Finite Group Databasebeta

← Group #13168389

Character table — Group #13168389

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order122233366666666633346666666661212444436661212121212121212121212124444121212121212121212121212121212124412121212121212121212121212121212121212122244466661212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-11-1111111-1-1111111-1-1111111-11-11-1-1-1-111111111-1-11-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-1111111111-1-1-1-1-1-111-1-1-1-1-1-1111-11111-1-1-1-111111-1-11-111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-11-1-11-1-111-1-1-1111
χ51111111111111111111111111111111-1-1111111111111111111-1111-1-1-1-1-1-11111111111-1-1-1-1-1-11-11111111111-1-1-1-1-11-1-11-1-111-1-1-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-11-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-11-1-11-111-1-1-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-11-11-1-1-1-1-1-111-1-1-1-1-1-1111111111-11-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1111111-1-111-1-11111111-1-1-1-1-11111-1-111-1-11-1-1-1111-1-1-1-1-11-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-111-1-11111111111-1-11-111-1-111-1-111-1-1-11-11-1-1-111-1-11-11-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-11111-1-1111-1-1111111-1-11-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-1-11111-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1111-1-1-1-111111-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-111-111-1-111-1-1-1-111111-1-1111111-1-1-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-111-1-111-1-1-1-111111111-11-1-111-1-111-1-111-11-11-1-1-111-1-11-1-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1-1-1-1-111-1-111111111-111111-1-1-1-111-1-1111-1-1-1111-1-1-1-1-111-1
χ17222222-12-1222-1-1222-1-122-1-1-12-1-12-1222200-1-1-1-12-122-1-1-1-1-1-1-1-122022222-1-1-1-1000000220000002-1-10-1-1-1-10000-1-1-1-120020-1-10000-1000
χ18222222-12-1222-1-1222-1-122-1-1-12-1-12-1222200-1-1-1-12-122-1-1-1-1-1-1-1-12-20-22222-1-111000000-2-2000000-2-11011110000-1-1-1-1-200-201100001000
χ19222222-12-1222-1-1222-1-122-1-1-12-1-12-122-2-200-1-1-1-12-122-1-1-1-1-1-1-1-1-2202-2-2-2-211-1-10000002200000021-10-1-1-1-100001111-200-201100001000
χ20222222-12-1222-1-1222-1-122-1-1-12-1-12-122-2-200-1-1-1-12-122-1-1-1-1-1-1-1-1-2-20-2-2-2-2-21111000000-2-2000000-211011110000111120020-1-10000-1000
χ21222222-12-1222-1-1222-1-1-22-1-1-12-1-12-1-2-22200-1-1-1-1-21-2-211111111-220-222-2-2-1-1-1-1000000-2-2000000211011-1-10000-1-111200-20-1-100001000
χ22222222-12-1222-1-1222-1-1-22-1-1-12-1-12-1-2-22200-1-1-1-1-21-2-211111111-2-20222-2-2-1-11100000022000000-21-10-1-1110000-1-111-20020110000-1000
χ23222222-12-1222-1-1222-1-1-22-1-1-12-1-12-1-2-2-2-200-1-1-1-1-21-2-211111111220-2-2-22211-1-1000000-2-20000002-11011-1-1000011-1-1-20020110000-1000
