Finite Group Databasebeta

← Group #13161997

Character table — Group #13161997

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818181836363636363636363636363636363636363636363636363672727272
order122233344666666666333334466666666666666612121212121212121212121212121212121212121212121212121212121212121212121212121212121212124444121212124444448888121212121212242424242424242412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ511111111111111111111111-1-1111111111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111111-1-1111111111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1
χ711111111111111111111111-1-1111111111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-111
χ811111111111111111111111-1-1111111111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-111-1-1
χ911-1-11111-1-1-1-111-1-11-1111111-1-1-1-1-1-1-1-1-1-1-11111111-111-1-1-1-111-11-111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i1-1i−ii−i1-1i−ii−iii−i−i11-1-1ii−i−ii−i1-1
χ1011-1-11111-1-1-1-111-1-11-1111111-1-1-1-1-1-1-1-1-1-1-11111111-111-1-1-1-111-11-111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i-11i−i−ii-11−iii−iii−i−i-1-111−i−iii−ii-11
χ1111-1-11111-1-1-1-111-1-11-1111111-1-1-1-1-1-1-1-1-1-1-11111111-111-1-1-1-111-11-111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii1-1−ii−ii1-1−ii−ii−i−iii11-1-1−i−iii−ii1-1
χ1211-1-11111-1-1-1-111-1-11-1111111-1-1-1-1-1-1-1-1-1-1-11111111-111-1-1-1-111-11-111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii-11−iii−i-11i−i−ii−i−iii-1-111ii−i−ii−i-11
χ1311-1-11111-1-1-1-111-1-11-111111-11-1-1-1-1-1-1-1-1-1-11111111-1-1-111-1-11-11-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111ii−i−iii−i−i1-1−iii−i-11−iii−i−i−iii-1-111−i−iiii−i1-1
χ1411-1-11111-1-1-1-111-1-11-111111-11-1-1-1-1-1-1-1-1-1-11111111-1-1-111-1-11-11-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111ii−i−iii−i−i-11−ii−ii1-1i−ii−i−i−iii11-1-1ii−i−i−ii-11
χ1511-1-11111-1-1-1-111-1-11-111111-11-1-1-1-1-1-1-1-1-1-11111111-1-1-111-1-11-11-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−iii−i−iii1-1i−i−ii-11i−i−iiii−i−i-1-111ii−i−i−ii1-1
χ1611-1-11111-1-1-1-111-1-11-111111-11-1-1-1-1-1-1-1-1-1-11111111-1-1-111-1-11-11-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−iii−i−iii-11i−ii−i1-1−ii−iiii−i−i11-1-1−i−iiii−i-11
χ172222222-2-22222222222222200222222222222222-2-2-20000-2-2-20000-2-2-2-2-2-2-2-2-2-2000000000000000000002-22-222220000000000-2-20000000000000000
χ182222222-2-22222222222222200222222222222222-2-2-20000-2-2-20000-2-2-2-2-2-2-2-2-2-200000000000000000000-22-22-2-2-2-20000000000220000000000000000
