Finite Group Databasebeta

← Group #13172031

Character table — Group #13172031

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order122233366666666623336666666666622443666666666666666444466661212121212121212121212124412121212661212121212121212121212121212224441212121212126624
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-11-11111111111-1-1-1-111111111111-11-1111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-11111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-1-111111-11-1-111-1-1-1-1-11-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-1-1-1-11-11-1-1-111-1-11-111
χ51111111111111111111111111111111-1-1111111111111111111-1111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111-1-111111111-11-11-1-1-111-1-11-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-11-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-11-11-1-111-1-1-1-1-1111
χ71111111111111111111111111111111-1-1-1-11111111111111111-11-11-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-11-11-1-1-1-1-1-11111-1-1-1-11-1-1-1-111-1-111
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
χ91111111111111111-1111-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-1-11111-1-111-1-111-1-11111111111-11-1-1-1-111-1-111-1-11-1-11-1-1-111-1-1-11-11
χ101111111111111111-1111-1-111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111111-1-111-1-1-1-1111111111111-1-1-11-1-111-1-1-1-111-111-1-111-1-1-1-11-11-1
χ111111111111111111-1111-1-111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-111-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-11111-1-111-1-11-1-1-1-111111-1
χ121111111111111111-1111-1-111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-1111111111-1-1-11
χ131111111111111111-1111-1-1111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1111111111-1-11-1
χ141111111111111111-1111-1-1111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-11-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1-111111-1-1-1-11111-1-11-1-1-1-11111-11
χ151111111111111111-1111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1-111-1-11111-1-1-1-1111111-1-1111-111-1-11111-1-1-111-1-111-1-1-1-11-1-11
χ161111111111111111-1111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-111-1-1-1-111-1-111-1-111-1-1111111-1-11-11111-1-111-1-1111-1-11-1-1-111-1-1-111-1
χ17222222-1-12222-1-12222-1-1222-1-1-122-1-1-12200-12-122-1-1-1-1-1-1-1-1-1-1-1220222-1-122000022-1-100000000-1-1-1-102-1-10000-1-1-1-120200-1-100000-100
χ18222222-1-12222-1-12222-1-1222-1-1-122-1-1-12200-12-122-1-1-1-1-1-1-1-1-1-1-12-20-222-1-1220000-2-21100000000-1-1-110-2-1-100001111-20-2001100000100
χ19222222-1-12222-1-12222-1-1222-1-1-122-1-1-1-2-200-12-122-1-1-1-1-1-1-1-1-1-1-1-2202-2-211-2-2000022-1-100000000111-102110000-1-1-1-1-20-2001100000100
χ20222222-1-12222-1-12222-1-1222-1-1-122-1-1-1-2-200-12-122-1-1-1-1-1-1-1-1-1-1-1-2-20-2-2-211-2-20000-2-2110000000011110-2110000111120200-1-100000-100
χ21222222-1-12222-1-122-22-1-1-2-22-1-1-122-1-1-12200-1-21-2-21111-1-1-11111-220-222-1-1-2-20000221100000000-1-11-10-2110000-1-11120-2001100000-100
