Finite Group Databasebeta

← Group #13156256

Character table — Group #13156256

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size11222222222222244444444444444444444444666666888888888888121212121212121212121212121212121212121212242424242424242424242424242424363636363636727272727272216
order1223334466612121212333666666661212121212121212121212128824242424366666121212121212246681212242424242424242424242424242466681212122424242424242424882424242448121224244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11-1-111111111111111-1-1-11-1-1-111111111-1-1-1-1-1-1-11-1-111-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-11-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11
χ511111111111111111111111111111111111111-1-1-1-1-1-11111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-11-111-1-1-1
χ611111111111111111111111111111111111111-1-1-1-1-1-11111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ711111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111111111111-1-1-1-1-1-11
χ811111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1
χ9222222-2-2222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000222222-2-2-2-2-2-20000000000000000000000000000000000002i−2i2i2i−2i−2i0000000
χ10222222-2-2222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000222222-2-2-2-2-2-2000000000000000000000000000000000000−2i2i−2i−2i2i2i0000000
χ1122222-12222-122222-1-122-1222-1-12-122-1-12-122-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1222202200000000000000-1-1-12-1-1-122-1-1-1-1-1-100000020-1-1000
χ1222222-12222-122222-1-122-1222-1-12-122-1-12-122-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1222202200000000000000-1-1-1-2-1-1-1-2-2111111000000-2011000
χ1322222-12222-122222-1-122-1222-1-12-122-1-12-122-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20-2-200000000000000111211122-1-1-1-1-1-1000000-2011000
χ1422222-12222-122222-1-122-1222-1-12-122-1-12-122-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20-2-200000000000000111-2111-2-211111100000020-1-1000
χ152222-12222-1222-1-1-12-12-12-1-1-12-1-12-1-1-1-122-1-12222-1-1-1-1-12-1-1-1-12-1-1-1-1-122-1-12-1-1-1-12222-1-1-1-1-1-1-1-12-1-102-1-10000000022-1-1-1-10000000
χ162222-12222-1222-1-1-12-12-12-1-1-12-1-12-1-1-1-122-1-12222-1-1-1-1-12-1-1-1-12-1-1-1-1-1-2-211211-1-12222-1-1-1-1-1-1-1-1-2110-21100000000-2-211110000000
χ172222-12222-1222-1-1-12-12-12-1-1-12-1-12-1-1-1-122-1-122-2-21111-12-1-1-1-12-1-1-1-1-122-1-1-2-1-111-2-2-2-2111111112-1-102-1-100000000-2-211110000000
χ182222-12222-1222-1-1-12-12-12-1-1-12-1-12-1-1-1-122-1-122-2-21111-12-1-1-1-12-1-1-1-1-1-2-211-21111-2-2-2-211111111-2110-2110000000022-1-1-1-10000000
χ192222-12-2-22-12-2-211-12-12-12-1-1-12-11-21111-2-211-2-20033−3−3-12-1-1-1-1-21111100−i3i30−i3i33−300003333−3−3−3−30−i3i300−i3i3000000002i−2i−i−iii0000000
χ202222-12-2-22-12-2-211-12-12-12-1-1-12-11-21111-2-211-2-20033−3−3-12-1-1-1-1-21111100i3−i30i3−i33−300003333−3−3−3−30i3−i300i3−i300000000−2i2iii−i−i0000000
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χ222222-12-2-22-12-2-211-12-12-12-1-1-12-11-21111-2-211-2-200−3−333-12-1-1-1-1-21111100i3−i30i3−i3−330000−3−3−3−333330i3−i300i3−i3000000002i−2i−i−iii0000000
χ23222-12222-122-1-122-1-12-122-1-1-1-1222-1-122-12-1-1-1-1222222-1-12-1-1-1-12-1-1-1-1000020022-1-1-1-1-1-1-1-1-1-1-1-10002000-1-122-1-1-1-10000000200-1-10
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χ25222-12222-122-1-122-1-12-122-1-1-1-1222-1-122-12-1-1-1-1-2-2-2-2-2-2-1-12-1-1-1-12-1-1-1-10000-200-2-21111111111110002000-1-122-1-1-1-10000000-200110
χ26222-12222-122-1-122-1-12-122-1-1-1-1222-1-122-12-1-1-1-1-2-2-2-2-2-2-1-12-1-1-1-12-1-1-1-10000-200-2-2111111111111000-200011-2-211110000000200-1-10
χ2722-22222-222222-2-2222-2-2-2-2-22222-222-2-2-22-2-2220000002-2-2-2-22-2222-2-22-2220-2-2000000000000002220-2-2-2000000000000000000000
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χ3022-2222-22222-2-222222-2-2-2-2-2222-22-2-2222-222-2-2-2-2-2-2-2-22-2-2-2-222-2-2-222000020022-2-222-2-222-2-2220000000000000000000000000000
χ3122-222-12-222-122-2-22-1-1-2-21-2-22-1-1212211-2-1-2-2-1-1000000-11111-11-1-1-1112-2220-2-200000000000000-1-1-1011100−i3i3−i3−i3i3i300000000−i3i3000
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χ3322-222-12-222-122-2-22-1-1-2-21-2-22-1-1212211-2-1-2-2-1-1000000-11111-11-1-1-111-22-2-2022000000000000001110-1-1-100−i3i3−i3−i3i3i300000000i3−i3000
χ3422-222-12-222-122-2-22-1-1-2-21-2-22-1-1212211-2-1-2-2-1-1000000-11111-11-1-1-111-22-2-2022000000000000001110-1-1-100i3−i3i3i3−i3−i300000000−i3i3000
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χ3722-22-122-22-122211-12-1-21-211-12-1-1-2-1-111-22112200−3−333-1-2111-1-2-1-1-1112-2-1-10113−30000−3−33333−3−32-1-10-2110000000000−33−330000000
