Finite Group Databasebeta

← Group #13161771

Character table — Group #13161771

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818181836363636363636363636363636363636363636363636363672727272
order124423334666121212121212333336666666688121212121212121212121212122424242466666121212121224242424242424242424242424242424242424242424242422446612122244444468812121212121212121224242424661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11
χ51111111111111111111111111111111-1-11111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111-1-11111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1111111111-1-1-1-1-1-1-1-1
χ71111111111111111111111111111111-1-11111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-111-1-1-1-1-1111111111-11-1
χ81111111111111111111111111111111-1-11111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-111-11111-1-1-1-11111-11-11
χ911-1-1-11111111-1-1-1-1-1-111111-111111-1-1i−i111-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-111111ii−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−i−i1-11-111-1-11-1-11i−ii−i-1i−i1ii−i−iii−i−iii−i−i1-1-11
χ1011-1-1-11111111-1-1-1-1-1-111111-111111-1-1i−i111-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-111111ii−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−i−i1-11-111-1-1-111-1−ii−ii-1i−i1−i−iii−i−iiiii−i−i-111-1
χ1111-1-1-11111111-1-1-1-1-1-111111-111111-1-1i−i111-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-111111ii−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−i−i-11-11-1-11111-1-1i−i−ii1−ii-1ii−i−i−i−iii−i−iii11-1-1
χ1211-1-1-11111111-1-1-1-1-1-111111-111111-1-1i−i111-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-111111ii−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−i−i-11-11-1-111-1-111−iii−i1−ii-1−i−iiiii−i−i−i−iii-1-111
χ1311-1-1-11111111-1-1-1-1-1-111111-111111-1-1−ii111-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-111111−i−iii−i−i−i−i−i−i−i−i−i−iiiiiiiiiii1-11-111-1-11-1-11−ii−ii-1−ii1−i−iii−i−iii−i−iii1-1-11
χ1411-1-1-11111111-1-1-1-1-1-111111-111111-1-1−ii111-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-111111−i−iii−i−i−i−i−i−i−i−i−i−iiiiiiiiiii1-11-111-1-1-111-1i−ii−i-1−ii1ii−i−iii−i−i−i−iii-111-1
χ1511-1-1-11111111-1-1-1-1-1-111111-111111-1-1−ii111-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-111111−i−iii−i−i−i−i−i−i−i−i−i−iiiiiiiiiii-11-11-1-11111-1-1−iii−i1i−i-1−i−iiiii−i−iii−i−i11-1-1
χ1611-1-1-11111111-1-1-1-1-1-111111-111111-1-1−ii111-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-111111−i−iii−i−i−i−i−i−i−i−i−i−iiiiiiiiiii-11-11-1-111-1-111i−i−ii1i−i-1ii−i−i−i−iiiii−i−i-1-111
χ172222222-1222-12222-1-12-1-1-1-1-12-1-1-1-1222222-122-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-12-1-1-1-1222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-100000000-122-100000000-1-1-1-10000
