Finite Group Databasebeta

← Group #13155718

Character table — Group #13155718

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111222222222222224444444444444444444444666666666666888888888888121212121212121212121212121212121212121212121212242424242424242424242424363636363636363636363636363636363636108108
order12223334466666666633366666666612121212121212121212444412121212121212123666121212121212121222446666121212121212121212121212121212126666661212121212122244666688121212122424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ911-1-1111-11-1111-1-1-1-1-1111-1-1-1111-1-1-1111-1-111-1-1-1i−ii−iii−i−iii−i−i1-1-1111-1-111-1-11-1i−i11-1-1ii−i−iii−i−iiiii−i−i−i−i1-111-1-1i−iii−i−i1-1i−i11-1-1i−iii−i−iii−i−i1-1
χ1011-1-1111-11-1111-1-1-1-1-1111-1-1-1111-1-1-1111-1-111-1-1-1i−ii−iii−i−iii−i−i1-1-1111-1-111-1-11-1−ii11-1-1ii−i−i−i−iiiiiii−i−i−i−i1-111-1-1−ii−i−iii-11i−i-1-111−iiii−i−i−i−iii-11
χ1111-1-1111-11-1111-1-1-1-1-1111-1-1-1111-1-1-1111-1-111-1-1-1i−ii−iii−i−iii−i−i1-1-1111-1-111-1-1-11i−i-1-111ii−i−iii−i−iiiii−i−i−i−i-11-1-111i−iii−i−i1-1−ii11-1-1−ii−i−iii−i−iii-11
χ1211-1-1111-11-1111-1-1-1-1-1111-1-1-1111-1-1-1111-1-111-1-1-1i−ii−iii−i−iii−i−i1-1-1111-1-111-1-1-11−ii-1-111ii−i−i−i−iiiiiii−i−i−i−i-11-1-111−ii−i−iii-11−ii-1-111i−i−i−iiiii−i−i1-1
χ1311-1-1111-11-1111-1-1-1-1-1111-1-1-1111-1-1-1111-1-111-1-1-1−ii−ii−i−iii−i−iii1-1-1111-1-111-1-11-1i−i11-1-1−i−iiiii−i−i−i−i−i−iiiii1-111-1-1i−iii−i−i-11−ii-1-111i−i−i−iiiii−i−i-11
χ1411-1-1111-11-1111-1-1-1-1-1111-1-1-1111-1-1-1111-1-111-1-1-1−ii−ii−i−iii−i−iii1-1-1111-1-111-1-11-1−ii11-1-1−i−iii−i−iii−i−i−i−iiiii1-111-1-1−ii−i−iii1-1−ii11-1-1−ii−i−iii−i−iii1-1
χ1511-1-1111-11-1111-1-1-1-1-1111-1-1-1111-1-1-1111-1-111-1-1-1−ii−ii−i−iii−i−iii1-1-1111-1-111-1-1-11i−i-1-111−i−iiiii−i−i−i−i−i−iiiii-11-1-111i−iii−i−i-11i−i-1-111−iiii−i−i−i−iii1-1
χ1611-1-1111-11-1111-1-1-1-1-1111-1-1-1111-1-1-1111-1-111-1-1-1−ii−ii−i−iii−i−iii1-1-1111-1-111-1-1-11−ii-1-111−i−iii−i−iii−i−i−i−iiiii-11-1-111−ii−i−iii1-1i−i11-1-1i−iii−i−iii−i−i-11
χ172222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2000000002-22-2000022-2-222-2-200000000000000000000000000000000
χ182222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-200000000-22-220000-2-222-2-22200000000000000000000000000000000
χ19222222-122222-12-12-12-1-12-122-1-12-1-1-122-12-1-1-1-1-122222-1-1-1-12222-1-1-1-12-12-1-1-1-1-1002200002-12-1-1-1-1-1-1-1-1-1-1-1-1-100000022-1-1-1-12200-1-1-1-1000000000000
χ20222222-122222-12-12-12-1-12-122-1-12-1-1-122-12-1-1-1-1-122222-1-1-1-12222-1-1-1-12-12-1-1-1-1-100-2-200002-12-11111-1-1-1-1-1-1-1-1000000-2-21111-2-2001111000000000000
