Finite Group Databasebeta

← Group #13147848

Character table — Group #13147848

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222222222444444666666666666666666669999121212121212121212121212121212121212121212121818181818181818181818181818181818181818181836363636363636367272727272727272
order12223444444666121212121212336666661212121212121212121212124444366612121212121212121212121212121212121222444466661212121212121212121212122244444466121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ41111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ51111111-1-1-1-111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111-1-1-1-111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111-1-1-1-111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1
χ81111111-1-1-1-111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111
χ911111-1-111-1-1111-1-111-1-111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-11-11-11-11-11-11-1
χ1011111-1-111-1-1111-1-111-1-111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-11-11-11-11-11-11
χ1111111-1-111-1-1111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-11-1-11-111-1-11-111-1
χ1211111-1-111-1-1111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-111-11-1-111-11-1-11
χ1311111-1-1-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111-1-111-1-111-11-1-11-11
χ1411111-1-1-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-111-1-111-1-11-111-11-1
χ1511111-1-1-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-11-1-11-111-11-1-111-1-11
χ1611111-1-1-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-111-11-1-11-111-1-111-1
χ17222222222222222222222-1-1-1222-12222222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000022220000-1-10000-1-1
χ18222222222222222222222-1-1-1222-12222222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000-2-2-2-2000011000011
χ1922222222222222222222-1222-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2022222222222222222222-1222-1-1-12-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111111111110000000000000000
χ212222222-2-2-2-222222-2-2-2-22-1-1-1222-12222-2-2-2-2-2-2-2-20000-1-1-1-11111-1-1-1-1-1-111111111000000000000000000000022-2-20000-1-1000011
χ222222222-2-2-2-222222-2-2-2-22-1-1-1222-12222-2-2-2-2-2-2-2-20000-1-1-1-11111-1-1-1-1-1-1111111110000000000000000000000-2-2220000110000-1-1
χ232222222-2-2-2-222222-2-2-2-2-1222-1-1-12-1-1-1-1111111112222-1-1-1-1-2-2-2-222-1-1-1-111111111-2-222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ242222222-2-2-2-222222-2-2-2-2-1222-1-1-12-1-1-1-111111111-2-2-2-2-1-1-1-1-2-2-2-222-1-1-1-11111111122-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ2522222-2-222-2-2222-2-222-2-22-1-1-1222-1-2-2-2-22222-2-2-2-20000-1-1-1-1-1-111111111-1-1-1-1111100000000000000000000002-22-20000-110000-11
χ2622222-2-222-2-2222-2-222-2-22-1-1-1222-1-2-2-2-22222-2-2-2-20000-1-1-1-1-1-111111111-1-1-1-111110000000000000000000000-22-2200001-100001-1
χ2722222-2-222-2-2222-2-222-2-2-1222-1-1-121111-1-1-1-111112222-1-1-1-122-2-2-2-21111-1-1-1-1111122-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2822222-2-222-2-2222-2-222-2-2-1222-1-1-121111-1-1-1-11111-2-2-2-2-1-1-1-122-2-2-2-21111-1-1-1-11111-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ2922222-2-2-2-222222-2-2-2-2222-1-1-1222-1-2-2-2-2-2-2-2-222220000-1-1-1-111-1-11111111111-1-1-1-100000000000000000000002-2-220000-1100001-1
χ3022222-2-2-2-222222-2-2-2-2222-1-1-1222-1-2-2-2-2-2-2-2-222220000-1-1-1-111-1-11111111111-1-1-1-10000000000000000000000-222-200001-10000-11
χ3122222-2-2-2-222222-2-2-2-222-1222-1-1-1211111111-1-1-1-12222-1-1-1-1-2-222-2-211111111-1-1-1-1-2-2-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ3222222-2-2-2-222222-2-2-2-222-1222-1-1-1211111111-1-1-1-1-2-2-2-2-1-1-1-1-2-222-2-211111111-1-1-1-12222-2-2-1-1-1-11111-1-1-1-111110000000000000000
