Finite Group Databasebeta

← Group #13172923

Character table — Group #13172923

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444666666888888888888888899991212121212121212121212121212121212121218181818181818182424242424242424242424242424242436363636363636363654547272108
order12223336666666662333666666666664444443666666666666666444422466121212121212121212121212121222441212121266666661212121212121212122446612121212446124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11111111111111111-1-1-1-11-11-1-11111-1-1-1-111111111-1-1-1-1-1-111-111-1-11111111-1-1-11-111-1-1-1-1-1-1-11-1
χ3111111111111111111111111111111111-1-11111111111111111111111-1111111-1-1111111-1-111-1-1-1-11111-1-11-1-11111111-1-111-1-11-1-1-1-111-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-11-1-111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-111-1-1111-11
χ51111111111111111111111111111111-1-111111111111111111111-1-1-1-111-111-1-1111111-1-111-1-1-1-111-1-1-1-11111111-1-1-1-1-111111-1-1-1-111-1-1-1-11-1-1
χ61111111111111111111111111111111-1-111-1-1111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111-111-1-1-1-1-1-1-111-1-1-1-11-1-1-1-11111-1-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-11-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-111-11-111-1-1-1-111-111
χ81111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1
χ91111111111111111-1111-1-11111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1111111111111-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-11111-1-111-1-1-1
χ101111111111111111-1111-1-11111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-11-1111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11-1-111-111-1-111-1-11-1111-1-111-1-11-11
χ111111111111111111-1111-1-111111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1111
χ121111111111111111-1111-1-111111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111111-111-1-1-1-1-1-1-111-1-1111111-11-1
χ131111111111111111-1111-1-1111111111-1-111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1111111-111-1-11111-1-1-111
χ141111111111111111-1111-1-1111111111-1-111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11111-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11-1-1111-1-11111-1-111-1-1-1-1-1-1-11111-1
χ151111111111111111-1111-1-1111111111-1-1-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-111-1-11-1-111-1-1111-1111-1-111111-1-1
χ161111111111111111-1111-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-11
χ17222222-1222-1-12-12222-1-1222-1-1-1-122-1-1002222-12-122-1-1-1-1-1-1-1-1-1-1-100002202200-1-122-1-1002200002200002-1-1-1-1-1-100000-1-1-1-120000-1-10000-100
χ18222222-1222-1-12-12222-1-1222-1-1-1-122-1-10022-2-2-12-122-1-1-1-1-1-1-1-1-1-1-100002-20-2-200-1-1-2-21100220000-2-200002-11-1-11100000-1-111-20000110000100
χ19222222-1222-1-12-12222-1-1222-1-1-1-122-1-100-2-222-12-122-1-1-1-1-1-1-1-1-1-1-10000-22022001122-1-100-2-20000-2-20000-21-111-1-10000011-1-1-20000110000100
χ20222222-1222-1-12-12222-1-1222-1-1-1-122-1-100-2-2-2-2-12-122-1-1-1-1-1-1-1-1-1-1-10000-2-20-2-20011-2-21100-2-20000220000-211111100000111120000-1-10000-100
χ21222222-1222-1-12-122-22-1-1-2-22-1-1-1-122-1-1002222-1-21-2-21111-1-1-111110000-2-20-2-200-1-122-1-100220000220000-211111100000-1-1-1-1-20000-1-10000100
χ22222222-1222-1-12-122-22-1-1-2-22-1-1-1-122-1-10022-2-2-1-21-2-21111-1-1-111110000-2202200-1-1-2-21100220000-2-20000-21-111-1-100000-1-11120000110000-100
