Finite Group Databasebeta

← Group #13172278

Character table — Group #13172278

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444666666888888888888888899991212121212121212121212121212121212121218181818181818182424242424242424242424242424242436363636363636363654547272108
order1222333666666666233366666666666444444366666666666666644442446612121212121212121212121212122244121212126661212121212121212121212121244466121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11111111111111111111111-1111111-1-11111-1-111-1-1-1-111111111-1-1111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-1-1-1-11-111111-1-11111-1-111-1-1-1-111-1-1-1-1111-11111-1-1-1-11111-11-1-1-111-1-1-1-11-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-11-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-111
χ51111111111111111111111111111111-1-111111111111111111111-1-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1111-1-111111111-1-1111-1-1-1-1-1-1-11-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-11-1-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-11-1-1-111-1-1111-11
χ71111111111111111111111111111111-1-1-1-11111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111-1-1-1-1-1-11111-1-11
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
χ91111111111111111-1111-1-11111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1111111111111-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-1-11111-1-111-1-1-1
χ101111111111111111-1111-1-11111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11111-1-11-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-111-1-1-1-1-1-1-1-1111
χ111111111111111111-1111-1-111111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-11-1-1-111-1-11111-1-11111-1-111-1-1-1-1-1-1-11-1-111-1-11111-1-11-11-1-11111-1-1-111
χ121111111111111111-1111-1-111111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-111-1-11111-111-1-111111-1-1
χ131111111111111111-1111-1-1111111111-1-111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-111-1-11111-1-11111-1-111-1-1-1-1-1-1111-1-1-1-1-111-1-111-1-111-111-1-111-1-11-11
χ141111111111111111-1111-1-1111111111-1-111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1111-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-1111-111-1-111-1-1-1-1111-11-1-1111111-11-1
χ151111111111111111-1111-1-1111111111-1-1-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1111111-111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-111-1-1-1-1-1-11111-1
χ161111111111111111-1111-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-111-1-1-11111-1-1-1-1-1-11
χ17222222-1222-1-122-122-1-1222-1-122-1-1-1-12002222-12-1-1-1-1-122-1-1-1-1-1-1-100000220000222200-1-1-1-12222000000000-1-1200-1-1-1-1-1-1-1-1002-1-10000000-10
χ18222222-1222-1-122-122-1-1222-1-122-1-1-1-120022-2-2-12-1-1-1-1-122-1-1-1-1-1-1-1000002-2000022-2-200-1-11122-2-2000000000-11-200-1-1-1-1111100-211000000010
