Finite Group Databasebeta

← Group #13156237

Character table — Group #13156237

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size11222222222222244444444444444444444444666666888888888888121212121212121212121212121212121212121212242424242424242424242424242424363636363636727272727272216
order1223334466666121233366666666612121212121212121212128824242424366661212121212121224668121224242424242424242424242424242666666666661212128824242424266824248
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111-11-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1111111111111111-11111-1-11111-1-1-1-1-1-1-1-1-1111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-11-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111111-1-1-1-1-1-11111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1111-1
χ611111111111111111111111111111111111111-1-1-1-1-1-11111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1111-1-1-1-1-1-1111-1-1-11
χ711111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-11111-1-1-1111111-1-1-1-1-1-11
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
χ9222222-2-222222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-200000022222-2-2-2-2-2-2-20000000000000000000000000000000000002i−2i2i2i−2i−2i0000000
χ10222222-2-222222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-200000022222-2-2-2-2-2-2-2000000000000000000000000000000000000−2i2i−2i−2i2i2i0000000
χ1122222-122-1-1-12222-12-122-1-1-1-1-1-12-122-1-122-1-1-12222222-12-1-1-1-1-12-1-1-1-1000020022-1-1-1-1-1-1-1-1-1-1-1-12022-1-100-1-1-1-10000000002-1-10000
χ1222222-122-1-1-12222-12-122-1-1-1-1-1-12-122-1-122-1-1-12222222-12-1-1-1-1-12-1-1-1-1000020022-1-1-1-1-1-1-1-1-1-1-1-1-20-2-211001111000000000-2110000
χ1322222-122-1-1-12222-12-122-1-1-1-1-1-12-122-1-122-1-1-12-2-2-2-2-2-2-12-1-1-1-1-12-1-1-1-10000-200-2-21111111111112022-1-100-1-1-1-1000000000-2110000
χ1422222-122-1-1-12222-12-122-1-1-1-1-1-12-122-1-122-1-1-12-2-2-2-2-2-2-12-1-1-1-1-12-1-1-1-10000-200-2-2111111111111-20-2-2110011110000000002-1-10000
χ152222-12222222-1222-1-12-122-1-12-1-122-122-1-1222-1000000-1-1-1-1-1-1-1-1-1-1-1-12222022000000000000002-1-1-122-1-1-1-1-1-1-1-1-10000000002-1-10
χ162222-12222222-1222-1-12-122-1-12-1-122-122-1-1222-1000000-1-1-1-1-1-1-1-1-1-1-1-1222202200000000000000-2-111-2-2-1-11111-1-1-1000000000-2110
χ172222-12222222-1222-1-12-122-1-12-1-122-122-1-1222-1000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20-2-20000000000000021-1-12211-1-1-1-1111000000000-2110
χ182222-12222222-1222-1-12-122-1-12-1-122-122-1-1222-1000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20-2-200000000000000-2111-2-21111111110000000002-1-10
χ19222-12222222-12-1-1-1-12-12-1-122-12-12-12-1-1-1-12-1-1222-1-1-1-1-1-1-1-1-122-1-1-1-1-122-1-12-1-1-1-12222-1-1-1-1-1-1-1-1020000-1-100002-1-122-1-1-1-10000000
χ20222-12222222-12-1-1-1-12-12-1-122-12-12-12-1-1-1-12-1-1222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-2-211211-1-12222-1-1-1-1-1-1-1-10-20000110000-211-2-211110000000
χ21222-12222222-12-1-1-1-12-12-1-122-12-12-12-1-1-1-12-1-12-2-21111-1-1-1-1-122-1-1-1-1-122-1-1-2-1-111-2-2-2-211111111020000-1-100002-1-1-2-211110000000
χ22222-12222222-12-1-1-1-12-12-1-122-12-12-12-1-1-1-12-1-12-2-21111-1-1-1-1-122-1-1-1-1-1-2-211-21111-2-2-2-2111111110-20000110000-21122-1-1-1-10000000
χ23222-122-2-2222-1211-1-12-12-1-122-12-1-21-21111-211-20033−3−3-1-1-1-1-1-2-21111100−i3i30−i3i33−300003333−3−3−3−3000000−i3i300000−i3i32i−2i−i−iii0000000