χ23222222-1222-1-12-122-22-1-1-2-22-1-1-1-122-1-100-2-222-1-21-2-21111-1-1-1111100002-20-2-2001122-1-100-2-20000-2-200002-11-1-1110000011-1-120000110000-100
χ24222222-1222-1-12-122-22-1-1-2-22-1-1-1-122-1-100-2-2-2-2-1-21-2-21111-1-1-111110000220220011-2-21100-2-200002200002-1-1-1-1-1-1000001111-20000-1-10000100
χ2522222-12-12222-12-122-12-122-122-1-1-1-12-1222200-1-12-1-122-1-1-1-1-1-1-1-1-100002020022220000-1-1-1-12222000000-120-1-100-1-1-1-1-1-1-100020-1-10000000-10
χ2622222-12-12222-12-122-12-122-122-1-1-1-12-122-2-200-1-12-1-122-1-1-1-1-1-1-1-1-10000-2020022-2-20000-1-11122-2-20000001-201100-1-1-1-1-111000-2011000000010
χ2722222-12-12222-12-122-12-122-122-1-1-1-12-1-2-22200-1-12-1-122-1-1-1-1-1-1-1-1-1000020-200-2-222000011-1-1-2-2-2-2000000-120-1-10011111-1-1000-2011000000010
χ2822222-12-12222-12-122-12-122-122-1-1-1-12-1-2-2-2-200-1-12-1-122-1-1-1-1-1-1-1-1-10000-20-200-2-2-2-200001111-2-2220000001-201100111111100020-1-10000000-10
χ2922222-12-12222-12-12-2-12-1-2-2-122-1-1-1-12-1222200-11-211-2-211-1-1-111110000-20-20022220000-1-1-1-1-2-2220000001-2011001-1-111-1-1000-20-1-1000000010
χ3022222-12-12222-12-12-2-12-1-2-2-122-1-1-1-12-122-2-200-11-211-2-211-1-1-11111000020-20022-2-20000-1-111-2-2-2-2000000-120-1-1001-1-1111100020110000000-10
χ3122222-12-12222-12-12-2-12-1-2-2-122-1-1-1-12-1-2-22200-11-211-2-211-1-1-111110000-20200-2-222000011-1-122-2-20000001-201100-111-1-1-1-100020110000000-10
χ3222222-12-12222-12-12-2-12-1-2-2-122-1-1-1-12-1-2-2-2-200-11-211-2-211-1-1-11111000020200-2-2-2-2000011112222000000-120-1-100-111-1-111000-20-1-1000000010
χ332222-1222-1-122222-12-1-12-1-1-1-1-122-1-1-12220022-122-1-1-1-122-1-1-1-1-1-1-12222022-1-1-1-100-1-1222200-1-10000-1-1-1-100200-1-12-1-1-1-100-1-10020000-1-100000
χ342222-1222-1-122222-12-1-12-1-1-1-1-122-1-1-122200-2-2-122-1-1-1-122-1-1-1-1-1-1-1-2-2-2-20-2211-1-10011-2-22200-1-10000111100-200112-1-1-1-1001100-200001100000
χ352222-1222-1-122222-12-1-12-1-1-1-1-122-1-1-12-2-20022-122-1-1-1-122-1-1-1-1-1-1-1-2-2-2-202-2-1-11100-1-122-2-200110000111100200-1-1-2111100-1-100-200001100000
χ362222-1222-1-122222-12-1-12-1-1-1-1-122-1-1-12-2-200-2-2-122-1-1-1-122-1-1-1-1-1-1-122220-2-211110011-2-2-2-200110000-1-1-1-100-20011-2111100110020000-1-100000
χ372222-1222-1-122222-1-2-1-1211-1-1-122-1-1-12220022-1-2-21111-2-2-1-1-1111122220-2-211-1-100-1-1222200110000-1-1-1-100-20011-2-1-11100-1-100-200001100000
χ382222-1222-1-122222-1-2-1-1211-1-1-122-1-1-122200-2-2-1-2-21111-2-2-1-1-11111-2-2-2-202-2-1-1-1-10011-2-22200110000111100200-1-1-2-1-11100110020000-1-100000
χ392222-1222-1-122222-1-2-1-1211-1-1-122-1-1-12-2-20022-1-2-21111-2-2-1-1-11111-2-2-2-20-22111100-1-122-2-200-1-10000111100-20011211-1-100-1-10020000-1-100000
χ402222-1222-1-122222-1-2-1-1211-1-1-122-1-1-12-2-200-2-2-1-2-21111-2-2-1-1-111112222022-1-1110011-2-2-2-200-1-10000-1-1-1-100200-1-1211-1-1001100-200001100000
χ4122-2-2222-22-22-22-2-2-2022200-22-2-2-22-2-22002-2002000000002-2-200002i2i−2i−2i00000002-20000002-20000002i2i−2i−2i0000000000002-2000000000002i−2i000
χ4222-2-2222-22-22-22-2-2-2022200-22-2-2-22-2-22002-2002000000002-2-20000−2i−2i2i2i00000002-20000002-2000000−2i−2i2i2i0000000000002-200000000000−2i2i000
χ4322-2-2222-22-22-22-2-2-2022200-22-2-2-22-2-2200-22002000000002-2-200002i2i−2i−2i0000000-22000000-220000002i2i−2i−2i000000000000-2200000000000−2i2i000
