Finite Group Databasebeta

← Group #13140236

Character table — Group #13140236

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order122222223666666644121212123366666666666666366666661212121212121212121212121212121222224444444444444466661212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111-1-1-1-11111-1-1-11-1i−iii−i−i1111-1-1111-1-1-1-11-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-111-1-1i−ii−ii−i11-1-111-1-1ii−i−iii−i−i11-1-1ii−i−i
χ10111-1-1-1-11111-1-1-11-1i−iii−i−i1111-1-1111-1-1-1-11-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111-1-111i−i−ii−ii11-1-1-1-111−i−iiiii−i−i-1-111−i−iii
χ11111-1-1-1-11111-1-1-11-1i−iii−i−i1111-1-1111-1-1-1-11-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1-1-111−iii−i−ii-1-11111-1-1ii−i−i−i−iii-1-111−i−iii
χ12111-1-1-1-11111-1-1-11-1i−iii−i−i1111-1-1111-1-1-1-11-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-11111-1-1−ii−iii−i-1-111-1-111−i−iii−i−iii11-1-1ii−i−i
χ13111-1-1-1-11111-1-1-11-1−ii−i−iii1111-1-1111-1-1-1-11-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-111-1-1−ii−ii−ii11-1-111-1-1−i−iii−i−iii11-1-1−i−iii
χ14111-1-1-1-11111-1-1-11-1−ii−i−iii1111-1-1111-1-1-1-11-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111-1-111−iii−ii−i11-1-1-1-111ii−i−i−i−iii-1-111ii−i−i
χ15111-1-1-1-11111-1-1-11-1−ii−i−iii1111-1-1111-1-1-1-11-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1-1-111i−i−iii−i-1-11111-1-1−i−iiiii−i−i-1-111ii−i−i
χ16111-1-1-1-11111-1-1-11-1−ii−i−iii1111-1-1111-1-1-1-11-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-11111-1-1i−ii−i−ii-1-111-1-111ii−i−iii−i−i11-1-1−i−iii
χ1722222222222222222222222-12222-1-1-1-1-12-122-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1222200000000220000-1-1-1-100000000-1-1-1-100000000
χ1822222222222222222222222-12222-1-1-1-1-12-122-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-20000111100000000111100000000
χ192222222222222222222222-12-1-1-1-122222-12-1-12-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000000022220000220000000000000000-1-1-1-1-1-1-1-1
χ202222222222222222222222-12-1-1-1-122222-12-1-12-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-100000000-2-2-2-20000-2-2000000000000000011111111
χ212222222222222222-2-2-2-2-2-22-12222-1-1-1-1-12-122-1-1-1-1-1-1-1-1-1-2-211-2-21111111111222200000000-2-20000-1-1-1-100000000111100000000
χ222222222222222222-2-2-2-2-2-22-12222-1-1-1-1-12-122-1-1-1-1-1-1-1-1-1-2-211-2-21111111111-2-2-2-200000000220000111100000000-1-1-1-100000000
χ232222222222222222-2-2-2-2-2-2-12-1-1-1-122222-12-1-12-1-1-1-1-1-1-1-111-2-211-2-2111111110000000022220000-2-20000000000000000-1-1-1-11111
χ242222222222222222-2-2-2-2-2-2-12-1-1-1-122222-12-1-12-1-1-1-1-1-1-1-111-2-211-2-21111111100000000-2-2-2-200002200000000000000001111-1-1-1-1
χ25222-2-2-2-22222-2-2-22-22i−2i2i2i−2i−2i2-122-2-2-1-1-111-212-21-1-1-1-111112i2i−i−i−2i−2iii−i−i−i−iiiii22-2-2000000002i−2i0000-1-11100000000−i−iii00000000
χ26222-2-2-2-22222-2-2-22-22i−2i2i2i−2i−2i2-122-2-2-1-1-111-212-21-1-1-1-111112i2i−i−i−2i−2iii−i−i−i−iiiii-2-22200000000−2i2i000011-1-100000000ii−i−i00000000
χ27222-2-2-2-22222-2-2-22-22i−2i2i2i−2i−2i-12-1-111222-2-21-2-11-2-1-1-1-11111−i−i2i2iii−2i−2i−i−i−i−iiiii0000000022-2-200002i−2i0000000000000000-1-111−i−iii