χ19222222-1222222-1-122-12-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-12-1-1-1-1-1-122222222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-10022000000-1-1-1-1-1-1000000000000
χ20222222-1222222-1-122-12-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-12-1-1-1-1-1-122222222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2111100-2-2000000111111000000000000
χ21222222-1222222-1-122-12-1-1-1-1-2-222-1-1-1-1-1-1-1-12-1-1-1-12-1-11111222-2-2-2-22-1-1-1-12-1-1-1-1-2-211111111-2-2111111112222-1-1-1-100-2-2000000-1-11111000000000000
χ22222222-1222222-1-122-12-1-1-1-1-2-222-1-1-1-1-1-1-1-12-1-1-1-12-1-11111222-2-2-2-22-1-1-1-12-1-1-1-1-2-211111111-2-211111111-2-2-2-21111002200000011-1-1-1-1000000000000
χ23222222-1-2-22222-1-122-12-1-1-1-10022-1-1-1-1-1-1-1-12-1-1-1-1-211−i3i3−i3i3-2-2-20000-21111-2111100−i3−i3−i3−i3i3i3i3i300−i3−i3−i3−i3i3i3i3i32-22-2-1-1-1-1000000000011−i3i3−i3i3000000000000
χ24222222-1-2-22222-1-122-12-1-1-1-10022-1-1-1-1-1-1-1-12-1-1-1-1-211−i3i3−i3i3-2-2-20000-21111-2111100−i3−i3−i3−i3i3i3i3i300−i3−i3−i3−i3i3i3i3i3-22-2211110000000000-1-1i3−i3i3−i3000000000000
χ25222222-1-2-22222-1-122-12-1-1-1-10022-1-1-1-1-1-1-1-12-1-1-1-1-211i3−i3i3−i3-2-2-20000-21111-2111100i3i3i3i3−i3−i3−i3−i300i3i3i3i3−i3−i3−i3−i32-22-2-1-1-1-1000000000011i3−i3i3−i3000000000000
χ26222222-1-2-22222-1-122-12-1-1-1-10022-1-1-1-1-1-1-1-12-1-1-1-1-211i3−i3i3−i3-2-2-20000-21111-2111100i3i3i3i3−i3−i3−i3−i300i3i3i3i3−i3−i3−i3−i3-22-2211110000000000-1-1−i3i3−i3i3000000000000
χ2722222-122222-1-122-122-12-1-1-122-1-122-1-1-1-1-1-1-12-1-1-1-12222222-12-1-122-12-1-1-1-12-1-1-1-1-12-1-1-12-1-1-1-1-12-1-1-12-1-1-10000000000002200220000000000-1-1-1-1-1-100
χ2822222-122222-1-122-122-12-1-1-122-1-122-1-1-1-1-1-1-12-1-1-1-12222222-12-1-122-12-1-1-1-12-1-1-1-1-12-1-1-12-1-1-1-1-12-1-1-12-1-1-1000000000000-2-200-2-2000000000011111100
χ2922222-122222-1-122-122-12-1-1-1-2-2-1-122-1-1-1-1-1-1-12-1-1-1-122-2-2-2-22-1211-2-2-12-1-1-1-12-1-1-111-2111-211111-2111-21110000000000002200-2-200000000001111-1-100
χ3022222-122222-1-122-122-12-1-1-1-2-2-1-122-1-1-1-1-1-1-12-1-1-1-122-2-2-2-22-1211-2-2-12-1-1-1-12-1-1-111-2111-211111-2111-2111000000000000-2-200220000000000-1-1-1-11100
χ312222-12222-1-122222-12-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-12222222-12-122-1-1-1-12-1-1-1-12-1-1-1-1-12-1-1-12-1-1-1-1-12-1-1-12-1-1000000002200002200000000-1-1-1-1000000-1-1
χ322222-12222-1-122222-12-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-12222222-12-122-1-1-1-12-1-1-1-12-1-1-1-1-12-1-1-12-1-1-1-1-12-1-1-12-1-100000000-2-20000-2-200000000111100000011
χ332222-12222-1-122222-12-1-12-1-1-2-2-1-1-1-122-1-1-1-1-1-12-1-1222-2-2-2-2-12-1-2-211-1-12-1-1-1-12-1-1111-2111-211111-2111-21100000000220000-2-2000000001111000000-1-1
