Finite Group Databasebeta

← Group #13172094

Character table — Group #13172094

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222244444444444444444444466888888888888812121212121212121212121212121212121212121212121212181824242424242424242424242424243636363636363654547272727272108
order122233366666666623336666666666666666644366666666666624444121212121212121212121212121212121212121244666612121212121212121212244441212446121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-11-1-1-1111111111111111111-1-111111-1-1-111-1-1-1-11-11-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-111-11111111-1-1111111111111-1-1-1-1-1-1-1111-1-11111-11-11-1-1-1-1-1-1-11-11-1
χ41111111111111111111111111111111111111111111111111111-11-1-1-1-1-11111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-11-11
χ51111111111111111111111111111111111111-1-111111111111111-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111-1-1-1-1-11-1-1
χ61111111111111111111111111111111111111-1-111111111111111-1-11-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-1-1-1-11-11-1-1-111-1-11-111
χ71111111111111111111111111111111111111-1-11111111111111-1-11-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111-11-1-1-1-11111-1-1-11
χ81111111111111111111111111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111111-1
χ91111111111111111-1111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1111-1-1-1-11-11-1-11111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-11-1-111-1-111-1-11-1-1-1-11-1-1111
χ101111111111111111-1111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1111-1-1-1-11-1-1-11-1-111-1-1-1-111-1-11111-1-1-1-1111111-111-1-1-1-1-1111-1-11-111111-11-1-1-1
χ111111111111111111-1111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1111-1-1-1-1-1-111-11111-1-11111-1-11111-1-1-1-111-1-1-1-11-1-111111-1-1-111-1-11111-11-1-11-1
χ121111111111111111-1111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1111-1-1-1-1-1-1-111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111-111-1-111-1-1111-1-1-1-1-1111-11
χ131111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-11-1-1-1-1-1111-1-1-1-1111-1-111-1-111-1-1-1-111-1-1-1-11111-1-11111-1-1-11-1-111-1-1-1-1111-1-111-1111-1-1
χ141111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-11-1-1-1-1-1111-1-1-1-111-1-11-1-1-1-111-1-1-1-111-1-1-1-11111111111-111-1-1-1-1-111-111-1-111-1-1-11-1-111
χ151111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-11-1-1-1-1-1111-1-1-1-1-1111-111-1-11111-1-111-1-1-1-1111111-1-1-1-11-1-111111-1-11-1-11-111-1-11-11-1-11
χ161111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-11-1-1-1-1-1111-1-1-1-1-11-111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1111-111-1-11111-1-11-1-1111-1-111-1
χ17222222-12-12-122-12222-1-122-1-12-1-1-1-1-1-1-1-122-1-122-1222-1-1-1-1-1-1-1-1-12202000-1-1-1-1222222-1-1-1-1-1-1-1-1002-1-1-1-1000-1-10000202000000-1-10000
χ18222222-12-12-122-12222-1-122-1-12-1-1-1-1-1-1-1-122-1-122-1222-1-1-1-1-1-1-1-1-1-220-2000-1-1-1-1-2-22222-1-1-1-1-1-1-1-100-21111000110000-20-2000000110000
χ19222222-12-12-122-12222-1-122-1-12-1-1-1-1-1-1-1-122-1-1-2-2-1222-1-1-1-1-1-1-1-1-12-202000111122-2-2-2-211111111002-1-1-1-1000-1-10000-20-2000000110000
χ20222222-12-12-122-12222-1-122-1-12-1-1-1-1-1-1-1-122-1-1-2-2-1222-1-1-1-1-1-1-1-1-1-2-20-20001111-2-2-2-2-2-21111111100-21111000110000202000000-1-10000
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χ23222222-12-12-122-122-22-1-1-2-2112-1-11111-1-122-1-1-2-2-1-2-2-211-1-1-11111220-200011-1-1-2-2-2-2221111-1-1-1-1002-1-1-11000110000-2020000001-10000
χ24222222-12-12-122-122-22-1-1-2-2112-1-11111-1-122-1-1-2-2-1-2-2-211-1-1-11111-220200011-1-122-2-2221111-1-1-1-100-2111-1000-1-1000020-2000000-110000
χ2522222-1222-12-122-122-12-12222-1222222-1-1-1-1-1200-1-1-1-1-1-1-1-1-1-1-1-1-120222-1-10000-1-100000000000022-12-1-122-12-1-1-1-1-1-100002-1-100000-100
χ2622222-1222-12-122-122-12-12222-1222222-1-1-1-1-1200-1-1-1-1-1-1-1-1-1-1-1-1-120-22-2110000-1-1000000000000-2-2-12-1-12-21-2-1-111110000-21100000100
χ2722222-1222-12-122-122-12-12222-1222222-1-1-1-1-1200-1-1-1-1-1-1-1-1-1-1-1-1-1-202-22-1-1000011000000000000-2-21-211-22-1211-1-1-1-10000-21100000100