χ3822-22-122-22-122211-12-1-21-211-12-1-1-2-1-111-22112200−3−333-1-2111-1-2-1-1-111-22110-1-13−30000−3−33333−3−3-21102-1-100000000003−33−30000000
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χ4022-22-12-222-12-2-2-1-1-12-1-21-211-12-11211-1-12-2-1-1-2-222-1-1-1-1-1-2111-12111-1-100i3−i3-2−i3i31122-2-2-1-111-1-1110i3−i300−i3i30000000000i3−i3−i3i30000000
χ4122-22-12-222-12-2-2-1-1-12-1-21-211-12-11211-1-12-2-1-1-2-2-2-21111-1-2111-12111-1-100−i3i32i3−i3-1-1-2-22211-1-111-1-10−i3i300i3−i30000000000i3−i3−i3i30000000
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χ4422-2-122-22-1221122-1-121-2-211-1-12-221122-1-2-1-111222222-11-211-1-1-211-1-10000-200-2-2-1-111-1-111-1-1110000000−3300−33−330000000000−330
χ4522-2-122-22-1221122-1-121-2-211-1-12-221122-1-2-1-111-2-2-2-2-2-2-11-211-1-1-211-1-100002002211-1-111-1-111-1-100000003−3003−33−30000000000−330
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χ56444-24-2-4-4-24-222-4-4-21-2-24-2-2-2-21-2-4222222222-1-100000011-2111-12-1-1-1-100000000000000000000000000000000−3i3i3i−3i0000000000000
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χ864-40-2-240022-423−2323−231-2-20003-3-12200−3323−2300−3323−23−2222−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ231003-3-100−33−330000000002−2−66ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23ζ13−ζ23−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ230000000000000000000000000000
χ874-40-2-240022-423−23−23231-2-2000-33-12200−33−2323003−323−2322−222ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7100-33-100−333−3000000000−226−6−ζ13+ζ23ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ230000000000000000000000000000
χ884-40-2-240022-423−23−23231-2-2000-33-12200−33−2323003−323−23−2222−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7100-33-100−333−30000000002−2−66ζ13−ζ23−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ230000000000000000000000000000
χ894-40-2-240022-4−232323−231-2-2000-33-122003−323−2300−33−232322−222ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23100-33-1003−3−33000000000−22−66−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23−ζ13+ζ23ζ13−ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ230000000000000000000000000000
χ904-40-2-240022-4−232323−231-2-2000-33-122003−323−2300−33−2323−2222−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23100-33-1003−3−330000000002−26−6ζ5−ζ7−ζ5+ζ7ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23ζ13−ζ23−ζ13+ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ230000000000000000000000000000
χ914-40-2-240022-4−2323−23231-2-20003-3-122003−3−2323003−3−232322−222ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ71003-3-1003−33−3000000000−22−66−ζ13+ζ23ζ13−ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ230000000000000000000000000000
χ924-40-2-240022-4−2323−23231-2-20003-3-122003−3−2323003−3−2323−2222−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ71003-3-1003−33−30000000002−26−6ζ13−ζ23−ζ13+ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ230000000000000000000000000000
χ93888-4-4-488-4-4-4-4-4-4-4222-4-4-422222-4-42222-4-42222000000-122-1-1-122-1-1-1-10000000000000000000000000000000000000000000000000
χ94888-4-4-4-8-8-4-4-44444222-4-4-42222244-2-2-2-244-2-2-2-2000000-122-1-1-1-2-211110000000000000000000000000000000000000000000000000
χ9588-8-4-4-48-8-4-4-4-4-444222444-2-2222-4422-2-24-4-2-222000000-1-2-211-1-22-1-1110000000000000000000000000000000000000000000000000
χ9688-8-4-4-4-88-4-4-444-4-4222444-2-22224-4-2-222-4422-2-2000000-1-2-211-12-211-1-10000000000000000000000000000000000000000000000000
χ978-8088-400-8-8400008-4-400000-844000000000000000000-4000040000000000000000000000000000000000000000000000000000000
χ988-808-4-400-8440043−43-4-420000044-20000−23230043−430000000020000-20000−23230000000000000000000000000000000000000000000000000
χ998-808-4-400-84400−4343-4-420000044-2000023−2300−43430000000020000-2000023−230000000000000000000000000000000000000000000000000
χ1008-80-48-4004-8443−4300-42-4000004-240043−43000000−232300000020000-200−2323000000000000000000000000000000000000000000000000000
χ1018-80-48-4004-84−434300-42-4000004-2400−434300000023−2300000020000-20023−23000000000000000000000000000000000000000000000000000
χ1028-80-4-4-40044443−4343−432220006-6-2-2-200−2323−232300−2323−2323000000-100-331003−33−30000000000000000000000000000000000000000000000000
χ1038-80-4-4-40044443−43−4343222000-66-2-2-200−232323−230023−23−2323000000-1003-31003−3−330000000000000000000000000000000000000000000000000
χ1048-80-4-4-400444−434343−43222000-66-2-2-20023−23−232300−232323−23000000-1003-3100−333−30000000000000000000000000000000000000000000000000
χ1058-80-4-4-400444−4343−43432220006-6-2-2-20023−2323−230023−2323−23000000-100-33100−33−330000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.