χ22222222-1-12222-1-122-22-1-1-2-22-1-1-122-1-1-12200-1-21-2-21111-1-1-11111-2-20222-1-1-2-20000-2-2-1-100000000-1-1110211000011-1-1-20200-1-100000100
χ23222222-1-12222-1-122-22-1-1-2-22-1-1-122-1-1-1-2-200-1-21-2-21111-1-1-11111220-2-2-21122000022110000000011-1-10-2-1-10000-1-111-20200-1-100000100
χ24222222-1-12222-1-122-22-1-1-2-22-1-1-122-1-1-1-2-200-1-21-2-21111-1-1-111112-202-2-211220000-2-2-1-10000000011-1102-1-1000011-1-120-2001100000-100
χ2522222-12222-1-122-122-1-1222-1-122-1-1-1-120022-1-12-1-1-1-122-1-1-1-1-1-1-10222000000-1-122-1-122220000000002-1-100-1-1-1-1-1-1-1-10202000-1-100-1000
χ2622222-12222-1-122-122-1-1222-1-122-1-1-1-120022-1-12-1-1-1-122-1-1-1-1-1-1-10-22-2000000-1-12211-2-222000000000-2-1100-1-1-1-111110-20-200011001000
χ2722222-12222-1-122-122-1-1222-1-122-1-1-1-1200-2-2-1-12-1-1-1-122-1-1-1-1-1-1-102-2200000011-2-2-1-122-2-200000000021-1001111-1-1-1-10-20-200011001000
χ2822222-12222-1-122-122-1-1222-1-122-1-1-1-1200-2-2-1-12-1-1-1-122-1-1-1-1-1-1-10-2-2-200000011-2-211-2-2-2-2000000000-21100111111110202000-1-100-1000
χ2922222-12222-1-122-12-2-1-12-2-2-1-122-1-1-1-120022-11-21111-2-2-1-1-1111102-2-2000000-1-1-2-2-1-1-2-22200000000021100-1-111-1-1110-202000-1-1001000
χ3022222-12222-1-122-12-2-1-12-2-2-1-122-1-1-1-120022-11-21111-2-2-1-1-111110-2-22000000-1-1-2-2112222000000000-21-100-1-11111-1-1020-20001100-1000
χ3122222-12222-1-122-12-2-1-12-2-2-1-122-1-1-1-1200-2-2-11-21111-2-2-1-1-11111022-20000001122-1-1-2-2-2-20000000002-110011-1-1-1-111020-20001100-1000
χ3222222-12222-1-122-12-2-1-12-2-2-1-122-1-1-1-1200-2-2-11-21111-2-2-1-1-111110-22200000011221122-2-2000000000-2-1-10011-1-111-1-10-202000-1-1001000
χ332222-1222-1-122222-12-12-1-1-1-12-1-1-1-122-12222-122-1-122-1-1-1-1-1-1-1-1-12020-1-122-1-122-1-10000-1-122-1-1-1-1-1-12020-1-1-1-1-1-10000000020000-1-10000
χ342222-1222-1-122222-12-12-1-1-1-12-1-1-1-122-122-2-2-122-1-122-1-1-1-1-1-1-1-1-120-20-1-122-1-1-2-211000011-2-21111-1-120-20-1-1111100000000-20000110000
χ352222-1222-1-122222-12-12-1-1-1-12-1-1-1-122-1-2-222-122-1-122-1-1-1-1-1-1-1-1-1-202011-2-21122-1-10000-1-1-2-2111111-202011-1-1-1-100000000-20000110000
χ362222-1222-1-122222-12-12-1-1-1-12-1-1-1-122-1-2-2-2-2-122-1-122-1-1-1-1-1-1-1-1-1-20-2011-2-211-2-21100001122-1-1-1-111-20-201111110000000020000-1-10000
χ372222-1222-1-122222-1-2-12-111-12-1-1-1-122-12222-1-2-211-2-211-1-1-11111-20-20-1-1221122110000-1-122-1-1-1-1-1-1-20-2011-1-11100000000-20000110000
χ382222-1222-1-122222-1-2-12-111-12-1-1-1-122-122-2-2-1-2-211-2-211-1-1-11111-2020-1-12211-2-2-1-1000011-2-21111-1-1-20201111-1-10000000020000-1-10000
χ392222-1222-1-122222-1-2-12-111-12-1-1-1-122-1-2-222-1-2-211-2-211-1-1-1111120-2011-2-2-1-122110000-1-1-2-211111120-20-1-1-1-1110000000020000-1-10000
χ402222-1222-1-122222-1-2-12-111-12-1-1-1-122-1-2-2-2-2-1-2-211-2-211-1-1-11111202011-2-2-1-1-2-2-1-100001122-1-1-1-1112020-1-111-1-100000000-20000110000
χ4122-2-2222-22-22-22-2-2-20222002-2-2-2-2-22-222-22i−2i2000000002-2-2000000002-22-2002i−2i0000002i−2i2i−2i2i2i−2i−2i2-20000002i−2i000000000000000000000
χ4222-2-2222-22-22-22-2-2-20222002-2-2-2-2-22-222-2−2i2i2000000002-2-2000000002-22-200−2i2i000000−2i2i−2i2i−2i−2i2i2i2-2000000−2i2i000000000000000000000
