Finite Group Databasebeta

← Group #13168181

Character table — Group #13168181

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222444444444444444444444666666666688888888888881212121212121212121212121212121212121212121212121218181818242424242424242424242424363636363636363636365454727272108
order1222333666666666333466666666612121212121212124444441212121236661212121212121212124441212121212121212121212121212121212121212121222441212121212121212121212122444661212121244612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-11-111111111-1-1111111111111-1-111-1-11-1-1-1-1-11111-1-11-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-111111111111111111111-1111-1-1-1-1-1-111111111111111-1-1-1-111-111111-1-1-1-11-1-11-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111-1-11111111111111111111-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-111
χ51111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-11-1-111-1-1-1-1-1-1-1-11-1
χ61111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111111-11-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111111-1-11-1-1-1-1-1-11111-11
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111111-1-1-1-1-1-11-1-1-1111111-1-1-11
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1111-1-111-1-1-1111-1-111-1-1-1-1-1111
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-11111-1-1-1-111-1-11-1-1-1-1-11111-1-11-11-11111-1-1111-1-1-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-111111-1-1-1-111-1-1-1111-1-11111-11-1-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1111-11-1-1-111-1-11111-1-1-1-1-1-111-1-11-111
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1-11111-1-1-1-11111-1-111-11-1111-1-111-1-111-1-1-1-1-1-111111-11-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111111111-1-1-1-1111111111-1-1-1-1-11111-1-1-1-1-1111-1-111-1-1-11-11
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-111111-1-1-1-1111-11-11111-1-1-1-11-1-11
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11-11-1-1-111-1-111-1111-1-111-1-111-111-1
χ17222222-122-1-1222-122-1-1222-1-1-1-1-1-12-1-122-1-1-1-12200222222-1-1-1-12-1-122-1-1-1-1202-1-100000022-1-122-1-1-1-1-1-1-1-10000-1-102-1-1-1-10000200200000000-1-100
χ18222222-122-1-1222-122-1-1222-1-1-1-1-1-12-1-122-1-1-1-12200222222-1-1-1-12-1-122-1-1-1-1-20-2-1-1000000-2-2-1-122-1-1-1-1-1-1-1-10000110-211110000-200-2000000001100
χ19222222-122-1-1222-122-1-1222-1-1-1-1-1-12-1-122-1-1-1-1-2-200-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-1202110000002211-2-2111111110000-1-102-1-1-1-10000-200-2000000001100
χ20222222-122-1-1222-122-1-1222-1-1-1-1-1-12-1-122-1-1-1-1-2-200-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-1-20-211000000-2-211-2-2111111110000110-211110000200200000000-1-100
χ21222222-122-1-1222-122-1-1-222-1-1-1-1-1-1211-2-211112200-2-22222-1-1-1-1-211-2-2111120-2-1-1000000-2-211-2-2-1-1-1-1111100001-102-1-1110000-2002000000001-100
