-3-3-3-6-3-333330000000000000000000000000000000000000000000000000-2-20200200000000000000001-1-11
χ866666-6-6-366-3-3-3-633-3-33300000000000000000000000000000000000000000000000002-20-20020000000000000000-11-11
χ876666-6-6-366-3-3-3-633-3-3330000000000000000000000000000000000000000000000000-220200-200000000000000001-11-1
χ886666-6-6-3-6-6-3-3-363333-3-300000000000000000000000000000000000000000000000002-20200-20000000000000000-1-111
χ896666-6-6-3-6-6-3-3-363333-3-30000000000000000000000000000000000000000000000000-220-2002000000000000000011-1-1
χ901212-12-1212-12-60066-60-6600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ911212-12-12-1212-60066-606-600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9212-1212-1200-612i−12i-666000−6i6i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9312-1212-1200-6−12i12i-6660006i−6i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-121200-6006-660000063−630000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-121200-6006-6600000−63630000000000000000000000000000000000000000000000000000000000000000000000000000

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