χ4322-2-2222-22-22-22-2-2-20222002-2-2-2-2-22-22-222i−2i2000000002-2-200000000-22-22002i−2i0000002i−2i−2i2i−2i−2i2i2i-220000002i−2i000000000000000000000
χ4422-2-2222-22-22-22-2-2-20222002-2-2-2-2-22-22-22−2i2i2000000002-2-200000000-22-2200−2i2i000000−2i2i2i−2i2i2i−2i−2i-22000000−2i2i000000000000000000000
χ4522-2-2-122-2-112-22-2-210-12-1−i3i3-1-211112-2-12-22i−2i-100−i3i300−i3i3-111−i3−i3i3i30000-112-2−i3i32i−2i3−30000−ii2i−2i−i−iii-110000−i3i3−ii3−300000000000003−30000
χ4622-2-2-122-2-112-22-2-210-12-1−i3i3-1-211112-2-12-2−2i2i-100−i3i300−i3i3-111−i3−i3i3i30000-112-2−i3i3−2i2i−330000i−i−2i2iii−i−i-110000−i3i3i−i−330000000000000−330000
χ4722-2-2-122-2-112-22-2-210-12-1−i3i3-1-211112-2-1-222i−2i-100−i3i300−i3i3-111−i3−i3i3i300001-1-22i3−i32i−2i3−30000−ii−2i2iii−i−i1-10000i3−i3−ii3−30000000000000−330000
χ4822-2-2-122-2-112-22-2-210-12-1−i3i3-1-211112-2-1-22−2i2i-100−i3i300−i3i3-111−i3−i3i3i300001-1-22i3−i3−2i2i−330000i−i2i−2i−i−iii1-10000i3−i3i−i−3300000000000003−30000
χ4922-2-2-122-2-112-22-2-210-12-1i3−i3-1-211112-2-12-22i−2i-100i3−i300i3−i3-111i3i3−i3−i30000-112-2i3−i32i−2i−330000−ii2i−2i−i−iii-110000i3−i3−ii−330000000000000−330000
χ5022-2-2-122-2-112-22-2-210-12-1i3−i3-1-211112-2-12-2−2i2i-100i3−i300i3−i3-111i3i3−i3−i30000-112-2i3−i3−2i2i3−30000i−i−2i2iii−i−i-110000i3−i3i−i3−300000000000003−30000
χ5122-2-2-122-2-112-22-2-210-12-1i3−i3-1-211112-2-1-222i−2i-100i3−i300i3−i3-111i3i3−i3−i300001-1-22−i3i32i−2i−330000−ii−2i2iii−i−i1-10000−i3i3−ii−3300000000000003−30000
χ5222-2-2-122-2-112-22-2-210-12-1i3−i3-1-211112-2-1-22−2i2i-100i3−i300i3−i3-111i3i3−i3−i300001-1-22−i3i3−2i2i3−30000i−i2i−2i−i−iii1-10000−i3i3i−i3−30000000000000−330000
χ5344444-2-2-244-2-2-2-2-244-21-244-21-2-2-2-211-200001-2-2-2-211-2-2111111104040000000000-2-2-2-200000000000-20-20000001111000000000000000
χ5444444-2-2-244-2-2-2-2-244-21-244-21-2-2-2-211-200001-2-2-2-211-2-211111110-40-40000000000222200000000000202000000-1-1-1-1000000000000000
χ5544444-2-2-244-2-2-2-2-24-4-21-2-4-4-21-2-2-2-211-2000012222-1-122111-1-1-1-1040-40000000000-2-22200000000000-20200000011-1-1000000000000000
χ5644444-2-2-244-2-2-2-2-24-4-21-2-4-4-21-2-2-2-211-2000012222-1-122111-1-1-1-10-404000000000022-2-20000000000020-2000000-1-111000000000000000
χ574444-24-2-2-2-244-2-24-24-2-21-2-2-2-211-2-2-2-21440014-2-2-2-2-21111111114000-2-2-2-2-2-2000000000000000011-20001100000000000000000000000
χ584444-24-2-2-2-244-2-24-24-2-21-2-2-2-211-2-2-2-21-4-40014-2-2-2-2-2111111111-40002222220000000000000000-1-12000-1-100000000000000000000000
χ594444-24-2-2-2-244-2-24-2-4-2-2122-2-211-2-2-2-2144001-422222-1-1111-1-1-1-1-4000-2-2-2-2220000000000000000112000-1-100000000000000000000000
χ604444-24-2-2-2-244-2-24-2-4-2-2122-2-211-2-2-2-21-4-4001-422222-1-1111-1-1-1-140002222-2-20000000000000000-1-1-20001100000000000000000000000
χ614444-2-244-2-2-2-244-2-241-2-2-2-21-2-2-211-2-2-200441-2411-2-2-2-211111110040000000-2-2-2-20000-2-20000000000-200011110000000000000000000
χ624444-2-244-2-2-2-244-2-241-2-2-2-21-2-2-211-2-2-200-4-41-2411-2-2-2-2111111100-40000000222200002200000000002000-1-1-1-10000000000000000000