χ182222222-1222-12222-1-12-1-1-1-1-12-1-1-1-1222222-122-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-12-1-1-1-1222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21111000000001-2-210000000011110000
χ192222222-1222-12222-1-12-1-1-1-1-12-1-1-1-122-2-222-122-1-1-1-1-1-1-1-111112-1-1-1-12-1-1-1-1-2-2-2-2-2-211111111-2-2111111112222-1-1-1-100000000-1-2-2-10000000011110000
χ202222222-1222-12222-1-12-1-1-1-1-12-1-1-1-122-2-222-122-1-1-1-1-1-1-1-111112-1-1-1-12-1-1-1-1-2-2-2-2-2-211111111-2-211111111-2-2-2-2111100000000122100000000-1-1-1-10000
χ21222222-1222-1222-1-122-12-1-1-12-12-1-1-12-1222-12-1-122-1-1-1-1-1-12222-12-1-1-1-12-1-1-12-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000202002200000000-1-1-1-100000-10-1
χ22222222-1222-1222-1-122-12-1-1-12-12-1-1-12-1222-12-1-122-1-1-1-1-1-12222-12-1-1-1-12-1-1-12-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000-20-200-2-200000000111100000101
χ23222222-1222-1222-1-122-12-1-1-12-12-1-1-12-1-2-22-12-1-122-1-1-1-1-1-1-2-2-2-2-12-1-1-1-12-1-1-1-21-2111-2-211111111-2-211111100000000020200-2-200000000111100000-10-1
χ24222222-1222-1222-1-122-12-1-1-12-12-1-1-12-1-2-22-12-1-122-1-1-1-1-1-1-2-2-2-2-12-1-1-1-12-1-1-1-21-2111-2-211111111-2-2111111000000000-20-2002200000000-1-1-1-100000101
χ2522222-1222-122-1-12222-1-12-1-12-1-12-1-1-1222-122-1-1-1-122-1-1-1-12222-1-12-1-1-1-12-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000202022000000-1-1-1-100000000-10-10
χ2622222-1222-122-1-12222-1-12-1-12-1-12-1-1-1222-122-1-1-1-122-1-1-1-12222-1-12-1-1-1-12-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000-20-20-2-20000001111000000001010
χ2722222-1222-122-1-12222-1-12-1-12-1-12-1-1-12-2-2-122-1-1-1-122-1-1-1-1-2-2-2-2-1-12-1-1-1-12-1-11-21-21111-2-211111111-2-21111000000002020-2-2000000111100000000-10-10
χ2822222-1222-122-1-12222-1-12-1-12-1-12-1-1-12-2-2-122-1-1-1-122-1-1-1-1-2-2-2-2-1-12-1-1-1-12-1-11-21-21111-2-211111111-2-2111100000000-20-2022000000-1-1-1-1000000001010
χ292222-2222-222222222222222-222222-2-200-2-2-222222222220000-2-2-2-2-2-2-2-2-2-20000000000000000000000002-2-22222200000000-200-20000000000000000
χ302222-2222-222222222222222-222222-2-200-2-2-222222222220000-2-2-2-2-2-2-2-2-2-2000000000000000000000000-222-2-2-2-2-20000000020020000000000000000
χ312222-222-1-222-12222-1-12-1-1-1-112-1-1-1-1-2-200-2-2122-1-1-1-1-1-1-1-1−i3i3−i3i3-21111-21111000000−i3i3−i3i3−i3−i3i3i300−i3i3−i3i3−i3−i3i3i32-2-22-1-1-1-100000000100100000000−i3i3−i3i30000
χ322222-222-1-222-12222-1-12-1-1-1-112-1-1-1-1-2-200-2-2122-1-1-1-1-1-1-1-1−i3i3−i3i3-21111-21111000000−i3i3−i3i3−i3−i3i3i300−i3i3−i3i3−i3−i3i3i3-222-2111100000000-100-100000000i3−i3i3−i30000
χ332222-222-1-222-12222-1-12-1-1-1-112-1-1-1-1-2-200-2-2122-1-1-1-1-1-1-1-1i3−i3i3−i3-21111-21111000000i3−i3i3−i3i3i3−i3−i300i3−i3i3−i3i3i3−i3−i32-2-22-1-1-1-100000000100100000000i3−i3i3−i30000