χ22222222-122-1-1222-122-1-1-222-1-1-1-1-1-1211-2-211112200-2-22222-1-1-1-1-211-2-21111-202-1-10000002211-2-2-1-1-1-111110000-110-211-1-10000200-200000000-1100
χ23222222-122-1-1222-122-1-1-222-1-1-1-1-1-1211-2-21111-2-20022-2-2-2-2-1-1-1-1-211-2-2111120-211000000-2-2-1-1221111-1-1-1-100001-102-1-1110000200-200000000-1100
χ24222222-122-1-1222-122-1-1-222-1-1-1-1-1-1211-2-21111-2-20022-2-2-2-2-1-1-1-1-211-2-21111-2021100000022-1-1221111-1-1-1-10000-110-211-1-10000-2002000000001-100
χ2522222-12-12222-1-122-12-12-1-1-1222-1-1-1222222220022000000-1-1-1-1-1-1-1-1-1-1-1-1-1222002222-1-1-1-1000000000000220022-1-1-1-1-1-1-1-1-1-10200-1-100000000-10
χ2622222-12-12222-1-122-12-12-1-1-1222-1-1-1222222220022000000-1-1-1-1-1-1-1-1-1-1-1-1-1-22-2002222-1-111000000000000-2-200-2-2-111111-1-1-1-10-200110000000010
χ2722222-12-12222-1-122-12-12-1-1-1222-1-1-12222222200-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-12-2200-2-2-2-211-1-1000000000000-2-200221-1-1-1-1-111110-200110000000010
χ2822222-12-12222-1-122-12-12-1-1-1222-1-1-12222222200-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-200-2-2-2-211110000000000002200-2-211111111110200-1-100000000-10
χ2922222-12-12222-1-122-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-20022000000-1-1-1-11111111112-2-20022-2-2-1-111000000000000-2-200-221-1-1-111-1-11102001100000000-10
χ3022222-12-12222-1-122-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-20022000000-1-1-1-1111111111-2-220022-2-2-1-1-1-100000000000022002-21111-1-1-1-1110-200-1-10000000010
χ3122222-12-12222-1-122-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200-2-2000000-1-1-1-111111111122-200-2-22211110000000000002200-22-1-1-1-11111-1-10-200-1-10000000010
χ3222222-12-12222-1-122-12-1-2-1-1-1222-1-1-1-2-2-2-2-2-2-2-200-2-2000000-1-1-1-1111111111-22200-2-22211-1-1000000000000-2-2002-2-1111-1-111-1-102001100000000-10
χ332222-1222-122-1222-1-1-122-1-12-1-1-122-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-1-1-1-1-1-102022-1-1-1-1220022-1-1-1-1-1-1-1-1-1-1002200200000-1-1-1-1002000-1-1-1-1000000
χ342222-1222-122-1222-1-1-122-1-12-1-1-122-122-1-1-1-1-1-122-2-222-1-1-1-1-1-1-1-1222-1-1-1-1-1-10-20221111-2-20022-1-1-1-1-1-1-1-1-1-100-2-200-200000111100-20001111000000
χ352222-1222-122-1222-1-1-122-1-12-1-1-122-122-1-1-1-1-1-1-2-222-2-21111-1-1-1-1222-1-1-1-1-1-1020-2-2-1-1-1-12200-2-2111111111100-2-200200000-1-1-1-100-20001111000000
χ362222-1222-122-1222-1-1-122-1-12-1-1-122-122-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1222-1-1-1-1-1-10-20-2-21111-2-200-2-21111111111002200-2000001111002000-1-1-1-1000000
χ372222-1222-122-1222-1-1-12-2-1-12-1-1-122-1-2-21111112222-2-2-1-1-1-1-1-1-1-1-2-2-21111110-2022-1-1112200-2-211-1-1-1-1111100-2-200-200000-1-111002000-1-111000000
χ382222-1222-122-1222-1-1-12-2-1-12-1-1-122-1-2-211111122-2-2-2-2-1-1-1-1-1-1-1-1-2-2-21111110202211-1-1-2-200-2-211-1-1-1-1111100220020000011-1-100-200011-1-1000000