χ28222-2-2-2-22222-2-2-22-22i−2i2i2i−2i−2i-12-1-111222-2-21-2-11-2-1-1-1-11111−i−i2i2iii−2i−2i−i−i−i−iiiii00000000-2-2220000−2i2i000000000000000011-1-1ii−i−i
χ29222-2-2-2-22222-2-2-22-2−2i2i−2i−2i2i2i2-122-2-2-1-1-111-212-21-1-1-1-11111−2i−2iii2i2i−i−iiiii−i−i−i−i22-2-200000000−2i2i0000-1-11100000000ii−i−i00000000
χ30222-2-2-2-22222-2-2-22-2−2i2i−2i−2i2i2i2-122-2-2-1-1-111-212-21-1-1-1-11111−2i−2iii2i2i−i−iiiii−i−i−i−i-2-222000000002i−2i000011-1-100000000−i−iii00000000
χ31222-2-2-2-22222-2-2-22-2−2i2i−2i−2i2i2i-12-1-111222-2-21-2-11-2-1-1-1-11111ii−2i−2i−i−i2i2iiiii−i−i−i−i0000000022-2-20000−2i2i0000000000000000-1-111ii−i−i
χ32222-2-2-2-22222-2-2-22-2−2i2i−2i−2i2i2i-12-1-111222-2-21-2-11-2-1-1-1-11111ii−2i−2i−i−i2i2iiiii−i−i−i−i00000000-2-22200002i−2i000000000000000011-1-1−i−iii
χ3322-222-2-2-222-22-22-2-2000000222-2-2-22-2-22-222-22-222-2-22-2-22000000000000000000002i−2i2i−2i000000000000002i−2i2i−2i0000000000000000
χ3422-222-2-2-222-22-22-2-2000000222-2-2-22-2-22-222-22-222-2-22-2-2200000000000000000000−2i2i−2i2i00000000000000−2i2i−2i2i0000000000000000
χ3522-2-2-222-222-2-22-2-22000000222-2222-2-2-22-2-2-2-2222-2-2-222-2000000000000000000002i−2i−2i2i000000000000002i−2i−2i2i0000000000000000
χ3622-2-2-222-222-2-22-2-22000000222-2222-2-2-22-2-2-2-2222-2-2-222-200000000000000000000−2i2i2i−2i00000000000000−2i2i2i−2i0000000000000000
χ372-222-22-2-22-22-2-22-2200000022-222-2-22-2-2222-2-2-22-22-2-22-220000000000000000000000002i−2i2i−2i00000000000000000000002i−2i2i−2i0000
χ382-222-22-2-22-22-2-22-2200000022-222-2-22-2-2222-2-2-22-22-2-22-22000000000000000000000000−2i2i−2i2i0000000000000000000000−2i2i−2i2i0000
χ392-222-22-2-22-22-2-22-22000000-121-1-11-22-2-22-1211-2-11-111-11-1−i3i300−i3i300−i3−i3i3i3−i3−i3i3i3000000002i−2i2i−2i0000000000000000000000−ii−ii3−33−3
χ402-222-22-2-22-22-2-22-22000000-121-1-11-22-2-22-1211-2-11-111-11-1−i3i300−i3i300−i3−i3i3i3−i3−i3i3i300000000−2i2i−2i2i0000000000000000000000i−ii−i−33−33
χ412-222-22-2-22-22-2-22-22000000-121-1-11-22-2-22-1211-2-11-111-11-1i3−i300i3−i300i3i3−i3−i3i3i3−i3−i3000000002i−2i2i−2i0000000000000000000000−ii−ii−33−33
χ422-222-22-2-22-22-2-22-22000000-121-1-11-22-2-22-1211-2-11-111-11-1i3−i300i3−i300i3i3−i3−i3i3i3−i3−i300000000−2i2i−2i2i0000000000000000000000i−ii−i3−33−3
χ432-22-22-22-22-2222-2-2-200000022-22-22-22-22-2-2-2-2222-22-22-22-20000000000000000000000002i−2i−2i2i00000000000000000000002i−2i−2i2i0000
χ442-22-22-22-22-2222-2-2-200000022-22-22-22-22-2-2-2-2222-22-22-22-2000000000000000000000000−2i2i2i−2i0000000000000000000000−2i2i2i−2i0000
χ452-22-22-22-22-2222-2-2-2000000-121-11-1-22-22-21-21-12-11-11-11-113−300−330033−3−3−3−333000000002i−2i−2i2i0000000000000000000000−iii−ii3−i3−i3i3
χ462-22-22-22-22-2222-2-2-2000000-121-11-1-22-22-21-21-12-11-11-11-113−300−330033−3−3−3−33300000000−2i2i2i−2i0000000000000000000000i−i−ii−i3i3i3−i3
χ472-22-22-22-22-2222-2-2-2000000-121-11-1-22-22-21-21-12-11-11-11-11−33003−300−3−33333−3−3000000002i−2i−2i2i0000000000000000000000−iii−i−i3i3i3−i3
χ482-22-22-22-22-2222-2-2-2000000-121-11-1-22-22-21-21-12-11-11-11-11−33003−300−3−33333−3−300000000−2i2i2i−2i0000000000000000000000i−i−iii3−i3−i3i3
χ492-2-22-2-2222-2-2-2222-200000022-2-2-22-2-22-2-2222-222-2-22-2-22200000000000000002-22-2000000000000002-22-200000000000000000000
