Finite Group Databasebeta

← Group #13168495

Character table — Group #13168495

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order122233366666666633346666666661212444444366612121212121212121212121244412121212121212121212121212121212444412121212121212121212121212121212121212122244666612124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1111111111111111111-111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1111-111-1-111-1-111111-11-111-1-1-1-1-1-11-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-11-1-1111111-1-111-1-111-1-1-1-1-1-1-1-111-11-1-111-1-1111111-11-11-1-111-1-1-1-1-11-1
χ4111111111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11
χ51111111111111111111111111111111-1-111111111111111111111-1111111-1-1-1-11111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-11-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1-1-1-1-1-11-11-1-111-1-111-111
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-11-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-11-11-111-1-1-1-1111-11
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
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1111111-1-1-1-11
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-111-1-1111111-1-1-11-1-11111-1-111-1-11-1-1111-1-1-1-111-11-1
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111111-1-11111-1-1-1-1111111-1-11-111-1-1-1-11111-1-1-111-1-1-111-1-1111-1-1
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1111
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-1-1-1-1111111-1
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-111-1-1-1-111-1-111111111-11-1-11111-1-1-1-111-111-1-1-111-1-1-1-11-11
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-1111111111-111-1-1-1-111-1-1111-1-1111-1-1-1-1-1-1-111
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111111111-1-1-1
χ17222222-12-1222-12-122-1-122-1-1-12-12-1-122220022-1-1-1-12-122-1-1-1-1-1-1-1-1202002222-1-100-1-10022000000002-10-100-1-100-1-1-1-1-1-1020200-1-100000-10
χ18222222-12-1222-12-122-1-122-1-1-12-12-1-1222200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-120-200-2-222-1-1001100-2-2000000002-10100110011-1-1-1-10-20-200110000010
χ19222222-12-1222-12-122-1-122-1-1-12-12-1-122-2-20022-1-1-1-12-122-1-1-1-1-1-1-1-1-2020022-2-21100-1-1002200000000-210-100-1-100-1-111110-20-200110000010
χ20222222-12-1222-12-122-1-122-1-1-12-12-1-122-2-200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1-20-200-2-2-2-211001100-2-200000000-2101001100111111020200-1-100000-10
χ21222222-12-1222-12-122-1-1-22-1-1-12-12-1-1-2-2220022-1-1-1-1-21-2-211111111-20-2002222-1-100-1-100-2-200000000-2101001100-1-1-1-111020-200-1-10000010
χ22222222-12-1222-12-122-1-1-22-1-1-12-12-1-1-2-22200-2-2-1-1-1-1-21-2-211111111-20200-2-222-1-10011002200000000-210-100-1-10011-1-1110-202001100000-10
χ23222222-12-1222-12-122-1-1-22-1-1-12-12-1-1-2-2-2-20022-1-1-1-1-21-2-21111111120-20022-2-21100-1-100-2-2000000002-101001100-1-111-1-10-202001100000-10
χ24222222-12-1222-12-122-1-1-22-1-1-12-12-1-1-2-2-2-200-2-2-1-1-1-1-21-2-21111111120200-2-2-2-21100110022000000002-10-100-1-1001111-1-1020-200-1-10000010
χ2522222-12-1222-12-122-12-12-12-1-1-12-12-122222200-1-1-1-1-12-1-122-1-1-1-1-1-12202200-1-122-1-100220000000000-12-10-1-100-1-100-1-1-1-12020-1-1000000-100