χ342222-12222-1-122222-12-1-12-1-1-2-2-1-1-1-122-1-1-1-1-1-12-1-1222-2-2-2-2-12-1-2-211-1-12-1-1-1-12-1-1111-2111-211111-2111-21100000000-2-200002200000000-1-1-1-100000011
χ3522-2-2222-22-2-2-222-2-22-22222200-2-2-2-2-2-2-2-2-2-222222-2-22000022-20000-2-2-2-2-222222000000000000000000002i−2i−2i2i2i2i−2i−2i0000000000−2i2i0000000000000000
χ3622-2-2222-22-2-2-222-2-22-22222200-2-2-2-2-2-2-2-2-2-222222-2-22000022-20000-2-2-2-2-22222200000000000000000000−2i2i2i−2i−2i−2i2i2i00000000002i−2i0000000000000000
χ3722-2-222-12-2-2-2-22-11-2212-1-1-1-12-2-2-2111111112-1-1-1-12-11-1-111-2-222-22-22-1-1-1-1-2111122-1-1-1-1-1-1-1-1-2-2111111112i2i−2i−2i−i−iii002i−2i000000−ii−i−iii000000000000
χ3822-2-222-12-2-2-2-22-11-2212-1-1-1-12-2-2-2111111112-1-1-1-12-11-1-111-2-222-22-22-1-1-1-1-2111122-1-1-1-1-1-1-1-1-2-211111111−2i−2i2i2iii−i−i00−2i2i000000i−iii−i−i000000000000
χ3922-2-222-12-2-2-2-22-11-2212-1-1-1-1-22-2-2111111112-1-1-1-12-1111-1-1-2-22-22-222-1-1-1-1-21111-2-21111111122-1-1-1-1-1-1-1-12i2i−2i−2i−i−iii00−2i2i000000−iiii−i−i000000000000
χ4022-2-222-12-2-2-2-22-11-2212-1-1-1-1-22-2-2111111112-1-1-1-12-1111-1-1-2-22-22-222-1-1-1-1-21111-2-21111111122-1-1-1-1-1-1-1-1−2i−2i2i2iii−i−i002i−2i000000i−i−i−iii000000000000
χ4122-2-222-1-22-2-2-22-11-2212-1-1-1-100-2-2111111112-1-1-1-1-21-1−i3i3i3−i322-20000-211112-1-1-1-100−i3−i3−i3−i3i3i3i3i300i3i3i3i3−i3−i3−i3−i32i−2i−2i2i−i−iii0000000000i−i3−3−33000000000000
χ4222-2-222-1-22-2-2-22-11-2212-1-1-1-100-2-2111111112-1-1-1-1-21-1−i3i3i3−i322-20000-211112-1-1-1-100−i3−i3−i3−i3i3i3i3i300i3i3i3i3−i3−i3−i3−i3−2i2i2i−2iii−i−i0000000000−ii−333−3000000000000
χ4322-2-222-1-22-2-2-22-11-2212-1-1-1-100-2-2111111112-1-1-1-1-21-1i3−i3−i3i322-20000-211112-1-1-1-100i3i3i3i3−i3−i3−i3−i300−i3−i3−i3−i3i3i3i3i32i−2i−2i2i−i−iii0000000000i−i−333−3000000000000
χ4422-2-222-1-22-2-2-22-11-2212-1-1-1-100-2-2111111112-1-1-1-1-21-1i3−i3−i3i322-20000-211112-1-1-1-100i3i3i3i3−i3−i3−i3−i300−i3−i3−i3−i3i3i3i3i3−2i2i2i−2iii−i−i0000000000−ii3−3−33000000000000
χ4522-2-22-122-2-2-21-12-212-2-12-1-1-12-211-2-2111111-12-1-1-1-12-222-2-2-212-112-2-12-1-1-11-2111-1-12-1-1-12-1-1-111-2111-21110000000000002i−2i002i−2i0000000000−i−iii−ii00
χ4622-2-22-122-2-2-21-12-212-2-12-1-1-12-211-2-2111111-12-1-1-1-12-222-2-2-212-112-2-12-1-1-11-2111-1-12-1-1-12-1-1-111-2111-2111000000000000−2i2i00−2i2i0000000000ii−i−ii−i00
χ4722-2-22-122-2-2-21-12-212-2-12-1-1-1-2211-2-2111111-12-1-1-1-12-2-2-222-2121-1-22-12-1-1-11-211111-2111-2111-1-12-1-1-12-1-1-10000000000002i−2i00−2i2i0000000000ii−i−i−ii00
