Finite Group Databasebeta

← Group #13172672

Character table — Group #13172672

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order122233366666666623336666666666622224436666666666666664446666666612121212121212124444121212126666121212121212121212121212224412121212121222664
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1111111111111111111-111111111-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-1111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11-11111-1-111111-11-111-1-1-1-1-1-11-1-1
χ4111111111111111111111111111111111-1-1-1-111111111111111111-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11-1-1-111-1-1-1-1-1-1-11-11-1-111-1-111-111
χ51111111111111111111111111111111-1-111111111111111111111-111-1-111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1111-1-1111111-11-11-1-111-1-1-1-1-11-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-11-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-11-1-1-1-111-1-1-1-11-11-111-1-1-1-1111-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11
χ81111111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1
χ91111111111111111-1111-1-11111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11
χ101111111111111111-1111-1-11111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1
χ111111111111111111-1111-1-111111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-11-111-1-111-1-11111-1-111-1-111111111-1-1-11-1-1-1-11111-1-1-111-111-1-1-1-111-11-1
χ121111111111111111-1111-1-111111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1111-1-111-1-1111-1-11-1-111-1-1-1-11-11
χ131111111111111111-1111-1-1111111111-1-111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-111-1-111111111-1-1-1-1111111-1-1111-1-1-111-1-111-1-11-1-11-1-111-1-1111-1-1
χ141111111111111111-1111-1-1111111111-1-111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-11-1-111-1-111-1-1-1-111-1-1-1-1111111-1-1111-11111-1-1-1-111-111-111-1-1-1-1-1-1-111
χ151111111111111111-1111-1-1111111111-1-1-1-1111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-111-1-1111
χ161111111111111111-1111-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111111111-1-1-1
χ17222222-1222-12-12-122-12-122-122-1-1-1-12-1002222-12-1-1-122-1-1-1-1-1-1-1-1-1022002200-1-122-1-100220000000000-1-10-12-100-1-1-1-1-1-1020200-1-100000-10
χ18222222-1222-12-12-122-12-122-122-1-1-1-12-10022-2-2-12-1-1-122-1-1-1-1-1-1-1-1-102-2002200-1-1-2-21100220000000000-1-10-1-2100-1-111110-20-200110000010
χ19222222-1222-12-12-122-12-122-122-1-1-1-12-100-2-222-12-1-1-122-1-1-1-1-1-1-1-1-10-2200-2-2001122-1-100-2-2000000000011012-10011-1-1-1-10-20-200110000010
χ20222222-1222-12-12-122-12-122-122-1-1-1-12-100-2-2-2-2-12-1-1-122-1-1-1-1-1-1-1-1-10-2-200-2-20011-2-21100-2-200000000001101-2100111111020200-1-100000-10
χ21222222-1222-12-12-12-2-12-1-2-2-122-1-1-1-12-1002222-1-2111-2-211-1-1-111110-2-2002200-1-122-1-100-2-20000000000-1-101-210011-1-1110-20200-1-10000010
χ22222222-1222-12-12-12-2-12-1-2-2-122-1-1-1-12-10022-2-2-1-2111-2-211-1-1-111110-22002200-1-1-2-21100-2-20000000000-1-1012-1001111-1-1020-2001100000-10
χ23222222-1222-12-12-12-2-12-1-2-2-122-1-1-1-12-100-2-222-1-2111-2-211-1-1-1111102-200-2-2001122-1-100220000000000110-1-2100-1-1-1-111020-2001100000-10
χ24222222-1222-12-12-12-2-12-1-2-2-122-1-1-1-12-100-2-2-2-2-1-2111-2-211-1-1-1111102200-2-20011-2-21100220000000000110-12-100-1-111-1-10-20200-1-10000010
χ2522222-1222-12-12-1222-1-1222-1-1-122-1-1-12220022-1-12-1-1-1-122-1-1-1-1-1-1-12022200-1-100-1-122220000000000-1-100-10-12-1-100-1-1-1-12020-1-1000000-100
χ2622222-1222-12-12-1222-1-1222-1-1-122-1-1-122200-2-2-1-12-1-1-1-122-1-1-1-1-1-1-120-22200-1-10011-2-2220000000000-1-100-101-2-1-1001111-20-2011000000100
χ2722222-1222-12-12-1222-1-1222-1-1-122-1-1-12-2-20022-1-12-1-1-1-122-1-1-1-1-1-1-1-202-2-2001100-1-122-2-20000000000110010-121100-1-1-1-1-20-2011000000100