χ634444-2-244-2-2-2-244-2-2-41-2-2221-2-2-211-2-2-2004412-4-1-12222111-1-1-1-100-40000000-2-2220000-2-20000000000200011-1-10000000000000000000
χ644444-2-244-2-2-2-244-2-2-41-2-2221-2-2-211-2-2-200-4-412-4-1-12222111-1-1-1-1004000000022-2-20000220000000000-2000-1-1110000000000000000000
χ6544-4-444-224-44-4-22-4-404-2-2004222-4-4-22-24-400-200000000-222000000004-4-22000000000000000000-2200000000000000000000000000000
χ6644-4-444-224-44-4-22-4-404-2-2004222-4-4-22-2-4400-200000000-22200000000-442-20000000000000000002-200000000000000000000000000000
χ6744-4-44-24-44-4-224-42-40-2-2400-22-4-422-224004i−4i-200000000-22200000000000000−2i2i0000004i−4i00000000000000−2i2i000000000000000000000
χ6844-4-44-24-44-4-224-42-40-2-2400-22-4-422-22400−4i4i-200000000-222000000000000002i−2i000000−4i4i000000000000002i−2i000000000000000000000
χ6944-4-4-24-22-224-4-22-420-2-21−2i32i3-22-1-122-2214-400100−2i32i300i3−i31-1-1i3i3−i3−i30000-22-22−2i32i300000000000000001-10000i3−i300000000000000000000000
χ7044-4-4-24-22-224-4-22-420-2-21−2i32i3-22-1-122-221-4400100−2i32i300i3−i31-1-1i3i3−i3−i300002-22-22i3−2i30000000000000000-110000−i3i300000000000000000000000
χ7144-4-4-24-22-224-4-22-420-2-212i3−2i3-22-1-122-2214-4001002i3−2i300−i3i31-1-1−i3−i3i3i30000-22-222i3−2i300000000000000001-10000−i3i300000000000000000000000
χ7244-4-4-24-22-224-4-22-420-2-212i3−2i3-22-1-122-221-44001002i3−2i300−i3i31-1-1−i3−i3i3i300002-22-2−2i32i30000000000000000-110000i3−i300000000000000000000000
χ7344-4-4-2-24-4-22-224-42201-2-2−2i32i31222-1-1-22-2004i−4i100i3−i300−2i32i31-1-1i3i3−i3−i30000000000−2i2i23−230000−2i2i00000000000000i−i−330000000000000000000
χ7444-4-4-2-24-4-22-224-42201-2-2−2i32i31222-1-1-22-200−4i4i100i3−i300−2i32i31-1-1i3i3−i3−i300000000002i−2i−232300002i−2i00000000000000−ii3−30000000000000000000
χ7544-4-4-2-24-4-22-224-42201-2-22i3−2i31222-1-1-22-2004i−4i100−i3i3002i3−2i31-1-1−i3−i3i3i30000000000−2i2i−23230000−2i2i00000000000000i−i3−30000000000000000000
χ7644-4-4-2-24-4-22-224-42201-2-22i3−2i31222-1-1-22-200−4i4i100−i3i3002i3−2i31-1-1−i3−i3i3i300000000002i−2i23−2300002i−2i00000000000000−ii−330000000000000000000
χ774-44-4444-4-44-4-4-444-4044400-4-44-44-4-44-40000400000000-44-40000000000000000000000000000000000000000000000000000000000000
χ784-44-444-22-44-4-42-24-404-2-200-42-224-42-220000-2000000002-22000000000000000000000000000000000000000000000000000−2i32i300000000
χ794-44-444-22-44-4-42-24-404-2-200-42-224-42-220000-2000000002-220000000000000000000000000000000000000000000000000002i3−2i300000000
χ804-44-44-24-4-4422-44-2-40-2-2400224-4-222-2-40000-2000000002-2200000000000000000000000000000000000000000000000000000−2i32i3000000
χ814-44-44-24-4-4422-44-2-40-2-2400224-4-222-2-40000-2000000002-22000000000000000000000000000000000000000000000000000002i3−2i3000000
χ824-44-4-244-42-2-4-4-44420-24-2002-4-22-22-4420000-2000000002-220000000000000000000000000023−2323−230000000000000000000000000000000
χ834-44-4-244-42-2-4-4-44420-24-2002-4-22-22-4420000-2000000002-2200000000000000000000000000−2323−23230000000000000000000000000000000
χ844-4-444444-4-4-44-4-4-44044400-44-44-44-4-4-40000400000000-4-440000000000000000000000000000000000000000000000000000000000000