χ4822-2-22-122-2-2-21-12-212-2-12-1-1-1-2211-2-2111111-12-1-1-1-12-2-2-222-2121-1-22-12-1-1-11-211111-2111-2111-1-12-1-1-12-1-1-1000000000000−2i2i002i−2i0000000000−i−iiii−i00
χ4922-2-2-1222-211-222-2-2-1-2-1-12-1-12-21111-2-21111-1-12-1-122-222-2-21-2-12-2-11-1-12-1-111-211-1-1-12-1-1-12-1-1111-2111-211000000002-200002-200000000-1-111000000-11
χ5022-2-2-1222-211-222-2-2-1-2-1-12-1-12-21111-2-21111-1-12-1-122-222-2-21-2-12-2-11-1-12-1-111-211-1-1-12-1-1-12-1-1111-2111-21100000000-220000-220000000011-1-10000001-1
χ5122-2-2-1222-211-222-2-2-1-2-1-12-1-1-221111-2-21111-1-12-1-122-2-2-2221-2-1-221-1-1-12-1-111-211111-2111-211-1-1-12-1-1-12-1-1000000002-20000-220000000011-1-1000000-11
χ5222-2-2-1222-211-222-2-2-1-2-1-12-1-1-221111-2-21111-1-12-1-122-2-2-2221-2-1-221-1-1-12-1-111-211111-2111-211-1-1-12-1-1-12-1-100000000-2200002-200000000-1-1110000001-1
χ5344444-24-4-444-2-244-244-24-2-2-200-2-244-2-2-2-2-2-2-24-2-2-22-4-40000-42-400002-42222-422200000000000000000000000000000000000000000000000000000000
χ5444444-2-24444-2-2-2-2-24-2-2-211144-2-2-2-2111111-2-2111-2-2-2-2-2-2-24-24-2-244-2-2111-2-2111-2-2-2111-2111-2-2-2111-2111000000000000000000000000000000000000
χ5544444-2-24444-2-2-2-2-24-2-2-2111-4-4-2-2-2-2111111-2-2111-2-2-222224-2422-4-4-2-2111-2-2111222-1-1-12-1-1-1222-1-1-12-1-1-1000000000000000000000000000000000000
χ5644444-2-2-4-444-2-2-2-2-24-2-2-211100-2-2-2-2111111-2-2111222−2i32i3−2i32i3-42-4000022-1-1-122-1-1-100−2i3i3i3i32i3−i3−i3−i300−2i3i3i3i32i3−i3−i3−i3000000000000000000000000000000000000
χ5744444-2-2-4-444-2-2-2-2-24-2-2-211100-2-2-2-2111111-2-21112222i3−2i32i3−2i3-42-4000022-1-1-122-1-1-1002i3−i3−i3−i3−2i3i3i3i3002i3−i3−i3−i3−2i3i3i3i3000000000000000000000000000000000000
χ584444-244-4-4-2-244444-24-2-24-2-200-2-2-2-244-2-2-2-2-2-24-2-2-4-4-400002-42000022-42222-42200000000000000000000000000000000000000000000000000000000
χ594444-24-244-2-244-2-24-2-2-21-21144-2-211-2-21111-21-2114-2-2-2-2-2-2-24-244-2-2-21-211-21-211-2-21-2111-211-2-21-2111-211000000000000000000000000000000000000
χ604444-24-244-2-244-2-24-2-2-21-211-4-4-2-211-2-21111-21-2114-2-22222-24-2-4-422-21-211-21-21122-12-1-1-12-1-122-12-1-1-12-1-1000000000000000000000000000000000000
χ614444-24-2-4-4-2-244-2-24-2-2-21-21100-2-211-2-21111-21-211-422−2i32i3−2i32i32-4200002-12-1-12-12-1-100i3−2i3i3i3−i32i3−i3−i300i3−2i3i3i3−i32i3−i3−i3000000000000000000000000000000000000
χ624444-24-2-4-4-2-244-2-24-2-2-21-21100-2-211-2-21111-21-211-4222i3−2i32i3−2i32-4200002-12-1-12-12-1-100−i32i3−i3−i3i3−2i3i3i300−i32i3−i3−i3i3−2i3i3i3000000000000000000000000000000000000
χ634444-2-2444-2-2-2-244-2-241-2-2114411-2-2-2-211111-2-211-2444444-2-2-2-2-2-2-21-2-2111-2-21111-2-211-2-21111-2-211-2-211000000000000000000000000000000000000