χ392222-1222-122-1222-1-1-12-2-1-12-1-1-122-1-2-2111111-2-222221111-1-1-1-1-2-2-21111110-20-2-2-1-111220022-1-11111-1-1-1-1002200-200000-1-11100-200011-1-1000000
χ402222-1222-122-1222-1-1-12-2-1-12-1-1-122-1-2-2111111-2-2-2-2221111-1-1-1-1-2-2-2111111020-2-211-1-1-2-20022-1-11111-1-1-1-100-2-20020000011-1-1002000-1-111000000
χ412-22-2222-2-22-222-2-2-22220-2-2-22-2-2-22200000000002-22i−2i00002-2-22000000000000002-2002-2002i−2i2i−2i00002i2i−2i−2i002i−2i000000002-200000000002i−2i000000
χ422-22-2222-2-22-222-2-2-22220-2-2-22-2-2-22200000000002-2−2i2i00002-2-22000000000000002-2002-200−2i2i−2i2i0000−2i−2i2i2i00−2i2i000000002-20000000000−2i2i000000
χ432-22-2222-2-22-222-2-2-22220-2-2-22-2-2-2220000000000-222i−2i00002-2-2200000000000000-2200-22002i−2i2i−2i00002i2i−2i−2i00−2i2i00000000-220000000000−2i2i000000
χ442-22-2222-2-22-222-2-2-22220-2-2-22-2-2-2220000000000-22−2i2i00002-2-2200000000000000-2200-2200−2i2i−2i2i0000−2i−2i2i2i002i−2i00000000-2200000000002i−2i000000
χ452-22-2-122-212-2-12-2-21-1-12011-2-111-22-100−i3i3−i3−i3i3i3002-22i−2i33−3−3-111-1000−i3i3−i3−i3i3i300000-11−i3i32-2002i−2i−ii33−3−3−i−iii002i−2i00000000-11−i3i30000003−3−ii000000
χ462-22-2-122-212-2-12-2-21-1-12011-2-111-22-100−i3i3−i3−i3i3i3002-2−2i2i−3−333-111-1000−i3i3−i3−i3i3i300000-11−i3i32-200−2i2ii−i−3−333ii−i−i00−2i2i00000000-11−i3i3000000−33i−i000000
χ472-22-2-122-212-2-12-2-21-1-12011-2-111-22-100−i3i3−i3−i3i3i300-222i−2i33−3−3-111-1000−i3i3−i3−i3i3i3000001-1i3−i3-22002i−2i−ii33−3−3−i−iii00−2i2i000000001-1i3−i3000000−33i−i000000
χ482-22-2-122-212-2-12-2-21-1-12011-2-111-22-100−i3i3−i3−i3i3i300-22−2i2i−3−333-111-1000−i3i3−i3−i3i3i3000001-1i3−i3-2200−2i2ii−i−3−333ii−i−i002i−2i000000001-1i3−i30000003−3−ii000000
χ492-22-2-122-212-2-12-2-21-1-12011-2-111-22-100i3−i3i3i3−i3−i3002-22i−2i−3−333-111-1000i3−i3i3i3−i3−i300000-11i3−i32-2002i−2i−ii−3−333−i−iii002i−2i00000000-11i3−i3000000−33−ii000000
χ502-22-2-122-212-2-12-2-21-1-12011-2-111-22-100i3−i3i3i3−i3−i3002-2−2i2i33−3−3-111-1000i3−i3i3i3−i3−i300000-11i3−i32-200−2i2ii−i33−3−3ii−i−i00−2i2i00000000-11i3−i30000003−3i−i000000
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χ522-22-2-122-212-2-12-2-21-1-12011-2-111-22-100i3−i3i3i3−i3−i300-22−2i2i33−3−3-111-1000i3−i3i3i3−i3−i3000001-1−i3i3-2200−2i2ii−i33−3−3ii−i−i002i−2i000000001-1−i3i3000000−33−ii000000
χ532-2-222222-2-2-2-2-2-22222202-22-22-2-2-2-2000000002i−2i00002i−2i2i−2i22-2-20000000000002i−2i0000000000002i−2i2i−2i00002-20000000000000000002-200002i−2i0000
χ542-2-222222-2-2-2-2-2-22222202-22-22-2-2-2-2000000002i−2i00002i−2i2i−2i22-2-20000000000002i−2i0000000000002i−2i2i−2i0000-22000000000000000000-220000−2i2i0000
χ552-2-222222-2-2-2-2-2-22222202-22-22-2-2-2-200000000−2i2i0000−2i2i−2i2i22-2-2000000000000−2i2i000000000000−2i2i−2i2i00002-20000000000000000002-20000−2i2i0000
χ562-2-222222-2-2-2-2-2-22222202-22-22-2-2-2-200000000−2i2i0000−2i2i−2i2i22-2-2000000000000−2i2i000000000000−2i2i−2i2i0000-22000000000000000000-2200002i−2i0000