χ2822222-1222-12-12-1222-1-1222-1-1-122-1-1-12-2-200-2-2-1-12-1-1-1-122-1-1-1-1-1-1-1-20-2-2-200110011-2-2-2-200000000001100101-2110011112020-1-1000000-100
χ2922222-1222-12-12-122-2-1-12-2-2-1-1-122-1-1-12220022-11-21111-2-2-1-1-11111-20-22200-1-100-1-122-2-20000000000-1-100101-21100-1-111-2020-1-1000000100
χ3022222-1222-12-12-122-2-1-12-2-2-1-1-122-1-1-122200-2-2-11-21111-2-2-1-1-11111-2022200-1-10011-2-2-2-20000000000-1-10010-12110011-1-120-2011000000-100
χ3122222-1222-12-12-122-2-1-12-2-2-1-1-122-1-1-12-2-20022-11-21111-2-2-1-1-1111120-2-2-2001100-1-1222200000000001100-101-2-1-100-1-11120-2011000000-100
χ3222222-1222-12-12-122-2-1-12-2-2-1-1-122-1-1-12-2-200-2-2-11-21111-2-2-1-1-11111202-2-200110011-2-22200000000001100-10-12-1-10011-1-1-2020-1-1000000100
χ332222-122-1-1222222-122-1-1-1-12-1-1-1-122-1-1222200-12222-1-1-1-1-1-1-1-1-1-1-1220-1-1-1-122220000-1-1-1-12222-1-1-1-1-1-1-1-12200-1-1-1-1000000000000-1-100000
χ342222-122-1-1222222-122-1-1-1-12-1-1-1-122-1-122-2-200-12222-1-1-1-1-1-1-1-1-1-1-12-20-1-11122-2-20000-1-111-2-2-2-21111-1-1112-200-1-1110000000000001100000
χ352222-122-1-1222222-122-1-1-1-12-1-1-1-122-1-1-2-22200-12222-1-1-1-1-1-1-1-1-1-1-1-22011-1-1-2-222000011-1-1-2-2-2-2111111-1-1-220011-1-10000000000001100000
χ362222-122-1-1222222-122-1-1-1-12-1-1-1-122-1-1-2-2-2-200-12222-1-1-1-1-1-1-1-1-1-1-1-2-201111-2-2-2-2000011112222-1-1-1-11111-2-2001111000000000000-1-100000
χ372222-122-1-1222222-1-22-1-1112-1-1-1-122-1-1222200-1-2-2-2-21111-1-1-11111-2-20-1-1-1-122220000111122-2-21111-1-1-1-1-2-2001111000000000000-1-100000
χ382222-122-1-1222222-1-22-1-1112-1-1-1-122-1-122-2-200-1-2-2-2-21111-1-1-11111-220-1-11122-2-2000011-1-1-2-222-1-1-1-1-1-111-220011-1-10000000000001100000
χ392222-122-1-1222222-1-22-1-1112-1-1-1-122-1-1-2-22200-1-2-2-2-21111-1-1-111112-2011-1-1-2-2220000-1-111-2-222-1-1-1-111-1-12-200-1-1110000000000001100000
χ402222-122-1-1222222-1-22-1-1112-1-1-1-122-1-1-2-2-2-200-1-2-2-2-21111-1-1-111112201111-2-2-2-20000-1-1-1-122-2-2111111112200-1-1-1-1000000000000-1-100000
χ412-22-22222-222-2-2-2-2-202220022-22-2-2-2-2-200002i−2i2000000002-2-20000000000000002i−2i2i−2i0000002i−2i2i2i−2i−2i0000000000002i−2i0000000000002-2000
χ422-22-22222-222-2-2-2-2-202220022-22-2-2-2-2-200002i−2i2000000002-2-20000000000000002i−2i2i−2i000000−2i2i−2i−2i2i2i0000000000002i−2i000000000000-22000
χ432-22-22222-222-2-2-2-2-202220022-22-2-2-2-2-20000−2i2i2000000002-2-2000000000000000−2i2i−2i2i0000002i−2i2i2i−2i−2i000000000000−2i2i000000000000-22000
χ442-22-22222-222-2-2-2-2-202220022-22-2-2-2-2-20000−2i2i2000000002-2-2000000000000000−2i2i−2i2i000000−2i2i−2i−2i2i2i000000000000−2i2i0000000000002-2000
χ452-2-22222-2-2-2-222-2-22022200-2-2-2-2-22-2222-22-200200000000-22-200000002-22-22-22-2000000002-20000002-22-2000000000000000000002-200000
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χ472-2-22222-2-2-2-222-2-22022200-2-2-2-2-22-222-222-200200000000-22-20000000-222-2-222-200000000-22000000-222-200000000000000000000-2200000
χ482-2-22222-2-2-2-222-2-22022200-2-2-2-2-22-222-22-2200200000000-22-20000000-22-22-22-22000000002-2000000-22-22000000000000000000002-200000
χ492-2-22-12211-2-222-2-2-102-1-1−i3i3-211112-2-1-12-22-200-10000−i3i3−i3i31-11−i3−i3i3i3000-11-112-22-20000−i3i3−i3i32-200−i3i3−i3i3-11-110000−i3i3−i3i3000000000000-1100000
χ502-2-22-12211-2-222-2-2-102-1-1−i3i3-211112-2-1-12-2-2200-10000−i3i3−i3i31-11−i3−i3i3i3000-111-12-2-220000−i3i3i3−i3-2200i3−i3i3−i3-111-10000−i3i3i3−i30000000000001-100000
χ512-2-22-12211-2-222-2-2-102-1-1−i3i3-211112-2-1-1-222-200-10000−i3i3−i3i31-11−i3−i3i3i30001-1-11-222-20000i3−i3−i3i3-2200i3−i3i3−i31-1-110000i3−i3−i3i30000000000001-100000
χ522-2-22-12211-2-222-2-2-102-1-1−i3i3-211112-2-1-1-22-2200-10000−i3i3−i3i31-11−i3−i3i3i30001-11-1-22-220000i3−i3i3−i32-200−i3i3−i3i31-11-10000i3−i3i3−i3000000000000-1100000