χ19222222-1222-1-122-122-1-1222-1-122-1-1-1-1200-2-222-12-1-1-1-1-122-1-1-1-1-1-1-100000-220000-2-2220011-1-1-2-2-2-20000000001-12001111-1-1-1-100-211000000010
χ20222222-1222-1-122-122-1-1222-1-122-1-1-1-1200-2-2-2-2-12-1-1-1-1-122-1-1-1-1-1-1-100000-2-20000-2-2-2-2001111-2-22200000000011-20011111111002-1-10000000-10
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χ22222222-1222-1-122-12-2-1-12-2-2-1-122-1-1-1-120022-2-2-1-211111-2-2-1-1-1111100000-22000022-2-200-1-111-2-2-2-20000000001-1200-1-11111-1-1002110000000-10
χ23222222-1222-1-122-12-2-1-12-2-2-1-122-1-1-1-1200-2-222-1-211111-2-2-1-1-11111000002-20000-2-2220011-1-122-2-2000000000-11-20011-1-1-1-111002110000000-10
χ24222222-1222-1-122-12-2-1-12-2-2-1-122-1-1-1-1200-2-2-2-2-1-211111-2-2-1-1-1111100000220000-2-2-2-20011112222000000000-1-120011-1-111-1-100-2-1-1000000010
χ2522222-1222-122-1-12222-1-1222-1-1-122-1-1-1220022-1-1222-1-1-1-1-1-1-1-1-1-1-10000202222200-1-1-1-100220000220000-1-1-102-1-1-10000-1-1-1-102000-1-10000-100
χ2622222-1222-122-1-12222-1-1222-1-1-122-1-1-12200-2-2-1-1222-1-1-1-1-1-1-1-1-1-1-1000020-222220011-1-100-2-20000-2-20000-1-1-10-21-1-1000011110-2000110000100
χ2722222-1222-122-1-12222-1-1222-1-1-122-1-1-1-2-20022-1-1222-1-1-1-1-1-1-1-1-1-1-10000-202-2-2-2-200-1-11100220000-2-2000011102-1110000-1-1-1-10-2000110000100
χ2822222-1222-122-1-12222-1-1222-1-1-122-1-1-1-2-200-2-2-1-1222-1-1-1-1-1-1-1-1-1-1-10000-20-2-2-2-2-200111100-2-200002200001110-21110000111102000-1-10000-100
χ2922222-1222-122-1-122-22-1-1-2-22-1-1-122-1-1-1220022-11-2-2-21111-1-1-111110000-20-2-2-22200-1-1-1-1002200002200001110-21-1-10000-1-1110-2000-1-10000100
χ3022222-1222-122-1-122-22-1-1-2-22-1-1-122-1-1-12200-2-2-11-2-2-21111-1-1-111110000-202-2-2220011-1-100-2-20000-2-2000011102-1-1-1000011-1-102000110000-100
χ3122222-1222-122-1-122-22-1-1-2-22-1-1-122-1-1-1-2-20022-11-2-2-21111-1-1-11111000020-222-2-200-1-11100220000-2-20000-1-1-10-21110000-1-11102000110000-100
χ3222222-1222-122-1-122-22-1-1-2-22-1-1-122-1-1-1-2-200-2-2-11-2-2-21111-1-1-11111000020222-2-200111100-2-20000220000-1-1-102-111000011-1-10-2000-1-10000100
χ332222-122-1-1222222-12-12-1-1-1-12-1-1-1-122-1222200-122-1-122-1-1-1-1-1-1-1-1-12222220-1-1-1-1-1-100222200-1-10000-1-1-1-12-1-1200-1-1-1-1-1-100002000000-1-100000
χ342222-122-1-1222222-12-12-1-1-1-12-1-1-1-122-122-2-200-122-1-122-1-1-1-1-1-1-1-1-1-2-2-2-22-20-1-1-1-1110022-2-20011000011112-1-1-200-1-111110000-20000001100000
χ352222-122-1-1222222-12-12-1-1-1-12-1-1-1-122-1-2-22200-122-1-122-1-1-1-1-1-1-1-1-1-2-2-2-2-2201111-1-100-2-22200-1-100001111-21120011-1-1-1-10000-20000001100000
χ362222-122-1-1222222-12-12-1-1-1-12-1-1-1-122-1-2-2-2-200-122-1-122-1-1-1-1-1-1-1-1-12222-2-2011111100-2-2-2-200110000-1-1-1-1-211-20011111100002000000-1-100000