χ5744444-2-2-24-2-24-2-2-24-2-214-2-21-2-2-211-2-2-244-2-2-2-200000000001111-211-2-2111140400000000-2-20000000000000000-2-20-2111100000000000000000000
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χ7944-4-4-244-4-2-442-44-42-2-2402-2-422-24-42000000000000002i3−2i3−2i32i3-22-22000000000000000000000000002i3−2i3−2i32i3000000000000000000000000000000000000
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χ8144-4-4-24-2-4-22-22-4422-21-202-22-1-11-22223−2300−33−330000002i3−2i3−2i32i31-11-1023−2300−33−3300000000000000000−i3i3i3−i3−3i3i−3i3i00000000000000000000000000000000
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χ844-44-444-2-4-4-2244-42-44-2-20-4-42-2222-240000000000004i−4i0000-222-20000000000000000000000−2i2i4i−4i0000−2i−2i2i2i00000000000000000000000000000000
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χ864-44-44-242-44-44-22-4-4-24-202224-4-42-2-200000000004-4000000-222-2000000000000004-400-2200000000000000000000000000-22000000000000000000
χ874-44-44-242-44-44-22-4-4-24-202224-4-42-2-20000000000-44000000-222-200000000000000-44002-2000000000000000000000000002-2000000000000000000
χ884-44-4-24-2-42-22-24-422-21-202221-1-12-2-200−2i32i3i3i3−i3−i300004i−4i2323−23−231-1-11000−2i32i3i3i3−i3−i30000000000000−2i2i−2i2i−3−333ii−i−i00000000000000000000000000000000
χ894-44-4-24-2-42-22-24-422-21-202221-1-12-2-200−2i32i3i3i3−i3−i30000−4i4i−23−2323231-1-11000−2i32i3i3i3−i3−i300000000000002i−2i2i−2i33−3−3−i−iii00000000000000000000000000000000
χ904-44-4-24-2-42-22-24-422-21-202221-1-12-2-2002i3−2i3−i3−i3i3i300004i−4i−23−2323231-1-110002i3−2i3−i3−i3i3i30000000000000−2i2i−2i2i33−3−3ii−i−i00000000000000000000000000000000
χ914-44-4-24-2-42-22-24-422-21-202221-1-12-2-2002i3−2i3−i3−i3i3i30000−4i4i2323−23−231-1-110002i3−2i3−i3−i3i3i300000000000002i−2i2i−2i−3−333−i−iii00000000000000000000000000000000
χ924-44-4-2-24224-4-2-22-421-2-20-1-12-2222-2100−2i32i3−2i3−2i32i32i3004-40000001-1-11000i3−i3i3i3−i3−i300000-22−2i32i3-22000000000000000000000000001-1i3−i30000000000000000
χ934-44-4-2-24224-4-2-22-421-2-20-1-12-2222-2100−2i32i3−2i3−2i32i32i300-440000001-1-11000i3−i3i3i3−i3−i3000002-22i3−2i32-200000000000000000000000000-11−i3i30000000000000000
χ944-44-4-2-24224-4-2-22-421-2-20-1-12-2222-21002i3−2i32i32i3−2i3−2i3004-40000001-1-11000−i3i3−i3−i3i3i300000-222i3−2i3-22000000000000000000000000001-1−i3i30000000000000000
χ954-44-4-2-24224-4-2-22-421-2-20-1-12-2222-21002i3−2i32i32i3−2i3−2i300-440000001-1-11000−i3i3−i3−i3i3i3000002-2−2i32i32-200000000000000000000000000-11i3−i30000000000000000
χ964-4-4444-24-422-4-4-4-244-2-204-4-22-2222-4000000004i−4i00004i−4i4i−4i-2-222000000000000−2i2i000000000000−2i2i−2i2i000000000000000000000000000000000000
χ974-4-4444-24-422-4-4-4-244-2-204-4-22-2222-400000000−4i4i0000−4i4i−4i4i-2-2220000000000002i−2i0000000000002i−2i2i−2i000000000000000000000000000000000000