χ24222222-12-1222-1-1222-1-1-22-1-1-12-1-12-1-2-2-2-200-1-1-1-1-21-2-2111111112-202-2-222111100000022000000-2-1-10-1-111000011-1-1200-20-1-100001000
χ2522222-12-12-122222-1-12-12-122-1-1-1-1-12220022-1-1-1-1-12-1-1-1-122-1-1-1-10222000000222222-1-1-1-1000000-102-1-1-1-1-1-1-1-1-100000200200-1-1000-100
χ2622222-12-12-122222-1-12-12-122-1-1-1-1-12220022-1-1-1-1-12-1-1-1-122-1-1-1-10-22-2000000-2-22222-1-11100000010-2-11111-1-1-1-100000-200-20011000100
χ2722222-12-12-122222-1-12-12-122-1-1-1-1-122200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-102-2200000022-2-2-2-211-1-1000000-1021-1-1-1-1111100000-200-20011000100
χ2822222-12-12-122222-1-12-12-122-1-1-1-1-122200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-10-2-2-2000000-2-2-2-2-2-2111100000010-211111111100000200200-1-1000-100
χ2922222-12-12-122222-1-12-1-2-122-1-1-1-1-12-2-20022-1-1-1-11-21111-2-2111102-2-20000002222-2-2-1-111000000-10-2111-1-1-1-11100000-20020011000-100
χ3022222-12-12-122222-1-12-1-2-122-1-1-1-1-12-2-20022-1-1-1-11-21111-2-211110-2-22000000-2-222-2-2-1-1-1-10000001021-1-111-1-11100000200-200-1-1000100
χ3122222-12-12-122222-1-12-1-2-122-1-1-1-1-12-2-200-2-2-1-1-1-11-21111-2-21111022-200000022-2-2221111000000-10-2-111-1-111-1-100000200-200-1-1000100
χ3222222-12-12-122222-1-12-1-2-122-1-1-1-1-12-2-200-2-2-1-1-1-11-21111-2-211110-222000000-2-2-2-22211-1-1000000102-1-1-11111-1-100000-20020011000-100
χ332222-122222-1-122-12-1-122-1-1-12-122-1-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-12020-1-1-1-12200-1-1-1-1220022-1-1-1-102020000-1-1-1-1-1-1-1-1002000000-1-10000
χ342222-122222-1-122-12-1-122-1-1-12-122-1-1-1-122-2-2-1-1-1-122-1-122-1-1-1-1-1-120-20-1-1-1-122001111-2-200-2-21111020-200001111-1-1-1-100-2000000110000
χ352222-122222-1-122-12-1-122-1-1-12-122-1-1-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-1-20201111-2-200-1-1-1-12200-2-211110-2020000-1-1-1-1111100-2000000110000
χ362222-122222-1-122-12-1-122-1-1-12-122-1-1-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-1-20-201111-2-2001111-2-20022-1-1-1-10-20-2000011111111002000000-1-10000
χ372222-122222-1-122-12-1-12-2-1-1-12-122-1-1112222-1-1-1-1-2-211-2-2111111-20-20-1-1112200-1-111220022-1-1-1-10-20-20000-1-111-1-11100-2000000110000
χ382222-122222-1-122-12-1-12-2-1-1-12-122-1-11122-2-2-1-1-1-1-2-211-2-2111111-2020-1-111220011-1-1-2-200-2-211110-202000011-1-1-1-111002000000-1-10000
χ392222-122222-1-122-12-1-12-2-1-1-12-122-1-111-2-222-1-1-1-1-2-211-2-211111120-2011-1-1-2-200-1-1112200-2-21111020-20000-1-11111-1-1002000000-1-10000
χ402222-122222-1-122-12-1-12-2-1-1-12-122-1-111-2-2-2-2-1-1-1-1-2-211-2-2111111202011-1-1-2-20011-1-1-2-20022-1-1-1-10202000011-1-111-1-100-2000000110000
χ4122-2-2222-2-222-22-2-2-22220-2-2-2-22-22-22002-22i−2i2-2-2200000000000000002-2002-2002i−2i002i−2i002i−2i2i2i−2i−2i000000002i−2i002-200000000000000000
χ4222-2-2222-2-222-22-2-2-22220-2-2-2-22-22-22002-2−2i2i2-2-2200000000000000002-2002-200−2i2i00−2i2i00−2i2i−2i−2i2i2i00000000−2i2i002-200000000000000000