χ372222-122-1-1222222-1-2-12-111-12-1-1-1-122-1222200-1-2-211-2-211-1-1-111112222-2-2011-1-1-1-100222200110000-1-1-1-1-211-200-1-1-1-1110000-20000001100000
χ382222-122-1-1222222-1-2-12-111-12-1-1-1-122-122-2-200-1-2-211-2-211-1-1-11111-2-2-2-2-22011-1-1110022-2-200-1-100001111-211200-1-111-1-100002000000-1-100000
χ392222-122-1-1222222-1-2-12-111-12-1-1-1-122-1-2-22200-1-2-211-2-211-1-1-11111-2-2-2-22-20-1-111-1-100-2-2220011000011112-1-1-20011-1-11100002000000-1-100000
χ402222-122-1-1222222-1-2-12-111-12-1-1-1-122-1-2-2-2-200-1-2-211-2-211-1-1-111112222220-1-1111100-2-2-2-200-1-10000-1-1-1-12-1-12001111-1-10000-20000001100000
χ4122-2-2222-2-2-22-22-2-22022200-222-22-2-2-2-200002i−2i2000000002-2-2000022-2-20000000002i−2i00002i−2i00000022-2-20000000000002i−2i000000000002i−2i000
χ4222-2-2222-2-2-22-22-2-22022200-222-22-2-2-2-200002i−2i2000000002-2-20000-2-2220000000002i−2i00002i−2i000000-2-2220000000000002i−2i00000000000−2i2i000
χ4322-2-2222-2-2-22-22-2-22022200-222-22-2-2-2-20000−2i2i2000000002-2-2000022-2-2000000000−2i2i0000−2i2i00000022-2-2000000000000−2i2i00000000000−2i2i000
χ4422-2-2222-2-2-22-22-2-22022200-222-22-2-2-2-20000−2i2i2000000002-2-20000-2-222000000000−2i2i0000−2i2i000000-2-222000000000000−2i2i000000000002i−2i000
χ452-22-22222-22-2-2-2-22-2022200-2-2-22-222-2-2000000200000000-22-200002i−2i2i−2i00000000000000000002-22i−2i2i−2i2i−2i00000000000000000002-22i−2i0000000
χ462-22-22222-22-2-2-2-22-2022200-2-2-22-222-2-2000000200000000-22-200002i−2i2i−2i0000000000000000000-22−2i2i2i−2i2i−2i0000000000000000000-22−2i2i0000000
χ472-22-22222-22-2-2-2-22-2022200-2-2-22-222-2-2000000200000000-22-20000−2i2i−2i2i00000000000000000002-2−2i2i−2i2i−2i2i00000000000000000002-2−2i2i0000000
χ482-22-22222-22-2-2-2-22-2022200-2-2-22-222-2-2000000200000000-22-20000−2i2i−2i2i0000000000000000000-222i−2i−2i2i−2i2i0000000000000000000-222i−2i0000000
χ492-2-22222-22-2-22-22-2-20222002-2-2-2-2-2-2222-22i−2i00200000000-2-2200002i−2i−2i2i000002-22i−2i002-22i−2i000000002i−2i−2i2i0000002-22i−2i00000000000000000000
χ502-2-22222-22-2-22-22-2-20222002-2-2-2-2-2-2222-2−2i2i00200000000-2-220000−2i2i2i−2i000002-2−2i2i002-2−2i2i00000000−2i2i2i−2i0000002-2−2i2i00000000000000000000
χ512-2-22222-22-2-22-22-2-20222002-2-2-2-2-2-222-222i−2i00200000000-2-220000−2i2i2i−2i00000-222i−2i00-222i−2i00000000−2i2i2i−2i000000-222i−2i00000000000000000000
χ522-2-22222-22-2-22-22-2-20222002-2-2-2-2-2-222-22−2i2i00200000000-2-2200002i−2i−2i2i00000-22−2i2i00-22−2i2i000000002i−2i−2i2i000000-22−2i2i00000000000000000000
χ532-2-22-1221-1-2-22-22-210-12-1−i3i3-1-21111-22-12-22i−2i00-100−i3i300−i3i311-1−i3−i3i3i32i−2i−2i2i000−i3i3-11−ii002-22i−2i003−30000−iii−i0−i3i3000-11−ii3−3000000000003−300000
χ542-2-22-1221-1-2-22-22-210-12-1−i3i3-1-21111-22-12-2−2i2i00-100−i3i300−i3i311-1−i3−i3i3i3−2i2i2i−2i000−i3i3-11i−i002-2−2i2i00−330000i−i−ii0−i3i3000-11i−i−3300000000000−3300000