χ644444-2-2444-2-2-2-244-2-241-2-211-4-411-2-2-2-211111-2-211-244-4-4-4-4-2-2-222221-2-2111-2-211-1-122-1-122-1-1-1-122-1-122-1-1000000000000000000000000000000000000
χ654444-2-24-4-4-2-2-2-244-2-241-2-2110011-2-2-2-211111-2-2112-4-400002220000-122-1-1-122-1-13-3003-3003-33-3003-3003-3000000000000000000000000000000000000
χ664444-2-24-4-4-2-2-2-244-2-241-2-2110011-2-2-2-211111-2-2112-4-400002220000-122-1-1-122-1-1-3300-3300-33-3300-3300-33000000000000000000000000000000000000
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χ684444-2-2-244-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32-4-4111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32-2-2-22222-2-2-22222111−1−3i32−1+3i32111−1−3i32−1+3i32-1-1-1-11+3i321−3i32-1-11−3i321+3i32-1-1-1-11+3i321−3i32-1-11−3i321+3i32000000000000000000000000000000000000
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χ9344-4-4-2-2-2-44222-2-222-22111−1−3i32−1+3i3200-1-1-1-1-1-11+3i321+3i321−3i321−3i32111−1−3i32−1+3i3222-2−2i32i32i3−2i3-2-220000-1-1-11+3i321−3i32111−1−3i32−1+3i323-3i3i3−3−i323−i32−i3−i3−3+i323+i32-33−i3−i33+i32−3+i32i3i33−i32−3−i32000000000000000000000000000000000000
χ9444-4-4-2-2-2-44222-2-222-22111−1−3i32−1+3i3200-1-1-1-1-1-11+3i321+3i321−3i321−3i32111−1−3i32−1+3i3222-22i3−2i3−2i32i3-2-220000-1-1-11+3i321−3i32111−1−3i32−1+3i32-33−i3−i33+i32−3+i32i3i33−i32−3−i323-3i3i3−3−i323−i32−i3−i3−3+i323+i32000000000000000000000000000000000000
χ9544-4-4-2-2-2-44222-2-222-22111−1+3i32−1−3i3200-1-1-1-1-1-11−3i321−3i321+3i321+3i32111−1+3i32−1−3i3222-2−2i32i32i3−2i3-2-220000-1-1-11−3i321+3i32111−1+3i32−1−3i32-33i3i33−i32−3−i32−i3−i33+i32−3+i323-3−i3−i3−3+i323+i32i3i3−3−i323−i32000000000000000000000000000000000000
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χ1024-44-4-24400-224-4-4-4-424-2-24-2-200-22-224-4-22-2222-42200000000000000000000000000000000000000000000000000000000000000000000i6−i6i6−i600000000
χ1034-44-4-24400-224-4-4-4-424-2-24-2-200-22-224-4-22-2222-42200000000000000000000000000000000000000000000000000000000000000000000−i6i6−i6i600000000
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χ1148-88-8-4-4-400-44-444444-4222−1−3i3−1+3i3002-22-22-2−1−3i31+3i3−1+3i31−3i3-2-2-21+3i31−3i300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1158-88-8-4-4-400-44-444444-4222−1+3i3−1−3i3002-22-22-2−1+3i31−3i3−1−3i31+3i3-2-2-21−3i31+3i300000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1208-8-88-4-4-4004-4444-4-444222−1+3i3−1−3i300-22-22-221−3i3−1+3i31+3i3−1−3i3-2-2-21−3i31+3i300000000000000000000000000000000000000000000000000000000000000000000000000000000

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