χ21222222-122222-12-12-12-1-12-122-1-12-1-1-122-12-1-1-1-1-12-2-2-2-21111-2-2-2-2-1-1-1-12-12-1-1-1-1-100220000-21-21-1-1-1-11111111100000022-1-1-1-1-2-2001111000000000000
χ22222222-122222-12-12-12-1-12-122-1-12-1-1-122-12-1-1-1-1-12-2-2-2-21111-2-2-2-2-1-1-1-12-12-1-1-1-1-100-2-20000-21-21111111111111000000-2-211112200-1-1-1-1000000000000
χ23222222-1-2-2222-12-12-12-1-12-122-1-12-1-1-1-2-21-211111-222-2-2-1-1-1-1-2-2-2-2-1-1-1-1-21-211111000000002121−i3i3−i3i3-1-111-1-11100000000−i3i3−i3i30000−i3i3−i3i3000000000000
χ24222222-1-2-2222-12-12-12-1-12-122-1-12-1-1-1-2-21-211111-222-2-2-1-1-1-1-2-2-2-2-1-1-1-1-21-211111000000002121i3−i3i3−i3-1-111-1-11100000000i3−i3i3−i30000i3−i3i3−i3000000000000
χ25222222-1-2-2222-12-12-12-1-12-122-1-12-1-1-1-2-21-211111-2-2-22211112222-1-1-1-1-21-21111100000000-2-1-2-1−i3i3−i3i311-1-111-1-100000000−i3i3−i3i30000i3−i3i3−i3000000000000
χ26222222-1-2-2222-12-12-12-1-12-122-1-12-1-1-1-2-21-211111-2-2-22211112222-1-1-1-1-21-21111100000000-2-1-2-1i3−i3i3−i311-1-111-1-100000000i3−i3i3−i30000−i3i3−i3i3000000000000
χ2722222-122222-12-1222-12-1-12-1-12-1-1-1-122-12-12-1-1-1-1222222222-1-1-1-1-1-1-1-1-12-12-1-1-1-12200-1-1-1-1-12-120000-1-1-1-1-1-1-1-122-1-1-1-10000000022000000-1-1-1-1000000
χ2822222-122222-12-1222-12-1-12-1-12-1-1-1-122-12-12-1-1-1-1222222222-1-1-1-1-1-1-1-1-12-12-1-1-1-1-2-2001111-12-120000-1-1-1-1-1-1-1-1-2-2111100000000-2-20000001111000000
χ2922222-122222-12-1222-12-1-12-1-12-1-1-1-122-12-12-1-1-1-12-2-2-2-2-2-2-2-21111-1-1-1-1-12-12-1-1-1-12200-1-1-1-11-21-200001111111122-1-1-1-100000000-2-20000001111000000
χ3022222-122222-12-1222-12-1-12-1-12-1-1-1-122-12-12-1-1-1-12-2-2-2-2-2-2-2-21111-1-1-1-1-12-12-1-1-1-1-2-20011111-21-2000011111111-2-211110000000022000000-1-1-1-1000000
χ3122222-12-2-222-12-1222-12-1-12-1-12-1-1-1-12-21-21-21111-222-2-222221111-1-1-1-11-21-211110000−i3i3−i3i3-1-2-1-20000-1-111-1-11100−i3i3−i3i30000000000000000−i3i3−i3i3000000
χ3222222-12-2-222-12-1222-12-1-12-1-12-1-1-1-12-21-21-21111-222-2-222221111-1-1-1-11-21-211110000i3−i3i3−i3-1-2-1-20000-1-111-1-11100i3−i3i3−i30000000000000000i3−i3i3−i3000000
χ3322222-12-2-222-12-1222-12-1-12-1-12-1-1-1-12-21-21-21111-2-2-222-2-2-2-2-1-1-1-1-1-1-1-11-21-211110000−i3i3−i3i31212000011-1-111-1-100−i3i3−i3i30000000000000000i3−i3i3−i3000000
χ3422222-12-2-222-12-1222-12-1-12-1-12-1-1-1-12-21-21-21111-2-2-222-2-2-2-2-1-1-1-1-1-1-1-11-21-211110000i3−i3i3−i31212000011-1-111-1-100i3−i3i3−i30000000000000000−i3i3−i3i3000000
χ352222-12222-1-12222-122-12-1-1-1-1-12-122-1-122222222-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1222222220000222200000000-1-1-1-1-1-1-1-1-1-1-1-100000000220000-1-1-1-100