χ552-2-22-1221-1-2-22-22-210-12-1−i3i3-1-21111-22-1-222i−2i00-100−i3i300−i3i311-1−i3−i3i3i3−2i2i2i−2i000i3−i31-1−ii00-222i−2i003−30000i−i−ii0i3−i30001-1−ii3−300000000000−3300000
χ562-2-22-1221-1-2-22-22-210-12-1−i3i3-1-21111-22-1-22−2i2i00-100−i3i300−i3i311-1−i3−i3i3i32i−2i−2i2i000i3−i31-1i−i00-22−2i2i00−330000−iii−i0i3−i30001-1i−i−33000000000003−300000
χ572-2-22-1221-1-2-22-22-210-12-1i3−i3-1-21111-22-12-22i−2i00-100i3−i300i3−i311-1i3i3−i3−i32i−2i−2i2i000i3−i3-11−ii002-22i−2i00−330000−iii−i0i3−i3000-11−ii−3300000000000−3300000
χ582-2-22-1221-1-2-22-22-210-12-1i3−i3-1-21111-22-12-2−2i2i00-100i3−i300i3−i311-1i3i3−i3−i3−2i2i2i−2i000i3−i3-11i−i002-2−2i2i003−30000i−i−ii0i3−i3000-11i−i3−3000000000003−300000
χ592-2-22-1221-1-2-22-22-210-12-1i3−i3-1-21111-22-1-222i−2i00-100i3−i300i3−i311-1i3i3−i3−i3−2i2i2i−2i000−i3i31-1−ii00-222i−2i00−330000i−i−ii0−i3i30001-1−ii−33000000000003−300000
χ602-2-22-1221-1-2-22-22-210-12-1i3−i3-1-21111-22-1-22−2i2i00-100i3−i300i3−i311-1i3i3−i3−i32i−2i−2i2i000−i3i31-1i−i00-22−2i2i003−30000−iii−i0−i3i30001-1i−i3−300000000000−3300000
χ6144444-2-244-2-2-2-2-2-244-21-244-21-2-2-2-211-20000441-2-2-2-211-2-211111110000004000000-2-20000-2-200000000000000-2-2000000111100000000000000
χ6244444-2-244-2-2-2-2-2-244-21-244-21-2-2-2-211-20000-4-41-2-2-2-211-2-21111111000000-4000000220000220000000000000022000000-1-1-1-100000000000000
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χ834-44-444-24-4422-4-4-2-40-2-240022-442-2-22-4000000-2000000002-220000000000000000000000000004-40000000000000000000000000-22000000000
χ844-44-444-24-4422-4-4-2-40-2-240022-442-2-22-4000000-2000000002-22000000000000000000000000000-4400000000000000000000000002-2000000000
χ854-44-44-244-4-2-4-4224-404-2-200-422-2-44-222000000-2000000002-22000000000000000000000000000004i−4i0000000000000000000000000−2i2i0000000
χ864-44-44-244-4-2-4-4224-404-2-200-422-2-44-222000000-2000000002-2200000000000000000000000000000−4i4i00000000000000000000000002i−2i0000000
χ874-44-4-244-224-4-4-4-4420-24-2002-42-22-24-42000000-2000000002-2200004i−4i4i−4i00000000000000000000000−2i2i−2i2i000000000000000000000000000000
χ884-44-4-244-224-4-4-4-4420-24-2002-42-22-24-42000000-2000000002-220000−4i4i−4i4i000000000000000000000002i−2i2i−2i000000000000000000000000000000
χ894-4-4444-2-44-42-2-442-40-2-2400-22-4-4222-24004i−4i00-20000000022-20000000000000004i−4i0000−2i2i00000000000000000000−2i2i00000000000000000000
χ904-4-4444-2-44-42-2-442-40-2-2400-22-4-4222-2400−4i4i00-20000000022-2000000000000000−4i4i00002i−2i000000000000000000002i−2i00000000000000000000
χ914-4-444-24-442-442-2-4-404-2-2004222-4-42-2-24-40000-20000000022-200000000000004-40000-2200000000000000000000-220000000000000000000000
χ924-4-444-24-442-442-2-4-404-2-2004222-4-42-2-2-440000-20000000022-20000000000000-4400002-2000000000000000000002-20000000000000000000000