χ24222-122-2-2222-1211-1-12-12-1-122-12-1-21-21111-211-20033−3−3-1-1-1-1-1-2-21111100i3−i30i3−i33−300003333−3−3−3−3000000i3−i300000i3−i3−2i2iii−i−i0000000
χ25222-122-2-2222-1211-1-12-12-1-122-12-1-21-21111-211-200−3−333-1-1-1-1-1-2-21111100−i3i30−i3i3−330000−3−3−3−33333000000−i3i300000−i3i3−2i2iii−i−i0000000
χ26222-122-2-2222-1211-1-12-12-1-122-12-1-21-21111-211-200−3−333-1-1-1-1-1-2-21111100i3−i30i3−i3−330000−3−3−3−33333000000i3−i300000i3−i32i−2i−i−iii0000000
χ2722-22222-2-2-222222222-2-2-2-2-2-2222-2-22-2-222222-22222222-2-2-222-2-222-2-20000-200-2-222-2-222-2-222-2-20000000000000000000000000000
χ2822-22222-2-2-222222222-2-2-2-2-2-2222-2-22-2-222222-2-2-2-2-2-2-22-2-2-222-2-222-2-2000020022-2-222-2-222-2-2220000000000000000000000000000
χ2922-2222-22-2-2222-2-2222-2-2-2-2-2-222222-222-2-2-2-2-220000002-2-2-22-222-2-2222-2220-2-200000000000000020000220000-2-2-20000000000000
χ3022-2222-22-2-2222-2-2222-2-2-2-2-2-222222-222-2-2-2-2-220000002-2-2-22-222-2-222-22-2-2022000000000000000-20000-2-200002220000000000000
χ3122-222-12-211-12222-12-1-2-21111-1-121-221122-1-1-1-2222222-1-211-1-11-2-1-1110000-200-2-2-1-111-1-111-1-1110000−i3i300−i3−i3i3i30000000000−i3i30000
χ3222-222-12-211-12222-12-1-2-21111-1-121-221122-1-1-1-2222222-1-211-1-11-2-1-1110000-200-2-2-1-111-1-111-1-1110000i3−i300i3i3−i3−i30000000000i3−i30000
χ3322-222-12-211-12222-12-1-2-21111-1-121-221122-1-1-1-2-2-2-2-2-2-2-1-211-1-11-2-1-11100002002211-1-111-1-111-1-10000−i3i300−i3−i3i3i30000000000i3−i30000
χ3422-222-12-211-12222-12-1-2-21111-1-121-221122-1-1-1-2-2-2-2-2-2-2-1-211-1-11-2-1-11100002002211-1-111-1-111-1-10000i3−i300i3i3−i3−i30000000000−i3i30000
χ3522-22-12-22-2-222-1-2-22-1-1-21-2-2112-1-12212211-2-2-2-1000000-1111-11-1-111-1-12-2220-2-2000000000000000-1−i3i300-1-1−i3i3−i3i31110000000000−i3i30
χ3622-22-12-22-2-222-1-2-22-1-1-21-2-2112-1-12212211-2-2-2-1000000-1111-11-1-111-1-12-2220-2-2000000000000000-1i3−i300-1-1i3−i3i3−i31110000000000i3−i30
χ3722-22-12-22-2-222-1-2-22-1-1-21-2-2112-1-12212211-2-2-2-1000000-1111-11-1-111-1-1-22-2-20220000000000000001−i3i30011−i3i3−i3i3-1-1-10000000000i3−i30
χ3822-22-12-22-2-222-1-2-22-1-1-21-2-2112-1-12212211-2-2-2-1000000-1111-11-1-111-1-1-22-2-20220000000000000001i3−i30011i3−i3i3−i3-1-1-10000000000−i3i30
χ3922-2-1222-2-2-22-12-1-1-1-121-211-2-2-12-1-21211-1-12-1-1-222-1-1-1-1-1111-12-21-1-11100−i3i3-2i3−i31122-2-2-1-111-1-111000000−i3i300000i3−i300−i3i3−i3i30000000
χ4022-2-1222-2-2-22-12-1-1-1-121-211-2-2-12-1-21211-1-12-1-1-222-1-1-1-1-1111-12-21-1-11100i3−i3-2−i3i31122-2-2-1-111-1-111000000i3−i300000−i3i300i3−i3i3−i30000000
χ4122-2-1222-2-2-22-12-1-1-1-121-211-2-2-12-1-21211-1-12-1-1-2-2-21111-1111-12-21-1-11100−i3i32i3−i3-1-1-2-22211-1-111-1-1000000−i3i300000i3−i300i3−i3i3−i30000000
χ4222-2-1222-2-2-22-12-1-1-1-121-211-2-2-12-1-21211-1-12-1-1-2-2-21111-1111-12-21-1-11100i3−i32−i3i3-1-1-2-22211-1-111-1-1000000i3−i300000−i3i300−i3i3−i3i30000000
χ4322-2-122-22-2-22-1211-1-121-211-2-2-12-12-1-2-1-111-21120033−3−3-1111-1-22-111-1-12-2-1-1011−33000033−3−3−3−333020000-1-10000-211003−3−330000000
χ4422-2-122-22-2-22-1211-1-121-211-2-2-12-12-1-2-1-111-21120033−3−3-1111-1-22-111-1-1-22110-1-1−33000033−3−3−3−3330-200001100002-1-100−333−30000000
χ4522-2-122-22-2-22-1211-1-121-211-2-2-12-12-1-2-1-111-211200−3−333-1111-1-22-111-1-12-2-1-10113−30000−3−33333−3−3020000-1-10000-21100−333−30000000
χ4622-2-122-22-2-22-1211-1-121-211-2-2-12-12-1-2-1-111-211200−3−333-1111-1-22-111-1-1-22110-1-13−30000−3−33333−3−30-200001100002-1-1003−3−330000000