χ532-2-22-12211-2-222-2-2-102-1-1i3−i3-211112-2-1-12-22-200-10000i3−i3i3−i31-11i3i3−i3−i3000-11-112-22-20000i3−i3i3−i32-200i3−i3i3−i3-11-110000i3−i3i3−i3000000000000-1100000
χ542-2-22-12211-2-222-2-2-102-1-1i3−i3-211112-2-1-12-2-2200-10000i3−i3i3−i31-11i3i3−i3−i3000-111-12-2-220000i3−i3−i3i3-2200−i3i3−i3i3-111-10000i3−i3−i3i30000000000001-100000
χ552-2-22-12211-2-222-2-2-102-1-1i3−i3-211112-2-1-1-222-200-10000i3−i3i3−i31-11i3i3−i3−i30001-1-11-222-20000−i3i3i3−i3-2200−i3i3−i3i31-1-110000−i3i3i3−i30000000000001-100000
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χ894-4-444-24-4-42-4-242-440-2-2400222-4-4-22-24-440000-2000000002-220000000-44002-20000000000000000002-200000000000000000000000000000
χ904-4-44-24-222-424-2-42-20-2-21−2i32i3222-1-1-22-21004-40010000−2i32i3i3−i3-11-1i3i3−i3−i300000-2200-22000000−2i32i300000000001-1000000i3−i30000000000000000000
χ914-4-44-24-222-424-2-42-20-2-21−2i32i3222-1-1-22-2100-440010000−2i32i3i3−i3-11-1i3i3−i3−i3000002-2002-20000002i3−2i30000000000-11000000−i3i30000000000000000000
χ924-4-44-24-222-424-2-42-20-2-212i3−2i3222-1-1-22-21004-400100002i3−2i3−i3i3-11-1−i3−i3i3i300000-2200-220000002i3−2i300000000001-1000000−i3i30000000000000000000
χ934-4-44-24-222-424-2-42-20-2-212i3−2i3222-1-1-22-2100-4400100002i3−2i3−i3i3-11-1−i3−i3i3i3000002-2002-2000000−2i32i30000000000-11000000i3−i30000000000000000000
χ944-4-44-2-24222-4-242-4-20-21-2−2i32i32-1-122-221-24-4000010000i3−i3−2i32i3-11-1i3i3−i3−i3000-2200-22000000−2i32i300000000001-1000000i3−i3000000000000000000000
χ954-4-44-2-24222-4-242-4-20-21-2−2i32i32-1-122-221-2-44000010000i3−i3−2i32i3-11-1i3i3−i3−i30002-2002-20000002i3−2i30000000000-11000000−i3i3000000000000000000000
χ964-4-44-2-24222-4-242-4-20-21-22i3−2i32-1-122-221-24-4000010000−i3i32i3−2i3-11-1−i3−i3i3i3000-2200-220000002i3−2i300000000001-1000000−i3i3000000000000000000000
χ974-4-44-2-24222-4-242-4-20-21-22i3−2i32-1-122-221-2-44000010000−i3i32i3−2i3-11-1−i3−i3i3i30002-2002-2000000−2i32i30000000000-11000000i3−i3000000000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-48222-4-4222222222000000-1-4-4222222-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4-822244222222222000000-144-2-2-2-2-2-2-1-1-111110000000000000000000000000000000000000000000000000000000000
χ10088-8-88-4-4-884444-4-4-802-4-400-24-44-4-2244000000200000000-2-2200000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-44-4-84-848-440-4-420044-4-224-44-2000000200000000-2-2200000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-484-44-84-8-4840-42-4004-224-44-4-24000000200000000-2-2200000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-44-44444-4-44022200-2-22-22-22-2-2000000-10000000011-1−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-44-44444-4-44022200-2-22-22-22-2-2000000-10000000011-13i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000000
χ1058-88-8-48-4-448-4-84-8440-4-4200-4-442-2444-20000002000000002-2-200000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-48-44-484-84-840-42-400-42-2-4444-240000002000000002-2-200000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-4-44-4-44444402220022-22-2-2-2-2-2000000-1006-60000-111-33-330000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-4-44-4-44444402220022-22-2-2-2-2-2000000-100-660000-1113-33-30000000000000000000000000000000000000000000000000000000000
χ1098-8-888-4-4-8-844-4-444802-4-400-244442-2-4-4000000200000000-22-200000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-44444-4-444-40222−4i34i3-2-2-2-2-22-222000000-100002i3−2i32i3−2i31-11−i3−i3i3i30000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-44444-4-444-402224i3−4i3-2-2-2-2-22-222000000-10000−2i32i3−2i32i31-11i3i3−i3−i30000000000000000000000000000000000000000000000000000000000

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