χ4322-2-2222-2-222-22-2-2-22220-2-2-2-22-22-2200-222i−2i2-2-220000000000000000-2200-22002i−2i002i−2i00−2i2i−2i−2i2i2i000000002i−2i00-2200000000000000000
χ4422-2-2222-2-222-22-2-2-22220-2-2-2-22-22-2200-22−2i2i2-2-220000000000000000-2200-2200−2i2i00−2i2i002i−2i2i2i−2i−2i00000000−2i2i00-2200000000000000000
χ4522-2-2-122-2-22-112-21-2-1-120111-2-1-221-1−i3i32-22i−2i-111-100−i3i300−i3i3−i3−i3i3i30000-11−i3i32-200−ii3−32i−2i002i−2i−i−iii00000000−ii3−3-11−i3i30000000003−30000
χ4622-2-2-122-2-22-112-21-2-1-120111-2-1-221-1−i3i32-2−2i2i-111-100−i3i300−i3i3−i3−i3i3i30000-11−i3i32-200i−i−33−2i2i00−2i2iii−i−i00000000i−i−33-11−i3i3000000000−330000
χ4722-2-2-122-2-22-112-21-2-1-120111-2-1-221-1−i3i3-222i−2i-111-100−i3i300−i3i3−i3−i3i3i300001-1i3−i3-2200−ii3−32i−2i00−2i2iii−i−i00000000−ii3−31-1i3−i3000000000−330000
χ4822-2-2-122-2-22-112-21-2-1-120111-2-1-221-1−i3i3-22−2i2i-111-100−i3i300−i3i3−i3−i3i3i300001-1i3−i3-2200i−i−33−2i2i002i−2i−i−iii00000000i−i−331-1i3−i30000000003−30000
χ4922-2-2-122-2-22-112-21-2-1-120111-2-1-221-1i3−i32-22i−2i-111-100i3−i300i3−i3i3i3−i3−i30000-11i3−i32-200−ii−332i−2i002i−2i−i−iii00000000−ii−33-11i3−i3000000000−330000
χ5022-2-2-122-2-22-112-21-2-1-120111-2-1-221-1i3−i32-2−2i2i-111-100i3−i300i3−i3i3i3−i3−i30000-11i3−i32-200i−i3−3−2i2i00−2i2iii−i−i00000000i−i3−3-11i3−i30000000003−30000
χ5122-2-2-122-2-22-112-21-2-1-120111-2-1-221-1i3−i3-222i−2i-111-100i3−i300i3−i3i3i3−i3−i300001-1−i3i3-2200−ii−332i−2i00−2i2iii−i−i00000000−ii−331-1−i3i30000000003−30000
χ5222-2-2-122-2-22-112-21-2-1-120111-2-1-221-1i3−i3-22−2i2i-111-100i3−i300i3−i3i3i3−i3−i300001-1−i3i3-2200i−i3−3−2i2i002i−2i−i−iii00000000i−i3−31-1−i3i3000000000−330000
χ5344444-2-2-2-2-244-2-24-2-2-214-2-2-21-211-2-24400001111-2-2-2-211-2-211110404000000-2-2000000-2-2000000-20-20111100000000000000000000000
χ5444444-2-2-2-2-244-2-24-2-2-214-2-2-21-211-2-24400001111-2-2-2-211-2-211110-40-400000022000000220000002020-1-1-1-100000000000000000000000
χ5544444-2-2-2-2-244-2-24-2-2-21-4-2-2-21-211-2-2-4-4000011112222-1-122-1-1-1-1040-4000000-2-200000022000000-2020-1-11100000000000000000000000
χ5644444-2-2-2-2-244-2-24-2-2-21-4-2-2-21-211-2-2-4-4000011112222-1-122-1-1-1-10-40400000022000000-2-200000020-2011-1-100000000000000000000000
χ574444-24-24-24-2-2-2-2-24-21-24-211-2-2-2-2-21-2-2440011114-2-2-2-2-21111114000-2-2-2-2-2-200000000000000000-200000000001111000000000000000
χ584444-24-24-24-2-2-2-2-24-21-24-211-2-2-2-2-21-2-2-4-40011114-2-2-2-2-2111111-40002222220000000000000000020000000000-1-1-1-1000000000000000
χ594444-24-24-24-2-2-2-2-24-21-2-4-211-2-2-2-2-212244001111-422222-1-1-1-1-1-1-4000-2-222-2-2000000000000000002000000000011-1-1000000000000000
χ604444-24-24-24-2-2-2-2-24-21-2-4-211-2-2-2-2-2122-4-4001111-422222-1-1-1-1-1-1400022-2-22200000000000000000-20000000000-1-111000000000000000
