Finite Group Databasebeta

← Group #13156253

Character table — Group #13156253

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size11222222222222244444444444444444444444666666888888888888121212121212121212121212121212121212121212242424242424242424242424242424363636363636727272727272216
order12233344666661212333666666666121212121212121212121288242424243666612121212121212246681212242424242424242424242424242446661212121212121212121212882424242448121224248
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11-111-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-11-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ511111111111111111111111111111111111111-1-1-1-1-1-11111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-11-1-111-1
χ611111111111111111111111111111111111111-1-1-1-1-1-11111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-111-1-11
χ711111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-11111111111-1-1-1-1-1-11
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
χ1122222-122222-12222-1-12-122-1-12-1-12-1222-1-1222-1000000-1-1-1-1-1-1-1-1-1-1-1-12222022000000000000002-1-1-1-1-1-122-1-1-1-1-1-10000000200-1-10
χ1222222-122222-12222-1-12-122-1-12-1-12-1222-1-1222-1000000-1-1-1-1-1-1-1-1-1-1-1-1222202200000000000000-2-1-1-1-111-2-2-1-111110000000-200110
χ1322222-122222-12222-1-12-122-1-12-1-12-1222-1-1222-1000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20-2-20000000000000021111-1-12211-1-1-1-10000000-200110
χ1422222-122222-12222-1-12-122-1-12-1-12-1222-1-1222-1000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20-2-200000000000000-2111111-2-21111110000000200-1-10
χ152222-122222-122-1-1-12-1-12-1-122-1-12-122-1-1-1-12-1-1222-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-12-1-1-1-12222-1-1-1-1-1-1-1-102-1-120000-1-1000022-1-1-1-10000000
χ162222-122222-122-1-1-12-1-12-1-122-1-12-122-1-1-1-12-1-1222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-211211-1-12222-1-1-1-1-1-1-1-10-211-20000110000-2-211110000000
χ172222-122222-122-1-1-12-1-12-1-122-1-12-122-1-1-1-12-1-12-2-21111-1-1-1-1-1-122-1-1-1-122-1-1-2-1-111-2-2-2-21111111102-1-120000-1-10000-2-211110000000
χ182222-122222-122-1-1-12-1-12-1-122-1-12-122-1-1-1-12-1-12-2-21111-1-1-1-1-1-122-1-1-1-1-2-211-21111-2-2-2-2111111110-211-2000011000022-1-1-1-10000000
χ192222-12-2-222-12211-12-1-12-1-122-1-121-2-21111-211-20033−3−3-1-1-1-1-11-2-2111100−i3i30−i3i33−300003333−3−3−3−300−i3i300000−i3i300002i−2i−i−iii0000000
χ202222-12-2-222-12211-12-1-12-1-122-1-121-2-21111-211-20033−3−3-1-1-1-1-11-2-2111100i3−i30i3−i33−300003333−3−3−3−300i3−i300000i3−i30000−2i2iii−i−i0000000
χ212222-12-2-222-12211-12-1-12-1-122-1-121-2-21111-211-200−3−333-1-1-1-1-11-2-2111100−i3i30−i3i3−330000−3−3−3−3333300−i3i300000−i3i30000−2i2iii−i−i0000000
χ222222-12-2-222-12211-12-1-12-1-122-1-121-2-21111-211-200−3−333-1-1-1-1-11-2-2111100i3−i30i3−i3−330000−3−3−3−3333300i3−i300000i3−i300002i−2i−i−iii0000000
χ23222-12222-1-122-122-1-1222-1-1-1-1-12-122-1-1-122-1-1-12222222-12-1-1-12-1-1-1-1-1-1000020022-1-1-1-1-1-1-1-1-1-1-1-12000022-1-100-1-1-1-100000020-1-1000
χ24222-12222-1-122-122-1-1222-1-1-1-1-12-122-1-1-122-1-1-12222222-12-1-1-12-1-1-1-1-1-1000020022-1-1-1-1-1-1-1-1-1-1-1-1-20000-2-211001111000000-2011000