χ854-4-4444-2-2-4-4-4422-4404-2-200-4-22-2-442220000-20000000022-20000000000000000000023−23000000000000000000000023−23000000000000000
χ864-4-4444-2-2-4-4-4422-4404-2-200-4-22-2-442220000-20000000022-200000000000000000000−23230000000000000000000000−2323000000000000000
χ874-4-444-244-4-42-2-4-4240-2-24002-2-442-222-40000-20000000022-200000000000000000023−23000000000000000000000023−2300000000000000000
χ884-4-444-244-4-42-2-4-4240-2-24002-2-442-222-40000-20000000022-2000000000000000000−23230000000000000000000000−232300000000000000000
χ894-4-444-2-2-2-4-42-222240-21-200212-22-2-1-120000100003-300-1-113-33-30000000000000023−2323−2300000000000000000000−33−33000000000000000
χ904-4-444-2-2-2-4-42-222240-21-200212-22-2-1-120000100003-300-1-113-33-300000000000000−2323−2323000000000000000000003−33−3000000000000000
χ914-4-444-2-2-2-4-42-222240-21-200212-22-2-1-12000010000-3300-1-11-33-330000000000000023−23−232300000000000000000000−333−3000000000000000
χ924-4-444-2-2-2-4-42-222240-21-200212-22-2-1-12000010000-3300-1-11-33-3300000000000000−232323−23000000000000000000003−3−33000000000000000
χ934-4-44-244422-44-4-4-4-20-24-200242-22-2-4-420000-20000000022-200000000000000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ944-4-44-244422-44-4-4-4-20-24-200242-22-2-4-420000-20000000022-2000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ958888-4-4-4-4-4-4-4-4-4-4-4-48222-4-42222222220000-1-4-4222222-1-1-1-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ968888-4-4-4-4-4-4-4-4-4-4-4-4-8222442222222220000-144-2-2-2-2-2-2-1-1-11111000000000000000000000000000000000000000000000000000000000
χ9788-8-88-4-448-8-44-444-80-42-400-4-244442-2-400002000000002-2-20000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-44-44-44-44440222−4i34i32-2-2-2-2-22-220000-1002i3−2i3002i3−2i3-111−i3−i3i3i3000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-44-44-44-444402224i3−4i32-2-2-2-2-22-220000-100−2i32i300−2i32i3-111i3i3−i3−i3000000000000000000000000000000000000000000000000000000000
χ1008-88-88-4-44-88444-4-4-80-42-4004-2-44-44-2240000200000000-22-20000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-48-444-4-8-84-4840-4-4200442-2-444-4-20000200000000-22-20000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-48-84-444-88-4402-4-400-24-442-24-440000200000000-22-20000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-444-4444-4-44022200-2-22-22-2-22-20000-1000000001-11−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-444-4444-4-44022200-2-22-22-2-22-20000-1000000001-113i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-4-444-8844-8-40-4-42004-4-224-444-20000200000000-2-220000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-488444-4-8-84-402-4-400-2-44-4-224440000200000000-2-220000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4-4444-4444-4022200-22-22-22-2-2-20000-100006-60011-1-33-33000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-4444-4444-4022200-22-22-22-2-2-20000-10000-660011-13-33-3000000000000000000000000000000000000000000000000000000000

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