χ2822222-1222-12-122-122-12-12222-1222222-1-1-1-1-1200-1-1-1-1-1-1-1-1-1-1-1-1-1-20-2-2-211000011000000000000221-211-2-21-211111100002-1-100000-100
χ2922222-1222-12-122-12-2-12-1-2-2-2-2-122-2-2-2-2-1-1-1-1-1200-111111-1-1-11111202-2-2-1-1000011000000000000-2-2-12-1-1-2-21211-1-111000021100000-100
χ3022222-1222-12-122-12-2-12-1-2-2-2-2-122-2-2-2-2-1-1-1-1-1200-111111-1-1-1111120-2-221100001100000000000022-12-1-1-22-1-21111-1-10000-2-1-100000100
χ3122222-1222-12-122-12-2-12-1-2-2-2-2-122-2-2-2-2-1-1-1-1-1200-111111-1-1-11111-2022-2-1-10000-1-1000000000000221-2112-212-1-1-1-1110000-2-1-100000100
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χ342222-122-12222-122-12-1-12-1-122-1-1-1-1-1-1-122-1-12-122-12-1-122-1-1-1-1-1-1-102-20-2-2-2222200-1-1-1-1-1-1-1-1-1-1-1-100000001-210011110-20-200000001010
χ352222-122-12222-122-12-1-12-1-122-1-1-1-1-1-1-122-1-12-1-2-2-12-1-122-1-1-1-1-1-1-10-220222-2-2-2-2001111111111110000000-12-100-1-1-1-10-20-200000001010
χ362222-122-12222-122-12-1-12-1-122-1-1-1-1-1-1-122-1-12-1-2-2-12-1-122-1-1-1-1-1-1-10-2-20-2-2-2-2-2-2-20011111111111100000001-2100111102020000000-10-10
χ372222-122-12222-122-1-2-1-1211-2-2-1-1-1111122-1-12-122-1-211-2-2-1-1-111110-220-22222-2-200-1-111-1-1-1-1111100000001-2-100-1-111020-2000000010-10
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χ392222-122-12222-122-1-2-1-1211-2-2-1-1-1111122-1-12-1-2-2-1-211-2-2-1-1-111110220-222-2-2220011-1-11111-1-1-1-100000001-2-100-1-1110-2020000000-1010
χ402222-122-12222-122-1-2-1-1211-2-2-1-1-1111122-1-12-1-2-2-1-211-2-2-1-1-1111102-202-2-2-2-2220011-1-11111-1-1-1-10000000-1210011-1-1020-2000000010-10
χ4122-2-2222-2-222-2-2-2-2202220000-2-2-200002-22-2-222-22000002-2-2000000000002-200002-20022-2-200002i−2i00000000000000000002i−2i2i−2i000000
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χ924-4-44-2442-4-4-4-4-24420-2-24000022-20000-4-42-24200-20000022-20000000000000000000−23230000−232323−230000000000000000000000000000000
χ934-4-44-24-222-42-4-2-2420-21-200−2i32i32-11i3−i3−i3i3222-2-2-1001000−2i32i3-1-11i3−i3−i3i300000000000000023−233i−3i−3i3i−333−30000000000000000000000000000000
χ944-4-44-24-222-42-4-2-2420-21-200−2i32i32-11i3−i3−i3i3222-2-2-1001000−2i32i3-1-11i3−i3−i3i3000000000000000−2323−3i3i3i−3i3−3−330000000000000000000000000000000
χ954-4-44-24-222-42-4-2-2420-21-2002i3−2i32-11−i3i3i3−i3222-2-2-10010002i3−2i3-1-11−i3i3i3−i300000000000000023−23−3i3i3i−3i−333−30000000000000000000000000000000
χ964-4-44-24-222-42-4-2-2420-21-2002i3−2i32-11−i3i3i3−i3222-2-2-10010002i3−2i3-1-11−i3i3i3−i3000000000000000−23233i−3i−3i3i3−3−330000000000000000000000000000000
χ978888-4-4-4-4-4-4-4-4-4-4-4-48222-4-4-4-4222222222222200-1-42222-1-1-1-1-1-1-100000000000000000000000000000000000000000000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-4-82224444222-2-2-2-222222200-14-2-2-2-2-1-1-1111100000000000000000000000000000000000000000000000000000000
χ9988-8-88-4-4-84-4-44-84480-4-42000044400002-2-44-2-4002000002-2-2000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-484-8-4844-84-402-4-40000-2440000-442-24-4002000002-2-2000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-444-4-44444-402220000-2-2-266-6-62-22-2-2200-100000-111-3-33300000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-444-4-44444-402220000-2-2-2-6-6662-22-2-2200-100000-11133-3-300000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-48-444-4-844-80-4-420000-4-440000-2244-2400200000-22-2000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-4-4-444-444440222−4i34i30022-22i3−2i32i3−2i3-22-2-2-2-200-102i3−2i3001-11−i3i3−i3i300000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-4-4-444-4444402224i3−4i30022-2−2i32i3−2i32i3-22-2-2-2-200-10−2i32i3001-11i3−i3i3−i300000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-484-84-84-48-4402-4-40000-24-4000044-22-4400200000-2-22000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-444444-4-4-44022200−4i34i3-2-222i3−2i3−2i32i3-2-2-222-200-10002i3−2i311-1−i3i3i3−i300000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-444444-4-4-440222004i3−4i3-2-22−2i32i32i3−2i3-2-2-222-200-1000−2i32i311-1i3−i3−i3i300000000000000000000000000000000000000000000000000000000

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