χ502-2-22-2-2222-2-2-2222-200000022-2-2-22-2-22-2-2222-222-2-22-2-2220000000000000000-22-2200000000000000-22-2200000000000000000000
χ512-2-22-2-2222-2-2-2222-20000002-1-2-2-2211-1112-12-2-1-111-111-1-100−i3i300−i3i3−i3i3−i3i3−i3i3−i3i32-22-200000000000000-11-1100000000−i3i3−i3i300000000
χ522-2-22-2-2222-2-2-2222-20000002-1-2-2-2211-1112-12-2-1-111-111-1-100−i3i300−i3i3−i3i3−i3i3−i3i3−i3i3-22-22000000000000001-11-100000000i3−i3i3−i300000000
χ532-2-22-2-2222-2-2-2222-20000002-1-2-2-2211-1112-12-2-1-111-111-1-100i3−i300i3−i3i3−i3i3−i3i3−i3i3−i32-22-200000000000000-11-1100000000i3−i3i3−i300000000
χ542-2-22-2-2222-2-2-2222-20000002-1-2-2-2211-1112-12-2-1-111-111-1-100i3−i300i3−i3i3−i3i3−i3i3−i3i3−i3-22-22000000000000001-11-100000000−i3i3−i3i300000000
χ552-2-2-222-222-2-22-2-22200000022-2-22-2-2-2222-2-222-22-2-2222-2-200000000000000002-2-22000000000000002-2-2200000000000000000000
χ562-2-2-222-222-2-22-2-22200000022-2-22-2-2-2222-2-222-22-2-2222-2-20000000000000000-222-200000000000000-222-200000000000000000000
χ572-2-2-222-222-2-22-2-2220000002-1-2-22-211-1-1-1-21221-111-1-1-111003−300−333−33−3−33−332-2-2200000000000000-111-1000000003−3−3300000000
χ582-2-2-222-222-2-22-2-2220000002-1-2-22-211-1-1-1-21221-111-1-1-111003−300−333−33−3−33−33-222-2000000000000001-1-1100000000−333−300000000
χ592-2-2-222-222-2-22-2-2220000002-1-2-22-211-1-1-1-21221-111-1-1-11100−33003−3−33−333−33−32-2-2200000000000000-111-100000000−333−300000000
χ602-2-2-222-222-2-22-2-2220000002-1-2-22-211-1-1-1-21221-111-1-1-11100−33003−3−33−333−33−3-222-2000000000000001-1-11000000003−3−3300000000
χ614444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000000000000000
χ624444444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000
χ63444-4-4-4-44444-4-4-44-44i−4i4i4i−4i−4i-2-2-2-222-2-2-22222-2221111-1-1-1-1−2i−2i−2i−2i2i2i2i2iiiii−i−i−i−i000000000000000000000000000000000000000000
χ64444-4-4-4-44444-4-4-44-4−4i4i−4i−4i4i4i-2-2-2-222-2-2-22222-2221111-1-1-1-12i2i2i2i−2i−2i−2i−2i−i−i−i−iiiii000000000000000000000000000000000000000000
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χ814-4-44-4-4444-4-4-4444-4000000-2-2222-222-222-2-2-22-21-1-11-1-111002i3−2i3002i3−2i3−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000000000000000
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χ9766-6-6-666-6-3-333-333-30033−33−3333000000000000000000000000000000000000000000002i−2i−2i2i00000000000000−iii−ii3−i3−i3i3000000000000
χ9866-6-6-666-6-3-333-333-30033−33−333300000000000000000000000000000000000000000000−2i2i2i−2i00000000000000i−i−ii−i3i3i3−i3000000000000
χ9966-6-6-666-6-3-333-333-300−333333−33000000000000000000000000000000000000000000002i−2i−2i2i00000000000000−iii−i−i3i3i3−i3000000000000
χ10066-6-6-666-6-3-333-333-300−333333−3300000000000000000000000000000000000000000000−2i2i2i−2i00000000000000i−i−iii3−i3−i3i3000000000000
χ10112-121212-1212-12-12-66-666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10212-1212-1212-1212-12-66-6-6-66660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-12-1212-12-121212-6666-6-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-12-121212-1212-666-666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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