χ25222-12222-1-122-122-1-1222-1-1-1-1-12-122-1-1-122-1-1-12-2-2-2-2-2-2-12-1-1-12-1-1-1-1-1-10000-200-2-21111111111112000022-1-100-1-1-1-1000000-2011000
χ26222-12222-1-122-122-1-1222-1-1-1-1-12-122-1-1-122-1-1-12-2-2-2-2-2-2-12-1-1-12-1-1-1-1-1-10000-200-2-2111111111111-20000-2-21100111100000020-1-1000
χ2722-22222-2-2-222222222-2-2-2-2-2-2222-22-2-2-222222-22222222-2-2-22-22-222-2-20000-200-2-222-2-222-2-222-2-20000000000000000000000000000
χ2822-22222-2-2-222222222-2-2-2-2-2-2222-22-2-2-222222-2-2-2-2-2-2-22-2-2-22-22-222-2-2000020022-2-222-2-222-2-2220000000000000000000000000000
χ2922-2222-22-2-2222-2-2222-2-2-2-2-2-22222-2222-2-2-2-2-220000002-2-2-222-22-2-2222-2220-2-2000000000000000222-20000-2-200000000000000000
χ3022-2222-22-2-2222-2-2222-2-2-2-2-2-22222-2222-2-2-2-2-220000002-2-2-222-22-2-222-22-2-2022000000000000000-2-2-2200002200000000000000000
χ3122-222-1-22-2-22-12-2-22-1-1-21-2-2112-1-12122211-2-2-2-1000000-1111-1-11-111-1-12-2220-2-2000000000000000-1-1-11−i3i30011−i3−i3i3i30000000000−i3i30
χ3222-222-1-22-2-22-12-2-22-1-1-21-2-2112-1-12122211-2-2-2-1000000-1111-1-11-111-1-12-2220-2-2000000000000000-1-1-11i3−i30011i3i3−i3−i30000000000i3−i30
χ3322-222-1-22-2-22-12-2-22-1-1-21-2-2112-1-12122211-2-2-2-1000000-1111-1-11-111-1-1-22-2-2022000000000000000111-1−i3i300-1-1−i3−i3i3i30000000000i3−i30
χ3422-222-1-22-2-22-12-2-22-1-1-21-2-2112-1-12122211-2-2-2-1000000-1111-1-11-111-1-1-22-2-2022000000000000000111-1i3−i300-1-1i3i3−i3−i30000000000−i3i30
χ3522-22-122-2-2-2-122-1-1-12-11-211-2-2-1-1212-211-1-12-1-1-222-1-1-1-1-1111-112-2-1-11100−i3i3-2i3−i31122-2-2-1-111-1-11100−i3i300000i3−i3000000−i3i3−i3i30000000
χ3622-22-122-2-2-2-122-1-1-12-11-211-2-2-1-1212-211-1-12-1-1-222-1-1-1-1-1111-112-2-1-11100i3−i3-2−i3i31122-2-2-1-111-1-11100i3−i300000−i3i3000000i3−i3i3−i30000000
χ3722-22-122-2-2-2-122-1-1-12-11-211-2-2-1-1212-211-1-12-1-1-2-2-21111-1111-112-2-1-11100−i3i32i3−i3-1-1-2-22211-1-111-1-100−i3i300000i3−i3000000i3−i3i3−i30000000
χ3822-22-122-2-2-2-122-1-1-12-11-211-2-2-1-1212-211-1-12-1-1-2-2-21111-1111-112-2-1-11100i3−i32−i3i3-1-1-2-22211-1-111-1-100i3−i300000−i3i3000000−i3i3−i3i30000000
χ3922-22-12-22-2-2-12211-12-11-211-2-2-1-12-1-22-1-111-21120033−3−3-1111-1-1-2211-1-12-2-1-1011−33000033−3−3−3−33302-1-1-20000110000003−3−330000000
χ4022-22-12-22-2-2-12211-12-11-211-2-2-1-12-1-22-1-111-21120033−3−3-1111-1-1-2211-1-1-22110-1-1−33000033−3−3−3−3330-21120000-1-1000000−333−30000000
χ4122-22-12-22-2-2-12211-12-11-211-2-2-1-12-1-22-1-111-211200−3−333-1111-1-1-2211-1-12-2-1-10113−30000−3−33333−3−302-1-1-2000011000000−333−30000000
χ4222-22-12-22-2-2-12211-12-11-211-2-2-1-12-1-22-1-111-211200−3−333-1111-1-1-2211-1-1-22110-1-13−30000−3−33333−3−30-21120000-1-10000003−3−330000000
χ4322-2-1222-21122-122-1-12-2-21111-12-1-2211122-1-1-1-2222222-1-211-1-2-11-1-1110000-200-2-2-1-111-1-111-1-1110000000−i3i300−i3i3−i3i300000000−i3i3000
χ4422-2-1222-21122-122-1-12-2-21111-12-1-2211122-1-1-1-2222222-1-211-1-2-11-1-1110000-200-2-2-1-111-1-111-1-1110000000i3−i300i3−i3i3−i300000000i3−i3000
χ4522-2-1222-21122-122-1-12-2-21111-12-1-2211122-1-1-1-2-2-2-2-2-2-2-1-211-1-2-11-1-11100002002211-1-111-1-111-1-10000000−i3i300−i3i3−i3i300000000i3−i3000