χ4744444-2-4-4-2-2-244-4-4-24-244-2-2-2-2-2-242-4-422-4-4222-4000000-24-2-2-222-422220000000000000000000000000000000000000000000000000
χ484444-24-4-44444-2-4-44-2-24-244-2-24-2-2-4-42-4-422-4-4-42000000-2-2-2-2-222222220000000000000000000000000000000000000000000000000
χ494444-2-244-2-2-24-244-2-214-2-2-211-21-2-24-2-2-2-2-2-2-2-2-20000001-211111-2111100000000000000000000040-2-2-2-20011110000000000000000
χ504444-2-244-2-2-24-244-2-214-2-2-211-21-2-24-2-2-2-2-2-2-2-2-20000001-211111-21111000000000000000000000-40222200-1-1-1-10000000000000000
χ514444-2-2-4-4-2-2-24-2-4-4-2-214-2-2-211-21-22-42222222220000001-2111-1-12-1-1-1-1000000000000000000000000000003-3-330000000000000000
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χ53444-24-244-2-2-2-24-2-21-2-2-2411-2-21-2-2-2-2411-2-2-211444-2-2-2-21-2111-2-2-211110000400-2-2-2-2-2-2111111110000000000000000000000000000
χ54444-24-244-2-2-2-24-2-21-2-2-2411-2-21-2-2-2-2411-2-2-2114-4-422221-2111-2-2-211110000-400222222-1-1-1-1-1-1-1-10000000000000000000000000000
χ55444-24-2-4-4-2-2-2-24221-2-2-2411-2-21-2-222-4-1-1222-1-1-4002323−23−231-2111222-1-1-1-1000000023−230000−3−3−3−333330000000000000000000000000000
χ56444-24-2-4-4-2-2-2-24221-2-2-2411-2-21-2-222-4-1-1222-1-1-400−23−2323231-2111222-1-1-1-10000000−232300003333−3−3−3−30000000000000000000000000000
χ57444-2-2444444-2-2-2-2-21-2-2-2-2-2-2-2-2-214-2-2-2-2114-2-2-200000011111-2-21111144-2-20-2-2000000000000000-20000110000-2110000000000000
χ58444-2-2444444-2-2-2-2-21-2-2-2-2-2-2-2-2-214-2-2-2-2114-2-2-200000011111-2-211111-4-42202200000000000000020000-1-100002-1-10000000000000
χ59444-2-24-4-4444-2-222-21-2-2-2-2-2-2-2-2-21-42222-1-1-42220000001111122-1-1-1-1-100−2i32i30−2i32i300000000000000000000i3−i300000i3−i30000000000000
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χ6244-44-244-4-4-444-2444-2-2-42-4-4224-2-2-4-4-2-4-4-2-24442000000-2222-2-222-2-2220000000000000000000000000000000000000000000000000
χ6344-44-2-24-422-24-244-2-21-4222-1-1-21-22-4-222-2-2-2-2-2200000012-1-111-1211-1-10000000000000000000000000−2i32i300i3i3−i3−i30000000000000000
χ6444-44-2-24-422-24-244-2-21-4222-1-1-21-22-4-222-2-2-2-2-2200000012-1-111-1211-1-100000000000000000000000002i3−2i300−i3−i3i3i30000000000000000
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χ6844-4-24-24-422-2-24-2-21-2-22-4-1-1221-2-2224-1-1-2-2-211-4-4-4222212-1-11-22211-1-10000400-2-222-2-2-1-111-1-1110000000000000000000000000000
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χ844-40-2440000-42-4−2323-2-240000002-4200000−23230−23230−2222−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7-20002000−232300000000000−222200−2ζ13+2ζ232ζ13−2ζ2300−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000000000
χ854-40-24-200−2i32i322-423−231-2-200i3−i3−2i32i3-1220003i−3i23−230−33022−222ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2310i3−i3-1000−333i−3i000000000−22i6−i6−ζ5+ζ7ζ5−ζ7ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−ζ13+ζ23ζ13−ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ230000000000000000000000000000
χ864-40-24-200−2i32i322-423−231-2-200i3−i3−2i32i3-1220003i−3i23−230−330−2222−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2310i3−i3-1000−333i−3i0000000002−2−i6i6ζ5−ζ7−ζ5+ζ7−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23ζ13−ζ23−ζ13+ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ230000000000000000000000000000