χ362222-12222-1-12222-122-12-1-1-1-1-12-122-1-122222222-1000000000000-1-1-1-1-1-1-1-1-1-1-1-122-2-222220000-2-2-2-200000000-1-1-1-1-1-111111100000000-2-20000111100
χ372222-12222-1-12222-122-12-1-1-1-1-12-122-1-122222222-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-20000222200000000111111-1-1-1-1-1-100000000-2-20000111100
χ382222-12222-1-12222-122-12-1-1-1-1-12-122-1-122222222-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-20000-2-2-2-20000000011111111111100000000220000-1-1-1-100
χ3922-2-22222-2-2222-2-2-2-2-2222-2-2-2222-2-2-2-2-2-222-2-22222i−2i−2i2i2i2i−2i−2i−2i−2i2i2i2-2-22-2-222-2-222000000002i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ4022-2-22222-2-2222-2-2-2-2-2222-2-2-2222-2-2-2-2-2-222-2-2222−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i2-2-22-2-222-2-22200000000−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ4122-2-222-12-2-222-1-21-21-2-1-121-2-2-1-12111-2-212-111-1-122i−2i−2i2i−i−iii−2i−2i2i2i-111-1-212-111-1-1000000002ii−2i−i3−3−33−i−iiiii−i−i000000003−3−330000−i3i3i3−i3000000000000
χ4222-2-222-12-2-222-1-21-21-2-1-121-2-2-1-12111-2-212-111-1-122i−2i−2i2i−i−iii−2i−2i2i2i-111-1-212-111-1-1000000002ii−2i−i−333−3−i−iiiii−i−i00000000−333−30000i3−i3−i3i3000000000000
χ4322-2-222-12-2-222-1-21-21-2-1-121-2-2-1-12111-2-212-111-1-12−2i2i2i−2iii−i−i2i2i−2i−2i-111-1-212-111-1-100000000−2i−i2ii3−3−33ii−i−i−i−iii000000003−3−330000i3−i3−i3i3000000000000
χ4422-2-222-12-2-222-1-21-21-2-1-121-2-2-1-12111-2-212-111-1-12−2i2i2i−2iii−i−i2i2i−2i−2i-111-1-212-111-1-100000000−2i−i2ii−333−3ii−i−i−i−iii00000000−333−30000−i3i3i3−i3000000000000
χ4522-2-222-1-22-222-1-21-21-2-1-121-2-2-1-1211122-1-21-1-111-22i−2i2i−2i−i−iii2i2i−2i−2i-111-12-1-21-1-111002i−2i00002i−i−2ii−i−iii−i−i−i−iiiii0000002i−2i−i−iii2-200-1-111000000000000
χ4622-2-222-1-22-222-1-21-21-2-1-121-2-2-1-1211122-1-21-1-111-22i−2i2i−2i−i−iii2i2i−2i−2i-111-12-1-21-1-11100−2i2i00002i−i−2iiii−i−i−i−i−i−iiiii000000−2i2iii−i−i-220011-1-1000000000000
χ4722-2-222-1-22-222-1-21-21-2-1-121-2-2-1-1211122-1-21-1-111-2−2i2i−2i2iii−i−i−2i−2i2i2i-111-12-1-21-1-111002i−2i0000−2ii2i−i−i−iiiiiii−i−i−i−i0000002i−2i−i−iii-220011-1-1000000000000
χ4822-2-222-1-22-222-1-21-21-2-1-121-2-2-1-1211122-1-21-1-111-2−2i2i−2i2iii−i−i−2i−2i2i2i-111-12-1-21-1-11100−2i2i0000−2ii2i−iii−i−iiiii−i−i−i−i000000−2i2iii−i−i2-200-1-111000000000000
χ4922-2-22-122-2-22-121-2-2-212-1-1-2112-1-111-2-21-2-1211-1-122i−2i−2i2i2i2i−2i−2iii−i−i-111-11-2-1211-1-10000−i3i3i3−i3−i−2ii2i0000−i−iiiii−i−i00−i3i3i3−i300000000000000003−3−33000000
χ5022-2-22-122-2-22-121-2-2-212-1-1-2112-1-111-2-21-2-1211-1-122i−2i−2i2i2i2i−2i−2iii−i−i-111-11-2-1211-1-10000i3−i3−i3i3−i−2ii2i0000−i−iiiii−i−i00i3−i3−i3i30000000000000000−333−3000000