χ2622222-12-1222-12-122-12-12-12-1-1-12-12-12222-2-200-1-1-1-1-12-1-122-1-1-1-1-1-12-20-2-200-1-1221100-2-20000000000-121011001100-1-1-1-1-20-2011000000100
χ2722222-12-1222-12-122-12-12-12-1-1-12-12-122-2-22200-1-1-1-1-12-1-122-1-1-1-1-1-1-220220011-2-2-1-1002200000000001-2-10-1-100-1-1001111-20-2011000000100
χ2822222-12-1222-12-122-12-12-12-1-1-12-12-122-2-2-2-200-1-1-1-1-12-1-122-1-1-1-1-1-1-2-20-2-20011-2-21100-2-200000000001-2101100110011112020-1-1000000-100
χ2922222-12-1222-12-122-12-1-2-12-1-1-12-12-1-2-2222200-1-1-1-11-211-2-2111111-2-202200-1-122-1-100-2-200000000001-2101100-1-100-1-11120-20-1-1000000100
χ3022222-12-1222-12-122-12-1-2-12-1-1-12-12-1-2-222-2-200-1-1-1-11-211-2-2111111-220-2-200-1-12211002200000000001-2-10-1-1001100-1-111-202011000000-100
χ3122222-12-1222-12-122-12-1-2-12-1-1-12-12-1-2-2-2-22200-1-1-1-11-211-2-21111112-20220011-2-2-1-100-2-20000000000-12101100-1-10011-1-1-202011000000-100
χ3222222-12-1222-12-122-12-1-2-12-1-1-12-12-1-2-2-2-2-2-200-1-1-1-11-211-2-2111111220-2-20011-2-21100220000000000-12-10-1-100110011-1-120-20-1-1000000100
χ332222-12222-1-12222-1-1-122-1-122-1-1-1-12-1-1002222-1-1-1-122-1-1-1-122-1-1-1-1022-1-1-1-100002222-1-1-1-12222-1-1-1-10022-1-1-1-1-1-1-1-1000000000000-1-100000
χ342222-12222-1-12222-1-1-122-1-122-1-1-1-12-1-10022-2-2-1-1-1-122-1-1-1-122-1-1-1-102-2-1-111000022-2-2-1-111-2-2-2-21111002-2-1-111-1-1110000000000001100000
χ352222-12222-1-12222-1-1-122-1-122-1-1-1-12-1-100-2-222-1-1-1-122-1-1-1-122-1-1-1-10-2211-1-10000-2-22211-1-1-2-2-2-2111100-2211-1-111-1-10000000000001100000
χ362222-12222-1-12222-1-1-122-1-122-1-1-1-12-1-100-2-2-2-2-1-1-1-122-1-1-1-122-1-1-1-10-2-211110000-2-2-2-211112222-1-1-1-100-2-211111111000000000000-1-100000
χ372222-12222-1-12222-1-1-12-2-1-122-1-1-1-1211002222-1-1-1-1-2-21111-2-211110-2-2-1-1-1-100002222111122-2-2111100-2-21111-1-1-1-1000000000000-1-100000
χ382222-12222-1-12222-1-1-12-2-1-122-1-1-1-12110022-2-2-1-1-1-1-2-21111-2-211110-22-1-111000022-2-211-1-1-2-222-1-1-1-100-2211-1-1-1-1110000000000001100000
χ392222-12222-1-12222-1-1-12-2-1-122-1-1-1-121100-2-222-1-1-1-1-2-21111-2-2111102-211-1-10000-2-222-1-111-2-222-1-1-1-1002-2-1-11111-1-10000000000001100000
χ402222-12222-1-12222-1-1-12-2-1-122-1-1-1-121100-2-2-2-2-1-1-1-1-2-21111-2-2111102211110000-2-2-2-2-1-1-1-122-2-211110022-1-1-1-11111000000000000-1-100000
χ4122-2-2222-2-22-222-2-2-22220-2-2-2-2-2-2222002-200002-2-2200000000000000000002-22-200000000002i−2i2i2i−2i−2i0000000000002-20000000000002i−2i000
χ4222-2-2222-2-22-222-2-2-22220-2-2-2-2-2-2222002-200002-2-2200000000000000000002-22-20000000000−2i2i−2i−2i2i2i0000000000002-2000000000000−2i2i000
χ4322-2-2222-2-22-222-2-2-22220-2-2-2-2-2-222200-2200002-2-220000000000000000000-22-2200000000002i−2i2i2i−2i−2i000000000000-22000000000000−2i2i000
χ4422-2-2222-2-22-222-2-2-22220-2-2-2-2-2-222200-2200002-2-220000000000000000000-22-220000000000−2i2i−2i−2i2i2i000000000000-220000000000002i−2i000
χ452-22-2222-2-2-2-2-2-22222220-2-22-222-2-2-200002i−2i2i−2i22-2-20000000000000002i−2i2i−2i00002i−2i2i−2i00002-2000000000000002i−2i2i−2i0000000000002-200000
χ462-22-2222-2-2-2-2-2-22222220-2-22-222-2-2-200002i−2i−2i2i22-2-20000000000000002i−2i−2i2i00002i−2i−2i2i0000-22000000000000002i−2i−2i2i000000000000-2200000