χ934-4-44-24-22-2-42-2-442201-2-2−2i32i31222-1-12-2-2004i−4i00100i3−i300−2i32i3-1-11i3i3−i3−i300000000000−2i2i0000−2i2i0023−230000000000000000i−i−33000000000000000000
χ944-4-44-24-22-2-42-2-442201-2-2−2i32i31222-1-12-2-200−4i4i00100i3−i300−2i32i3-1-11i3i3−i3−i3000000000002i−2i00002i−2i00−23230000000000000000−ii3−3000000000000000000
χ954-4-44-24-22-2-42-2-442201-2-22i3−2i31222-1-12-2-2004i−4i00100−i3i3002i3−2i3-1-11−i3−i3i3i300000000000−2i2i0000−2i2i00−23230000000000000000i−i3−3000000000000000000
χ964-4-44-24-22-2-42-2-442201-2-22i3−2i31222-1-12-2-200−4i4i00100−i3i3002i3−2i3-1-11−i3−i3i3i3000000000002i−2i00002i−2i0023−230000000000000000−ii−33000000000000000000
χ974-4-44-2-242-22-442-2-420-2-21−2i32i3-22-1-1222-214-40000100−2i32i300i3−i3-1-11i3i3−i3−i30000000−2i32i3-220000-22000000000000000i3−i30001-10000000000000000000000
χ984-4-44-2-242-22-442-2-420-2-21−2i32i3-22-1-1222-21-440000100−2i32i300i3−i3-1-11i3i3−i3−i300000002i3−2i32-200002-2000000000000000−i3i3000-110000000000000000000000
χ994-4-44-2-242-22-442-2-420-2-212i3−2i3-22-1-1222-214-400001002i3−2i300−i3i3-1-11−i3−i3i3i300000002i3−2i3-220000-22000000000000000−i3i30001-10000000000000000000000
χ1004-4-44-2-242-22-442-2-420-2-212i3−2i3-22-1-1222-21-4400001002i3−2i300−i3i3-1-11−i3−i3i3i30000000−2i32i32-200002-2000000000000000i3−i3000-110000000000000000000000
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
χ10388-8-8-48-444-8-448-84-402-4-400-2-4-442-24440000002000000002-2-200000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-484448-8-44-8-40-4-42004-42-2-4444-20000002000000002-2-200000000000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-4444-44-444-4022200-222-22-2-2-2-2000000-100006-600-111-33-330000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-4444-44-444-4022200-222-22-2-2-2-2000000-10000-6600-1113-33-30000000000000000000000000000000000000000000000000000000000000
χ1078-88-88-4-48-8-44444-4-80-42-4004-24-44-42-24000000200000000-22-200000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-48-4-44844-8-8-4402-4-400-244-4-22-444000000200000000-22-200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-48-44-4-8-844840-4-420044-224-4-44-2000000200000000-22-200000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4-44-44444-44022200-2-2-22-222-2-2000000-1000000001-11−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-4-44-44444-44022200-2-2-22-222-2-2000000-1000000001-113i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000000000
χ1128-8-888-4-4-8844-44-44-80-42-400-4-24444-22-4000000200000000-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-44-444-44-4440222−4i34i32-2-2-2-2-2-222000000-1002i3−2i3002i3−2i311-1−i3−i3i3i30000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-44-444-44-44402224i3−4i32-2-2-2-2-2-222000000-100−2i32i300−2i32i311-1i3i3−i3−i30000000000000000000000000000000000000000000000000000000000000

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