χ5122-2-22-122-2-22-121-2-2-212-1-1-2112-1-111-2-21-2-1211-1-12−2i2i2i−2i−2i−2i2i2i−i−iii-111-11-2-1211-1-10000−i3i3i3−i3i2i−i−2i0000ii−i−i−i−iii00−i3i3i3−i30000000000000000−333−3000000
χ5222-2-22-122-2-22-121-2-2-212-1-1-2112-1-111-2-21-2-1211-1-12−2i2i2i−2i−2i−2i2i2i−i−iii-111-11-2-1211-1-10000i3−i3−i3i3i2i−i−2i0000ii−i−i−i−iii00i3−i3−i3i300000000000000003−3−33000000
χ5322-2-22-12-22-22-121-2-2-212-1-1-2112-1-111-22-121-2-1-111-22i−2i2i−2i2i2i−2i−2i−i−iii-111-1-121-2-1-1112-200-1-111−i2ii−2i0000−i−i−i−iiiii2-2-1-111000000002i−2i000000−i−iii000000
χ5422-2-22-12-22-22-121-2-2-212-1-1-2112-1-111-22-121-2-1-111-22i−2i2i−2i2i2i−2i−2i−i−iii-111-1-121-2-1-111-220011-1-1−i2ii−2i0000−i−i−i−iiiii-2211-1-100000000−2i2i000000ii−i−i000000
χ5522-2-22-12-22-22-121-2-2-212-1-1-2112-1-111-22-121-2-1-111-2−2i2i−2i2i−2i−2i2i2iii−i−i-111-1-121-2-1-1112-200-1-111i−2i−i2i0000iiii−i−i−i−i2-2-1-11100000000−2i2i000000ii−i−i000000
χ5622-2-22-12-22-22-121-2-2-212-1-1-2112-1-111-22-121-2-1-111-2−2i2i−2i2i−2i−2i2i2iii−i−i-111-1-121-2-1-111-220011-1-1i−2i−i2i0000iiii−i−i−i−i-2211-1-1000000002i−2i000000−i−iii000000
χ5722-2-2-122-221-122-2-21-2-2-12-1111-12-1-2-21-122-2-222-2-21000000000000-111-1-1-111-1-1112-22i−2i22-2-200002i2i−2i−2i00000000-11-1-111−ii−i−iii000000002i−2i0000−i−iii00
χ5822-2-2-122-221-122-2-21-2-2-12-1111-12-1-2-21-122-2-222-2-21000000000000-111-1-1-111-1-1112-2−2i2i22-2-20000−2i−2i2i2i00000000-11-1-111i−iii−i−i00000000−2i2i0000ii−i−i00
χ5922-2-2-122-221-122-2-21-2-2-12-1111-12-1-2-21-122-2-222-2-21000000000000-111-1-1-111-1-111-222i−2i-2-22200002i2i−2i−2i000000001-111-1-1−ii−i−iii00000000−2i2i0000ii−i−i00
χ6022-2-2-122-221-122-2-21-2-2-12-1111-12-1-2-21-122-2-222-2-21000000000000-111-1-1-111-1-111-22−2i2i-2-2220000−2i−2i2i2i000000001-111-1-1i−iii−i−i000000002i−2i0000−i−iii00
χ6144444-2-24444-2-2-2-24-2-2-21-2-2-2-2-21-211-24-2-2-2-2111144444-2-2-2-2-2-2-2-21111-2-2-2-2111100000000-2-2-2-200001111111100000000000000000000000000000000
χ6244444-2-24444-2-2-2-24-2-2-21-2-2-2-2-21-211-24-2-2-2-211114-4-4-4-4222222221111-2-2-2-211110000000022220000-1-1-1-1-1-1-1-100000000000000000000000000000000
χ6344444-2-2-4-444-2-2-2-24-2-2-21-2-2-2-2-21-211-2-42222-1-1-1-1-444-4-4-2-2-2-2222211112222-1-1-1-100000000-22-22000011-1-111-1-100000000000000000000000000000000
χ6444444-2-2-4-444-2-2-2-24-2-2-21-2-2-2-2-21-211-2-42222-1-1-1-1-4-4-4442222-2-2-2-211112222-1-1-1-1000000002-22-20000-1-111-1-11100000000000000000000000000000000
χ654444-244-4-4-2-24444-244-24-2-2-2-2-24-244-22-4-4-4-4-4-4-4-42000000000000-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ664444-24-244-2-24-24-2-2-241-2-21-2-21-2-2-2-21-24-24-2-2-2-2-2-20000000000001111-21-211111004400000000-2-2-2-200000000000000-2-2111100000000000000000000