χ472-22-2222-2-2-2-2-2-22222220-2-22-222-2-2-20000−2i2i2i−2i22-2-2000000000000000−2i2i2i−2i0000−2i2i2i−2i0000-2200000000000000−2i2i2i−2i000000000000-2200000
χ482-22-2222-2-2-2-2-2-22222220-2-22-222-2-2-20000−2i2i−2i2i22-2-2000000000000000−2i2i−2i2i0000−2i2i−2i2i00002-200000000000000−2i2i−2i2i0000000000002-200000
χ492-22-2-122-2-211-2-222-1-1-120112-2-1-111-23−3002i−2i2i−2i-1-111003−33−30033−3−3000−ii−ii00002i−2i2i−2i−i3i3−i3i32-2003−33−30000−i3i3−i3i3−ii−ii000000000000-1100000
χ502-22-2-122-2-211-2-222-1-1-120112-2-1-111-23−3002i−2i−2i2i-1-111003−33−30033−3−3000−iii−i00002i−2i−2i2i−i3i3i3−i3-2200−33−330000−i3i3i3−i3−iii−i0000000000001-100000
χ512-22-2-122-2-211-2-222-1-1-120112-2-1-111-23−300−2i2i2i−2i-1-111003−33−30033−3−3000i−i−ii0000−2i2i2i−2ii3−i3−i3i3-2200−33−330000i3−i3−i3i3i−i−ii0000000000001-100000
χ522-22-2-122-2-211-2-222-1-1-120112-2-1-111-23−300−2i2i−2i2i-1-111003−33−30033−3−3000i−ii−i0000−2i2i−2i2ii3−i3i3−i32-2003−33−30000i3−i3i3−i3i−ii−i000000000000-1100000
χ532-22-2-122-2-211-2-222-1-1-120112-2-1-111-2−33002i−2i2i−2i-1-11100−33−3300−3−333000−ii−ii00002i−2i2i−2ii3−i3i3−i32-200−33−330000i3−i3i3−i3−ii−ii000000000000-1100000
χ542-22-2-122-2-211-2-222-1-1-120112-2-1-111-2−33002i−2i−2i2i-1-11100−33−3300−3−333000−iii−i00002i−2i−2i2ii3−i3−i3i3-22003−33−30000i3−i3−i3i3−iii−i0000000000001-100000
χ552-22-2-122-2-211-2-222-1-1-120112-2-1-111-2−3300−2i2i2i−2i-1-11100−33−3300−3−333000i−i−ii0000−2i2i2i−2i−i3i3i3−i3-22003−33−30000−i3i3i3−i3i−i−ii0000000000001-100000
χ562-22-2-122-2-211-2-222-1-1-120112-2-1-111-2−3300−2i2i−2i2i-1-11100−33−3300−3−333000i−ii−i0000−2i2i−2i2i−i3i3−i3i32-200−33−330000−i3i3−i3i3i−ii−i000000000000-1100000
χ5744444-2-2-2-244-2-2-2-24-2-214-2-211-2-2-2-21444400001111-2-2-2-2-2-21111114000000-2-2-2-20000000000000000-2-200000000001111000000000000000
χ5844444-2-2-2-244-2-2-2-24-2-214-2-211-2-2-2-2144-4-400001111-2-2-2-2-2-2111111-400000022220000000000000000220000000000-1-1-1-1000000000000000
χ5944444-2-2-2-244-2-2-2-24-2-21-4-2-211-2-2-2-21-4-44400001111222222-1-1-1-1-1-1-4000000-2-2-2-2000000000000000022000000000011-1-1000000000000000
χ6044444-2-2-2-244-2-2-2-24-2-21-4-2-211-2-2-2-21-4-4-4-400001111222222-1-1-1-1-1-1400000022220000000000000000-2-20000000000-1-111000000000000000
χ614444-24-24-2-2-24-24-2-2-21-24-21-2-2-21-21-2-2-200004411114-2-2-211-2-2111100400-2-2000000-2-200-2-200000000000-2001100110000000000000000000
χ624444-24-24-2-2-24-24-2-2-21-24-21-2-2-21-21-2-2-20000-4-411114-2-2-211-2-2111100-4002200000022002200000000000200-1-100-1-10000000000000000000
χ634444-24-24-2-2-24-24-2-2-21-2-4-21-2-2-21-21-2220000441111-4222-1-122-1-1-1-100-400-2-2000000-2-2002200000000000200-1-100110000000000000000000
χ644444-24-24-2-2-24-24-2-2-21-2-4-21-2-2-21-21-2220000-4-41111-4222-1-122-1-1-1-100400220000002200-2-200000000000-2001100-1-10000000000000000000
χ654444-2-24-24-2-2-24-24-21-2-241-2-2-21-21-2-2-2-20044001111-2411-2-2-2-21111040-2-2000000-2-200-2-2000000000000-20110011000000000000000000000
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χ7444-4-44-2-2224-4-2-222-4-2-21022-1-122-2-21004-400001-1-11000000-33-33-330000000-22-2200000000000000000000000000001-1-33000000000000000