χ874-40-24-200−2i32i322-4−23231-2-200i3−i3−2i32i3-122000−3i3i−232303−3022−222ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ710i3−i3-10003−3−3i3i000000000−22i6−i6−ζ13+ζ23ζ13−ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ230000000000000000000000000000
χ884-40-24-200−2i32i322-4−23231-2-200i3−i3−2i32i3-122000−3i3i−232303−30−2222−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ710i3−i3-10003−3−3i3i0000000002−2−i6i6ζ13−ζ23−ζ13+ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ230000000000000000000000000000
χ894-40-24-2002i3−2i322-423−231-2-200−i3i32i3−2i3-122000−3i3i23−230−33022−222ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2310−i3i3-1000−33−3i3i000000000−22−i6i6−ζ5+ζ7ζ5−ζ7−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ13+ζ23ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ230000000000000000000000000000
χ904-40-24-2002i3−2i322-423−231-2-200−i3i32i3−2i3-122000−3i3i23−230−330−2222−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2310−i3i3-1000−33−3i3i0000000002−2i6−i6ζ5−ζ7−ζ5+ζ7ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ13−ζ23−ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ230000000000000000000000000000
χ914-40-24-2002i3−2i322-4−23231-2-200−i3i32i3−2i3-1220003i−3i−232303−3022−222ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ710−i3i3-10003−33i−3i000000000−22−i6i6−ζ13+ζ23ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ230000000000000000000000000000
χ924-40-24-2002i3−2i322-4−23231-2-200−i3i32i3−2i3-1220003i−3i−232303−30−2222−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ710−i3i3-10003−33i−3i0000000002−2i6−i6ζ13−ζ23−ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ230000000000000000000000000000
χ93888-4-4-488-4-4-4-4-4-4-4222-4-42222222-4-4-42222-422-4000000-12-1-1-1222-1-1-1-10000000000000000000000000000000000000000000000000
χ94888-4-4-4-8-8-4-4-4-4-444222-4-42222222444-2-2-2-24-2-24000000-12-1-1-1-2-2-211110000000000000000000000000000000000000000000000000
χ9588-8-4-4-48-844-4-4-4-4-422244-2-2-2-222244-4-2-222-4224000000-1-211-12-2-2-1-1110000000000000000000000000000000000000000000000000
χ9688-8-4-4-4-8844-4-4-44422244-2-2-2-2222-4-4422-2-24-2-2-4000000-1-211-1-22211-1-10000000000000000000000000000000000000000000000000
χ978-808-480000-8-84008-4-4000000-84400000000000000000-4000400000000000000000000000000000000000000000000000000000000
χ988-808-4-400−4i34i34-8400-4-4200−4i34i32i3−2i34-2400000000000000000202i3−2i3-200000000000000000000000000000000000000000000000000000000
χ998-808-4-4004i3−4i34-8400-4-42004i3−4i3−2i32i34-240000000000000000020−2i32i3-200000000000000000000000000000000000000000000000000000000
χ1008-80-4-480000-84443−43-42-400000044-200000−2323043−4300000002000-2000−2323000000000000000000000000000000000000000000000000000
χ1018-80-4-480000-844−4343-42-400000044-20000023−230−434300000002000-200023−23000000000000000000000000000000000000000000000000000
χ1028-80-4-4-400−4i34i344443−43222002i3−2i32i3−2i3-2-2-20006i−6i−23230−23230000000-10−i3i310003−3−3i3i0000000000000000000000000000000000000000000000000
χ1038-80-4-4-400−4i34i3444−4343222002i3−2i32i3−2i3-2-2-2000−6i6i23−23023−230000000-10−i3i31000−333i−3i0000000000000000000000000000000000000000000000000
χ1048-80-4-4-4004i3−4i344443−4322200−2i32i3−2i32i3-2-2-2000−6i6i−23230−23230000000-10i3−i310003−33i−3i0000000000000000000000000000000000000000000000000
χ1058-80-4-4-4004i3−4i3444−434322200−2i32i3−2i32i3-2-2-20006i−6i23−23023−230000000-10i3−i31000−33−3i3i0000000000000000000000000000000000000000000000000

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