χ984-4-444-24-2-4-4-4-42244-24-20-22-2-44-4222000000000000000000-2-22200000000000000000000000000000000004-4000000000000000000-220000000000
χ994-4-444-24-2-4-4-4-42244-24-20-22-2-44-4222000000000000000000-2-2220000000000000000000000000000000000-440000000000000000002-20000000000
χ1004-4-44-24442-4-42-4-44-2-2-240-2242-22-4-42000000004i−4i0000−2i2i−2i2i-2-2220000000000004i−4i000000000000−2i2i−2i2i000000000000000000000000000000000000
χ1014-4-44-24442-4-42-4-44-2-2-240-2242-22-4-4200000000−4i4i00002i−2i2i−2i-2-222000000000000−4i4i0000000000002i−2i2i−2i000000000000000000000000000000000000
χ1024-4-44-24-242222-4-4-2-2-21-20-22-2-11-122200003i−3i−3i3i4i−4i0000−2i2i−2i2i11-1-1000003i−3i−3i3i000−2i2i000000000000i−ii−i3-3-3300000000000000000000000000000000
χ1034-4-44-24-242222-4-4-2-2-21-20-22-2-11-122200003i−3i−3i3i−4i4i00002i−2i2i−2i11-1-1000003i−3i−3i3i0002i−2i000000000000−ii−ii-333-300000000000000000000000000000000
χ1044-4-44-24-242222-4-4-2-2-21-20-22-2-11-12220000−3i3i3i−3i4i−4i0000−2i2i−2i2i11-1-100000−3i3i3i−3i000−2i2i000000000000i−ii−i-333-300000000000000000000000000000000
χ1054-4-44-24-242222-4-4-2-2-21-20-22-2-11-12220000−3i3i3i−3i−4i4i00002i−2i2i−2i11-1-100000−3i3i3i−3i0002i−2i000000000000−ii−ii3-3-3300000000000000000000000000000000
χ1068888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-422220000000000-1-1-1-1-42222-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ1078888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-20000000000-1-1-1-14-2-2-2-21111000000000000000000000000000000000000000000000000000000000
χ10888-8-8-4-484-4-8844-4-842-4-40-22444-4-44-20000000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
χ10988-8-8-4-4-44-44-444-4442220-22-2-2-222-2-243−4300−2323−23230000000000-11-110−2323003−33−3000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4-44-44-444-4442220-22-2-2-222-2-2−43430023−2323−230000000000-11-11023−2300−33−33000000000000000000000000000000000000000000000000000000000
χ1118-88-88-4-44-8-448-444-8-4-42044-2-444-22-40000000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000
χ1128-88-8-4-4-444-44-4-44442220-2-2-22-2-2-22200−4i34i32i32i3−2i3−2i30000000000-111-10002i3−2i3−i3−i3i3i3000000000000000000000000000000000000000000000000000000000
χ1138-88-8-4-4-444-44-4-44442220-2-2-22-2-2-222004i3−4i3−2i3−2i32i32i30000000000-111-1000−2i32i3i3i3−i3−i3000000000000000000000000000000000000000000000000000000000
χ1148-8-888-4-4-4-844-844-48-4-420-4424-44-2-2400000000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000
χ1158-8-88-4-48-44-8-84448-42-4-402-2-44-4444-200000000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-4-4444444-4-422202-22-22-2-2-2-200006i−6i−6i6i0000000000-1-11100000−3i3i3i−3i000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-4-4444444-4-422202-22-22-2-2-2-20000−6i6i6i−6i0000000000-1-111000003i−3i−3i3i000000000000000000000000000000000000000000000000000000000

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