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χ854-44-4-24-2-4222-424-2-2-21-202-1-22-212-12−232300004i−4i11-1-100−23233−30033−3−300000−2i2i000000−2i2i002i3−2i300000000000000−i3i300i−i0000000000000000000
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χ874-44-4-2-242-4222-4-24-21-2-20-12-221-2-12223−23004i−4i0011-1-100−3323−2300−3−333000−2i2i000000−2i2i00−2i32i300000000000000i3−i300i−i000000000000000000000
χ884-44-4-2-242-4222-4-24-21-2-20-12-221-2-12223−2300−4i4i0011-1-100−3323−2300−3−3330002i−2i0000002i−2i002i3−2i300000000000000−i3i300−ii000000000000000000000
χ894-44-4-2-242-4222-4-24-21-2-20-12-221-2-122−2323004i−4i0011-1-1003−3−23230033−3−3000−2i2i000000−2i2i002i3−2i300000000000000−i3i300i−i000000000000000000000
χ904-44-4-2-242-4222-4-24-21-2-20-12-221-2-122−232300−4i4i0011-1-1003−3−23230033−3−30002i−2i0000002i−2i00−2i32i300000000000000i3−i300−ii000000000000000000000
χ914-4-4444444-44-4-4-4-4-4444044-44-4-4-4-4-4000000004-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ924-4-4444-24-2-44-42-42-44-2-204-22-2-42-42200000000-22-220000000000000000000000000000000000000000000000000000000000000−2i32i30000000
χ934-4-4444-24-2-44-42-42-44-2-204-22-2-42-42200000000-22-2200000000000000000000000000000000000000000000000000000000000002i3−2i30000000
χ944-4-444-24-24-442-42-4-4-24-20-242-22-42-4200000000-22-2200000000000000000000000000000000000000000000000000000000000−2i32i3000000000
χ954-4-444-24-24-442-42-4-4-24-20-242-22-42-4200000000-22-22000000000000000000000000000000000000000000000000000000000002i3−2i3000000000
χ964-4-44-244442-2-4-4-4-42-2-240-2-2-442222-400000000-22-2200000000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ974-4-44-244442-2-4-4-4-42-2-240-2-2-442222-400000000-22-22000000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4000000-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244000000-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000
χ10088-8-8-48-4-84-448-4-844-42-404-2444-2-42-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-484-8-44-484-842-4-40-2444-242-4-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-444-44-4-44442220-2-2-2-2-2-222200000000-111-10000006-6-33-330000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-444-44-4-44442220-2-2-2-2-2-222200000000-111-1000000-663-33-30000000000000000000000000000000000000000000000000000000000
χ1048-88-88-4-444-8-844-4-48-4-420442-2-4-444-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-4444444-4-4-42220-2-22-222-2-2-243−43000000-1-11100−2323−23230033−3−30000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-4444444-4-4-42220-2-22-222-2-2-2−4343000000-1-1110023−2323−2300−3−3330000000000000000000000000000000000000000000000000000000000
χ1078-8-888-4-4-4-4-884444-8-4-420-4-4-224444-2000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-48-44-4-84-844-42-40-424-44-24-24000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-48-484-44-84-842-4-402-44-4-24-244000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4-4-44-444444222022-22-2-2-2-2-200000000-11-110000000033−33−33330000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-4-44-444444222022-22-2-2-2-2-200000000-11-1100000000−333333−330000000000000000000000000000000000000000000000000000000000

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