χ4422-2-2222-22-22-22-2-2-2022200-22-2-2-22-2-2200-22002000000002-2-20000−2i−2i2i2i0000000-22000000-22000000−2i−2i2i2i000000000000-22000000000002i−2i000
χ452-22-22222-22-22-2-2-2-20222002-2-22-2-2-22-22i−2i002-2200000000-22-200002i−2i2i−2i000002i−2i002-22-22i−2i000000002i−2i2i−2i000000002i−2i00002-200000000000000
χ462-22-22222-22-22-2-2-2-20222002-2-22-2-2-22-22i−2i00-22200000000-22-20000−2i2i−2i2i000002i−2i00-22-222i−2i00000000−2i2i−2i2i000000002i−2i0000-2200000000000000
χ472-22-22222-22-22-2-2-2-20222002-2-22-2-2-22-2−2i2i002-2200000000-22-20000−2i2i−2i2i00000−2i2i002-22-2−2i2i00000000−2i2i−2i2i00000000−2i2i00002-200000000000000
χ482-22-22222-22-22-2-2-2-20222002-2-22-2-2-22-2−2i2i00-22200000000-22-200002i−2i2i−2i00000−2i2i00-22-22−2i2i000000002i−2i2i−2i00000000−2i2i0000-2200000000000000
χ492-22-2-12221-1-22-2-2-210-1-12−i3i3-1112-211-1-22i−2i002-2-100−i3i3−i3i3001-11−i3−i3i3i32i−2i2i−2i000−i3i3−ii00-112-22i−2i003−30000−ii−ii00000−i3i30−ii3−300-1100000003−300000
χ502-22-2-12221-1-22-2-2-210-1-12−i3i3-1112-211-1-22i−2i00-22-100−i3i3−i3i3001-11−i3−i3i3i3−2i2i−2i2i000i3−i3−ii001-1-222i−2i003−30000i−ii−i00000i3−i30−ii3−3001-10000000−3300000
χ512-22-2-12221-1-22-2-2-210-1-12−i3i3-1112-211-1-2−2i2i002-2-100−i3i3−i3i3001-11−i3−i3i3i3−2i2i−2i2i000−i3i3i−i00-112-2−2i2i00−330000i−ii−i00000−i3i30i−i−3300-110000000−3300000
χ522-22-2-12221-1-22-2-2-210-1-12−i3i3-1112-211-1-2−2i2i00-22-100−i3i3−i3i3001-11−i3−i3i3i32i−2i2i−2i000i3−i3i−i001-1-22−2i2i00−330000−ii−ii00000i3−i30i−i−33001-100000003−300000
χ532-22-2-12221-1-22-2-2-210-1-12i3−i3-1112-211-1-22i−2i002-2-100i3−i3i3−i3001-11i3i3−i3−i32i−2i2i−2i000i3−i3−ii00-112-22i−2i00−330000−ii−ii00000i3−i30−ii−3300-110000000−3300000
χ542-22-2-12221-1-22-2-2-210-1-12i3−i3-1112-211-1-22i−2i00-22-100i3−i3i3−i3001-11i3i3−i3−i3−2i2i−2i2i000−i3i3−ii001-1-222i−2i00−330000i−ii−i00000−i3i30−ii−33001-100000003−300000
χ552-22-2-12221-1-22-2-2-210-1-12i3−i3-1112-211-1-2−2i2i002-2-100i3−i3i3−i3001-11i3i3−i3−i3−2i2i−2i2i000i3−i3i−i00-112-2−2i2i003−30000i−ii−i00000i3−i30i−i3−300-1100000003−300000
χ562-22-2-12221-1-22-2-2-210-1-12i3−i3-1112-211-1-2−2i2i00-22-100i3−i3i3−i3001-11i3i3−i3−i32i−2i2i−2i000−i3i3i−i001-1-22−2i2i003−30000−ii−ii00000−i3i30i−i3−3001-10000000−3300000
χ572-2-22222-2-2-2-2-2-2222022200-2-22-22-22-2-2000000200000000-2-2200002-2-2200000000000000000002-22-22-2-2200000000000000000002-22-20000000
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χ602-2-22222-2-2-2-2-2-2222022200-2-22-22-22-2-2000000200000000-2-220000-222-20000000000000000000-222-2-222-20000000000000000000-222-20000000
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χ864-44-44-24-2-44-442-42-40-24-200-2-4-4-222242−4i4i0000-2000000002-220000000000000−4i4i0000002i−2i000000000000000000002i−2i00000000000000000000
χ874-44-4-24-242-22-2-42-420-21-2−2i32i3-2-1-1-22221200004-4100−2i32i3i3−i300-11-1i3i3−i3−i30000000−2i32i30000-22-220000000000000000000i3−i300000001-100000000000000
χ884-44-4-24-242-22-2-42-420-21-2−2i32i3-2-1-1-2222120000-44100−2i32i3i3−i300-11-1i3i3−i3−i300000002i3−2i300002-22-20000000000000000000−i3i30000000-1100000000000000
χ894-44-4-24-242-22-2-42-420-21-22i3−2i3-2-1-1-22221200004-41002i3−2i3−i3i300-11-1−i3−i3i3i300000002i3−2i30000-22-220000000000000000000−i3i300000001-100000000000000