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χ3822-2-2200002i−2i-22-200002i−2i-122-2-111-2−3−333i3i3−i3−i3−i−iii-2-222-1-111002i−2i00−3−333i3i3−i3−i3−i−iii0000−2i2i−i3−i3i3i311-1-133−3−3ii−i−i0000000000000000
χ3922-2-220000−2i2i-22-20000−2i2i222-22-2-2-200000000−2i−2i2i2i22-2-222-2-200−2i2i0000000000−2i−2i2i2i0000−2i2i000022-2-20000−2i−2i2i2i0000000000000000
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χ4122-2-220000−2i2i-22-20000−2i2i-122-2-111-233−3−3i3i3−i3−i3ii−i−i22-2-2-1-11100−2i2i0033−3−3i3i3−i3−i3ii−i−i0000−2i2ii3i3−i3−i3-1-11133−3−3ii−i−i0000000000000000
χ4222-2-220000−2i2i-22-20000−2i2i-122-2-111-233−3−3i3i3−i3−i3ii−i−i-2-222-1-11100−2i2i0033−3−3i3i3−i3−i3ii−i−i00002i−2i−i3−i3i3i311-1-1−3−333−i−iii0000000000000000
χ4322-2-220000−2i2i-22-20000−2i2i-122-2-111-2−3−333−i3−i3i3i3ii−i−i22-2-2-1-11100−2i2i00−3−333−i3−i3i3i3ii−i−i0000−2i2i−i3−i3i3i3-1-111−3−333ii−i−i0000000000000000
χ4422-2-220000−2i2i-22-20000−2i2i-122-2-111-2−3−333−i3−i3i3i3ii−i−i-2-222-1-11100−2i2i00−3−333−i3−i3i3i3ii−i−i00002i−2ii3i3−i3−i311-1-133−3−3−i−iii0000000000000000
χ452-22-22002i−2i00-2-22002i−2i0022-22-22-2-200002i−2i2i−2i00002i−2i2i−2i2-22-22i−2i000000002i−2i2i−2i00002-200002-22-22i−2i2i−2i000000000000000000000000
χ462-22-22002i−2i00-2-22002i−2i0022-22-22-2-200002i−2i2i−2i0000−2i2i−2i2i2-22-22i−2i000000002i−2i2i−2i0000-220000-22-22−2i2i−2i2i000000000000000000000000
χ472-22-22002i−2i00-2-22002i−2i00-12-221-11-23−33−3−ii−ii−i3i3−i3i32i−2i2i−2i-11-112i−2i00003−33−3−ii−ii−i3i3−i3i32-20000-11-11−ii−ii−i3i3−i3i33−33−30000000000000000
χ482-22-22002i−2i00-2-22002i−2i00-12-221-11-23−33−3−ii−ii−i3i3−i3i3−2i2i−2i2i-11-112i−2i00003−33−3−ii−ii−i3i3−i3i3-2200001-11-1i−ii−ii3−i3i3−i3−33−330000000000000000
χ492-22-22002i−2i00-2-22002i−2i00-12-221-11-2−33−33−ii−iii3−i3i3−i32i−2i2i−2i-11-112i−2i0000−33−33−ii−iii3−i3i3−i32-20000-11-11−ii−iii3−i3i3−i3−33−330000000000000000
χ502-22-22002i−2i00-2-22002i−2i00-12-221-11-2−33−33−ii−iii3−i3i3−i3−2i2i−2i2i-11-112i−2i0000−33−33−ii−iii3−i3i3−i3-2200001-11-1i−ii−i−i3i3−i3i33−33−30000000000000000
χ512-22-2200−2i2i00-2-2200−2i2i0022-22-22-2-20000−2i2i−2i2i00002i−2i2i−2i2-22-2−2i2i00000000−2i2i−2i2i0000-220000-22-222i−2i2i−2i000000000000000000000000
χ522-22-2200−2i2i00-2-2200−2i2i0022-22-22-2-20000−2i2i−2i2i0000−2i2i−2i2i2-22-2−2i2i00000000−2i2i−2i2i00002-200002-22-2−2i2i−2i2i000000000000000000000000
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χ542-22-2200−2i2i00-2-2200−2i2i00-12-221-11-23−33−3i−ii−ii3−i3i3−i3−2i2i−2i2i-11-11−2i2i00003−33−3i−ii−ii3−i3i3−i32-20000-11-11i−ii−ii3−i3i3−i33−33−30000000000000000
χ552-22-2200−2i2i00-2-2200−2i2i00-12-221-11-2−33−33i−ii−i−i3i3−i3i32i−2i2i−2i-11-11−2i2i0000−33−33i−ii−i−i3i3−i3i3-2200001-11-1−ii−iii3−i3i3−i33−33−30000000000000000
χ562-22-2200−2i2i00-2-2200−2i2i00-12-221-11-2−33−33i−ii−i−i3i3−i3i3−2i2i−2i2i-11-11−2i2i0000−33−33i−ii−i−i3i3−i3i32-20000-11-11i−ii−i−i3i3−i3i3−33−330000000000000000
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χ582-2-2222-200002-2-22-2000022-2-2-2-2222-2-2200000000−2i2i2i−2i2-2-2200002-22-2-220000000000−2i2i000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ592-2-2222-200002-2-22-20000-12-2-211-12-111-13−3−33−333−32i−2i−2i2i-111-100002-2-111-13−3−33−333−3002i−2i00−i3i3i3−i3−iii−ii−i−ii−i3i3i3−i30000000000000000
χ602-2-2222-200002-2-22-20000-12-2-211-12-111-13−3−33−333−3−2i2i2i−2i-111-100002-2-111-13−3−33−333−300−2i2i00i3−i3−i3i3i−i−ii−iii−ii3−i3−i3i30000000000000000
χ612-2-2222-200002-2-22-20000-12-2-211-12-111-1−333−33−3−332i−2i−2i2i-111-100002-2-111-1−333−33−3−33002i−2i00i3−i3−i3i3−iii−ii−i−iii3−i3−i3i30000000000000000
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χ652-2-222-2200002-2-2-220000-12-2-211-121-1-113−3−333−3−332i−2i−2i2i-111-10000-221-1-113−3−333−3−3300−2i2i00−i3i3i3−i3−iii−i−iii−ii3−i3−i3i30000000000000000