χ614444-2-24-24-2-2-244-2-21-2-241-2-2-21-2-21-2-2-200441111-2411-2-2-2-21111004000000000-2-2-2-2-2-200000000000-2000011110000000000000000000
χ624444-2-24-24-2-2-244-2-21-2-241-2-2-21-2-21-2-2-200-4-41111-2411-2-2-2-2111100-40000000002222220000000000020000-1-1-1-10000000000000000000
χ634444-2-24-24-2-2-244-2-21-2-2-41-2-2-21-2-21-222004411112-4-1-12222-1-1-1-100-4000000000-2-222-2-2000000000002000011-1-10000000000000000000
χ644444-2-24-24-2-2-244-2-21-2-2-41-2-2-21-2-21-22200-4-411112-4-1-12222-1-1-1-100400000000022-2-22200000000000-20000-1-1110000000000000000000
χ6544-4-444-2-4244-4-22-4-44-2-20-422242-2-4-2004-400-222-200000000000000004-400-220000000000000000000000000000-2200000000000000000
χ6644-4-444-2-4244-4-22-4-44-2-20-422242-2-4-200-4400-222-20000000000000000-44002-200000000000000000000000000002-200000000000000000
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χ6944-4-4-24-2-424-22-222-4-21-202-1-12-22-221−2i32i34-4001-1-1100−2i32i300i3−i3i3i3−i3−i30000-22−2i32i3-2200000000000000000000000000001-1i3−i3000000000000000
χ7044-4-4-24-2-424-22-222-4-21-202-1-12-22-221−2i32i3-44001-1-1100−2i32i300i3−i3i3i3−i3−i300002-22i3−2i32-20000000000000000000000000000-11−i3i3000000000000000
χ7144-4-4-24-2-424-22-222-4-21-202-1-12-22-2212i3−2i34-4001-1-11002i3−2i300−i3i3−i3−i3i3i30000-222i3−2i3-2200000000000000000000000000001-1−i3i3000000000000000
χ7244-4-4-24-2-424-22-222-4-21-202-1-12-22-2212i3−2i3-44001-1-11002i3−2i300−i3i3−i3−i3i3i300002-2−2i32i32-20000000000000000000000000000-11i3−i3000000000000000
χ7344-4-4-2-242-4-2-224-4221-2-20-122212-2-1-2−2i32i3004i−4i1-1-1100i3−i300−2i32i3i3i3−i3−i3000000000000−2i2i23−23−2i2i0000000000000000i−i−330000000000000000000
χ7444-4-4-2-242-4-2-224-4221-2-20-122212-2-1-2−2i32i300−4i4i1-1-1100i3−i300−2i32i3i3i3−i3−i30000000000002i−2i−23232i−2i0000000000000000−ii3−30000000000000000000
χ7544-4-4-2-242-4-2-224-4221-2-20-122212-2-1-22i3−2i3004i−4i1-1-1100−i3i3002i3−2i3−i3−i3i3i3000000000000−2i2i−2323−2i2i0000000000000000i−i3−30000000000000000000
χ7644-4-4-2-242-4-2-224-4221-2-20-122212-2-1-22i3−2i300−4i4i1-1-1100−i3i3002i3−2i3−i3−i3i3i30000000000002i−2i23−232i−2i0000000000000000−ii−330000000000000000000
χ774-44-444444-4-44-4-4-4-4444044-44-4-4-4-4-400000044-4-4000000000000000000000000000000000000000000000000000000000000000000000
χ784-44-444-24-2-4-4422-4-44-2-204-22-2-422-42000000-2-22200000000000000000000000000000000000000000000000000000000000−2i32i300000000
χ794-44-444-24-2-4-4422-4-44-2-204-22-2-422-42000000-2-222000000000000000000000000000000000000000000000000000000000002i3−2i300000000
χ804-44-44-24-242-44-4-4-42-24-20-24-4-22222-4000000-2-2220000000000000000000000000000000000000000000000000000000000000−2i32i3000000
χ814-44-44-24-242-44-4-4-42-24-20-24-4-22222-4000000-2-22200000000000000000000000000000000000000000000000000000000000002i3−2i3000000
χ824-44-4-24444-42-2-4-42-4-2-240-2-2242-4-422000000-2-2220000000000000000000000000000000000−2i32i3−2i32i30000000000000000000000000000000