χ904-44-4-24-242-22-2-42-420-21-22i3−2i3-2-1-1-2222120000-441002i3−2i3−i3i300-11-1−i3−i3i3i30000000−2i32i300002-22-20000000000000000000i3−i30000000-1100000000000000
χ914-44-4-2-24-22-2-442-42201-2-2−2i32i3122-22-1-1-224i−4i0000100i3−i3−2i32i300-11-1i3i3−i3−i3000000000−2i2i000000−2i2i0023−230000000000000000i−i−33000000000000000000
χ924-44-4-2-24-22-2-442-42201-2-2−2i32i3122-22-1-1-22−4i4i0000100i3−i3−2i32i300-11-1i3i3−i3−i30000000002i−2i0000002i−2i00−23230000000000000000−ii3−3000000000000000000
χ934-44-4-2-24-22-2-442-42201-2-22i3−2i3122-22-1-1-224i−4i0000100−i3i32i3−2i300-11-1−i3−i3i3i3000000000−2i2i000000−2i2i00−23230000000000000000i−i3−3000000000000000000
χ944-44-4-2-24-22-2-442-42201-2-22i3−2i3122-22-1-1-22−4i4i0000100−i3i32i3−2i300-11-1−i3−i3i3i30000000002i−2i0000002i−2i0023−230000000000000000−ii−33000000000000000000
χ954-4-4444-2-4-4-422-4-24404-2-200-42-22-2-4422000000-20000000022-2000000000000000000000000000004-40000000000000000000000000-220000000
χ964-4-4444-2-4-4-422-4-24404-2-200-42-22-2-4422000000-20000000022-200000000000000000000000000000-4400000000000000000000000002-20000000
χ974-4-444-242-4-4-4-424-240-24-2002-442-22-2-42000000-20000000022-20000000000000000000000000004-40000000000000000000000000-22000000000
χ984-4-444-242-4-4-4-424-240-24-2002-442-22-2-42000000-20000000022-2000000000000000000000000000-4400000000000000000000000002-2000000000
χ994-4-44-244-422-4-4-444-20-2-240022-2-442-22-4000000-20000000022-200004-4-4400000000000000000000000-222-2000000000000000000000000000000
χ1004-4-44-244-422-4-4-444-20-2-240022-2-442-22-4000000-20000000022-20000-444-4000000000000000000000002-2-22000000000000000000000000000000
χ1018888-4-4-4-4-4-4-4-4-4-4-4-48222-4-4222222222000000-1-4-4222222-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000000000000
χ1028888-4-4-4-4-4-4-4-4-4-4-4-4-822244222222222000000-144-2-2-2-2-2-2-1-1-111110000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-48-4-8-44-4484-840-42-40042-244-44-2-40000002000000002-2-200000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-484-448-8-4-84402-4-400-2-44442-24-40000002000000002-2-200000000000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-44-44-44-4444022200-22-2-2-22-2-22000000-10000006-6-111-33-330000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-44-44-44-4444022200-22-2-2-22-2-22000000-1000000-66-1113-33-30000000000000000000000000000000000000000000000000000000000000
χ1078-88-88-4-4-4-884-4444-80-4-4200-4442-244-4-2000000200000000-22-200000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-4-44-44-444440222−4i34i32-2-22-2-2-22-2000000-1002i3−2i32i3−2i3001-11−i3−i3i3i30000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-4-44-44-4444402224i3−4i32-2-22-2-2-22-2000000-100−2i32i3−2i32i3001-11i3i3−i3−i30000000000000000000000000000000000000000000000000000000000000
χ1108-8-888-4-44-8-8444-4-480-4-420044-4-224-44-2000000200000000-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-48-4-84444-8-48-40-42-4004-224-44-4-24000000200000000-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-48444-8-848-4-402-4-400-24-44-4-2244000000200000000-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4444444-4-4-4022200-2-22-22-22-2-2000000-10000000011-1−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4444444-4-4-4022200-2-22-22-22-2-2000000-10000000011-13i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000000000

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