χ662-2-222-2200002-2-2-220000-12-2-211-121-1-113−3−333−3−33−2i2i2i−2i-111-10000-221-1-113−3−333−3−33002i−2i00i3−i3−i3i3i−i−iii−i−ii−i3i3i3−i30000000000000000
χ672-2-222-2200002-2-2-220000-12-2-211-121-1-11−333−3−333−32i−2i−2i2i-111-10000-221-1-11−333−3−333−300−2i2i00i3−i3−i3i3−iii−i−iii−i−i3i3i3−i30000000000000000
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χ704444444-4-4-4-444444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-222222222000011112222-2-21111-1-1-1-1-1-1-1-100000000000000000000000000000000000000
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χ794-44-44004i−4i00-4-44004i−4i004-22-2-44-4200004i−4i4i−4i00000000-22-22−2i2i00000000−2i2i−2i2i000000000000000000000000000000000000000000
χ804-44-44004i−4i00-4-44004i−4i00-2-22-22-22223−2323−23−2i2i−2i2i−2i32i3−2i32i300001-11-1−2i2i0000−33−33i−ii−ii3−i3i3−i300000000000000000000000000000000000000
χ814-44-44004i−4i00-4-44004i−4i00-2-22-22-222−2323−2323−2i2i−2i2i2i3−2i32i3−2i300001-11-1−2i2i00003−33−3i−ii−i−i3i3−i3i300000000000000000000000000000000000000
χ824-44-4400−4i4i00-4-4400−4i4i004-22-2-44-420000−4i4i−4i4i00000000-22-222i−2i000000002i−2i2i−2i000000000000000000000000000000000000000000
χ834-44-4400−4i4i00-4-4400−4i4i00-2-22-22-22223−2323−232i−2i2i−2i2i3−2i32i3−2i300001-11-12i−2i0000−33−33−ii−ii−i3i3−i3i300000000000000000000000000000000000000
χ844-44-4400−4i4i00-4-4400−4i4i00-2-22-22-222−2323−23232i−2i2i−2i−2i32i3−2i32i300001-11-12i−2i00003−33−3−ii−iii3−i3i3−i300000000000000000000000000000000000000
χ854-4-4444-400004-4-44-400004-222-4-44-24-4-44000000000000-222-20000-22-222-20000000000000000000000000000000000000000000000
χ864-4-4444-400004-4-44-40000-2-22222-2-2-222-223−23−2323−232323−2300001-1-110000-221-1-11−333−33−3−3300000000000000000000000000000000000000
χ874-4-4444-400004-4-44-40000-2-22222-2-2-222-2−232323−2323−23−232300001-1-110000-221-1-113−3−33−333−300000000000000000000000000000000000000
χ884-4-444-4400004-4-4-4400004-222-4-44-2-444-4000000000000-222-200002-22-2-220000000000000000000000000000000000000000000000
χ894-4-444-4400004-4-4-440000-2-22222-2-22-2-2223−23−232323−23−232300001-1-1100002-2-111-1−333−3−333−300000000000000000000000000000000000000
χ904-4-444-4400004-4-4-440000-2-22222-2-22-2-22−232323−23−232323−2300001-1-1100002-2-111-13−3−333−3−3300000000000000000000000000000000000000
χ916666-3666666-3-3-3-3-3-3-3-3-3000000000000000000000000000000000000000000000000000000000000000000000000222200-1-1-1-100
χ926666-3666666-3-3-3-3-3-3-3-3-3000000000000000000000000000000000000000000000000000000000000000000000000-2-2-2-200111100
χ936666-366-6-6-6-6-3-3-3-3-3333300000000000000000000000000000000000000000000000000000000000000000000000022-2-200-1-11100
χ946666-366-6-6-6-6-3-3-3-3-33333000000000000000000000000000000000000000000000000000000000000000000000000-2-2220011-1-100
χ956666-3-6-666-6-6-3-3-333-3-3330000000000000000000000000000000000000000000000000000000000000000000000002-22-200-11-1100
χ966666-3-6-666-6-6-3-3-333-3-333000000000000000000000000000000000000000000000000000000000000000000000000-22-22001-11-100
χ976666-3-6-6-6-666-3-3-33333-3-30000000000000000000000000000000000000000000000000000000000000000000000002-2-2200-111-100
χ986666-3-6-6-6-666-3-3-33333-3-3000000000000000000000000000000000000000000000000000000000000000000000000-222-2001-1-1100
χ991212-12-12-6000012i−12i6-660000−6i6i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1001212-12-12-60000−12i12i6-6600006i−6i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10112-1212-12-60012i−12i0066-600−6i6i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10212-1212-12-600−12i12i0066-6006i−6i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-12-1212-612-120000-666-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-1212-6-12120000-6666-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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