χ834-44-4-24444-42-2-4-42-4-2-240-2-2242-4-422000000-2-22200000000000000000000000000000000002i3−2i32i3−2i30000000000000000000000000000000
χ844-4-44444-4-4-4-4-4-44444440-4-44-4-44-44-40000004-44-4000000000000000000000000000000000000000000000000000000000000000000000
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χ864-4-4444-2-42-4-4-42-2444-2-20-42-22-4-2242000000-22-220000000000000000000000−232300000000000000000000−232300000000000000000000000
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χ894-4-444-2-2222-4-42-24-2-2-21022-2-121-1-220000001-11-100003i−3i003i−3i3i−3i000000000023−23000000−2i32i30000000000i3−i3−3300000000000000000000000
χ904-4-444-2-2222-4-42-24-2-2-21022-2-121-1-220000001-11-100003i−3i003i−3i3i−3i0000000000−23230000002i3−2i30000000000−i3i33−300000000000000000000000
χ914-4-444-2-2222-4-42-24-2-2-21022-2-121-1-220000001-11-10000−3i3i00−3i3i−3i3i000000000023−230000002i3−2i30000000000−i3i3−3300000000000000000000000
χ924-4-444-2-2222-4-42-24-2-2-21022-2-121-1-220000001-11-10000−3i3i00−3i3i−3i3i0000000000−2323000000−2i32i30000000000i3−i33−300000000000000000000000
χ934-4-44-244-4-4-422-44-24-2-24022-2-424-4-22000000-22-22000000000000000000000000000000000023−23−23230000000000000000000000000000000
χ944-4-44-244-4-4-422-44-24-2-24022-2-424-4-22000000-22-220000000000000000000000000000000000−232323−230000000000000000000000000000000
χ958888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ968888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000
χ9788-8-88-4-444-48-8-44-84-4-420444-2-4-224-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-444-4-44-44442220-2-2-2-22-22-22−4i34i30000-111-1002i3−2i3002i3−2i3−i3−i3i3i3000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-444-4-44-44442220-2-2-2-22-22-224i3−4i30000-111-100−2i32i300−2i32i3i3i3−i3−i3000000000000000000000000000000000000000000000000000000000
χ1008-88-88-4-4-4-44-8844-84-4-420-4-4424-2-24400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-48-48-4-84-4444-8-42-40-42-2-44444-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-48-4844-4-8-8442-4-402-44-4-244-2400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-4-4-444-44444222022-22-2-2-2-2-2000000-1-1110000000033−33−3333000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-4-4-444-44444222022-22-2-2-2-2-2000000-1-11100000000−333333−33000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-4-84-8444-4-48-42-404-2244-44-4-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-484-8444-88-4-42-4-40-24-44-2-44240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4444444-4-4-42220-2-22-2-22-22-2000000-11-1100006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4444444-4-4-42220-2-22-2-22-22-2000000-11-110000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000000

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