χ4622-2-1222-21122-122-1-12-2-21111-12-1-2211122-1-1-1-2-2-2-2-2-2-2-1-211-1-2-11-1-11100002002211-1-111-1-111-1-10000000i3−i300i3−i3i3−i300000000−i3i3000
χ4744444-2-4-4444-24-4-44-2-24-244-2-24-2-2-42-4-4-422-4-4-42000000-2-2-2-2-222222220000000000000000000000000000000000000000000000000
χ484444-2-24444-2-24-2-2-2-21-2-2-2-2-2-2-21-2-2-24-2-2114-2-2-2000000111111-2-2111144-2-20-2-2000000000000000-211-200001100000000000000000
χ494444-2-24444-2-24-2-2-2-21-2-2-2-2-2-2-21-2-2-24-2-2114-2-2-2000000111111-2-21111-4-4220220000000000000002-1-120000-1-100000000000000000
χ504444-2-2-4-444-2-2422-2-21-2-2-2-2-2-2-21-222-422-1-1-422200000011111-122-1-1-1-100−2i32i30−2i32i30000000000000000i3−i300000i3−i300000000000000000
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χ52444-244-4-4-2-244-2-4-4-2-2444-2-2-2-2-24-2-4-4222-4-4222-4000000-24-2-2-2-42222220000000000000000000000000000000000000000000000000
χ53444-24-244-2-24-2-244-21-24-2-2-211-2-214-2-2-2-2-2-2-2-2-2-20000001-2111-211111100000000000000000000040000-2-2-2-20011110000000000000
χ54444-24-244-2-24-2-244-21-24-2-2-211-2-214-2-2-2-2-2-2-2-2-2-20000001-2111-2111111000000000000000000000-40000222200-1-1-1-10000000000000
χ55444-24-2-4-4-2-24-2-2-4-4-21-24-2-2-211-2-21-422222222220000001-21112-1-1-1-1-1-1000000000000000000000000000000003-3-330000000000000
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χ854-40-2-2400−2i32i32-4223−231-2-200i3−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
χ864-40-2-2400−2i32i32-4223−231-2-200i3−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
χ874-40-2-2400−2i32i32-42−23231-2-200i3−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
χ884-40-2-2400−2i32i32-42−23231-2-200i3−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
χ894-40-2-24002i3−2i32-4223−231-2-200−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
χ904-40-2-24002i3−2i32-4223−231-2-200−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
χ914-40-2-24002i3−2i32-42−23231-2-200−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
χ924-40-2-24002i3−2i32-42−23231-2-200−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
χ9588-8-4-4-48-844-4-4-4-4-422244-2-2-2-22224-44-2-222-4224000000-1-211-1-22-2-1-1110000000000000000000000000000000000000000000000000
χ9688-8-4-4-4-8844-4-4-44422244-2-2-2-2222-44-422-2-24-2-2-4000000-1-211-12-2211-1-10000000000000000000000000000000000000000000000000
χ978-8088-40000-84-8008-4-4000000-84400000000000000000-4000400000000000000000000000000000000000000000000000000000000
χ988-808-4-4000044-843−43-4-420000004-2400000−2323043−4300000002000-2000−2323000000000000000000000000000000000000000000000000000
χ998-808-4-4000044-8−4343-4-420000004-240000023−230−434300000002000-200023−23000000000000000000000000000000000000000000000000000
χ1008-80-48-400−4i34i3-84400-42-400−4i34i32i3−2i344-200000000000000000202i3−2i3-200000000000000000000000000000000000000000000000000000000
χ1018-80-48-4004i3−4i3-84400-42-4004i3−4i3−2i32i344-20000000000000000020−2i32i3-200000000000000000000000000000000000000000000000000000000
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.