χ674444-24-244-2-24-24-2-2-241-2-21-2-21-2-2-2-21-24-24-2-2-2-2-2-20000000000001111-21-21111100-4-40000000022220000000000000022-1-1-1-100000000000000000000
χ684444-24-2-4-4-2-24-24-2-2-241-2-21-2-21-2-2-2-212-42-422222200000000000011112-12-1-1-1-1-1000000000000−2i32i3−2i32i30000000000000000i3−i3i3−i300000000000000000000
χ694444-24-2-4-4-2-24-24-2-2-241-2-21-2-21-2-2-2-212-42-422222200000000000011112-12-1-1-1-1-10000000000002i3−2i32i3−2i30000000000000000−i3i3−i3i300000000000000000000
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χ7744-4-44-2-2-44-44-2-222-422-21-2222-21-2-1-124-2-22211-1-1-4−4i4i−4i4i2i2i−2i−2i2i2i−2i−2i1-1-11-2-22211-1-1000000002i2i−2i−2i0000−i−i−i−iiiii00000000000000000000000000000000
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χ984-4-44444004-4-4-4-44-4-444444-44-4-4-4-44-400000000000000000000004-44-40000000000000000000000000000000000000000000000000000000000000000
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χ1044-4-444-2-2004-4222-2-42-2-21-2-22-22-12-112000003i−3i−3i3i00000−232323−23−2i32i32i3−2i31-11-100003i−3i−3i3i00000000000000003−3i3−i3−33−i3i300000000000000000000000000000000
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χ1064-4-444-2-2004-4222-2-42-2-21-2-22-22-12-11200000−3i3i3i−3i00000−232323−232i3−2i3−2i32i31-11-10000−3i3i3i−3i00000000000000003−3−i3i3−33i3−i300000000000000000000000000000000
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χ1108888-4-4-4-8-8-4-4-4-4-4-4-4-4-422222222222244444-2-2-2-24000000000000-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ11188-8-8-4-4-48-84-4-4-444444222-2-2-2222-2-2-2444-4-4-2-222-4000000000000-111-1-2-22211-1-100000000000000000000000000000000000000000000000000000000
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χ1138-88-8-48-40044-8484-4-4-82-4-4-2-44-244-442000000000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000000
χ1148-88-8-4-4800444-8-4-8-484-4-4242-244-2-44-4000000000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000000
χ1158-88-8-4-4-4004444-44-4-44222-22-2-2-2-22-22000006i−6i6i−6i0000000000000-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
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χ1178-8-88-48-400-44-84-8-44482-4-424-4-2444-4-200000000000000000000002-22-20000000000000000000000000000000000000000000000000000000000000000
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χ1198-8-88-4-4-400-44444-444-42222-22-2-2-2-22-2000006i−6i−6i6i0000000000000-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000
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Here i is the imaginary unit (i² = −1).