χ342222-222-1-222-12222-1-12-1-1-1-112-1-1-1-1-2-200-2-2122-1-1-1-1-1-1-1-1i3−i3i3−i3-21111-21111000000i3−i3i3−i3i3i3−i3−i300i3−i3i3−i3i3i3−i3−i3-222-2111100000000-100-100000000−i3i3−i3i30000
χ3522-2-22222-2222-2-2-2-2-2-2222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-2000022222-2-2-2-2-200000000000000000000000022-2-222-2-200000000200-20000000000000000
χ3622-2-22222-2222-2-2-2-2-2-2222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-2000022222-2-2-2-2-2000000000000000000000000-2-222-2-22200000000-20020000000000000000
χ3722-2-2222-1-222-1-2-2-2-2112-1-1-1-1-12-1-1-1-12200-2-21-2-2111111113−3−332-1-1-1-1-211110000003−33−333−3−300−33−33−3−33322-2-2-1-11100000000-1001000000003−3−330000
χ3822-2-2222-1-222-1-2-2-2-2112-1-1-1-1-12-1-1-1-12200-2-21-2-2111111113−3−332-1-1-1-1-211110000003−33−333−3−300−33−33−3−333-2-22211-1-100000000100-100000000−333−30000
χ3922-2-2222-1-222-1-2-2-2-2112-1-1-1-1-12-1-1-1-12200-2-21-2-211111111−333−32-1-1-1-1-21111000000−33−33−3−333003−33−333−3−322-2-2-1-11100000000-100100000000−333−30000
χ4022-2-2222-1-222-1-2-2-2-2112-1-1-1-1-12-1-1-1-12200-2-21-2-211111111−333−32-1-1-1-1-21111000000−33−33−3−333003−33−333−3−3-2-22211-1-100000000100-1000000003−3−330000
χ4122-2-2-222-1222-1-2-2-2-2112-1-1-1-112-1-1-1-1-2-22i−2i22-1-2-211111111−i−iii-211112-1-1-1-12i2i−2i−2i2i2i−i−i−i−i−i−i−i−i−2i−2iiiiiiiii2-22-2-1-1110000000012i−2i-100000000−i−iii0000
χ4222-2-2-222-1222-1-2-2-2-2112-1-1-1-112-1-1-1-1-2-22i−2i22-1-2-211111111−i−iii-211112-1-1-1-12i2i−2i−2i2i2i−i−i−i−i−i−i−i−i−2i−2iiiiiiiii-22-2211-1-100000000-1−2i2i100000000ii−i−i0000
χ4322-2-2-222-1222-1-2-2-2-2112-1-1-1-112-1-1-1-1-2-2−2i2i22-1-2-211111111ii−i−i-211112-1-1-1-1−2i−2i2i2i−2i−2iiiiiiiii2i2i−i−i−i−i−i−i−i−i2-22-2-1-111000000001−2i2i-100000000ii−i−i0000
χ4422-2-2-222-1222-1-2-2-2-2112-1-1-1-112-1-1-1-1-2-2−2i2i22-1-2-211111111ii−i−i-211112-1-1-1-1−2i−2i2i2i−2i−2iiiiiiiii2i2i−i−i−i−i−i−i−i−i-22-2211-1-100000000-12i−2i100000000−i−iii0000
χ4522-2-2-22-1222-12-2-211-2-2-12-1-1-1-2-12-1-1-1-212i−2i2-1211-2-21111112i2i−2i−2i1-2111-12-1-1-12i−i−2ii−i−i2i2i−i−i−i−i−i−iii−2i−2iiiiiii00000000020-200−2i2i00000000ii−i−i00000-101
χ4622-2-2-22-1222-12-2-211-2-2-12-1-1-1-2-12-1-1-1-212i−2i2-1211-2-21111112i2i−2i−2i1-2111-12-1-1-12i−i−2ii−i−i2i2i−i−i−i−i−i−iii−2i−2iiiiiii000000000-202002i−2i00000000−i−iii0000010-1
χ4722-2-2-22-1222-12-2-211-2-2-12-1-1-1-2-12-1-1-1-21−2i2i2-1211-2-2111111−2i−2i2i2i1-2111-12-1-1-1−2ii2i−iii−2i−2iiiiiii−i−i2i2i−i−i−i−i−i−i00000000020-2002i−2i00000000−i−iii00000-101
χ4822-2-2-22-1222-12-2-211-2-2-12-1-1-1-2-12-1-1-1-21−2i2i2-1211-2-2111111−2i−2i2i2i1-2111-12-1-1-1−2ii2i−iii−2i−2iiiiiii−i−i2i2i−i−i−i−i−i−i000000000-20200−2i2i00000000ii−i−i0000010-1
χ4922-2-2-2-1222-12211-2-2-2-2-1-12-1-1-2-1-12-1-11-22i−2i-1221111-2-211112i2i−2i−2i11-211-1-12-1-1−i2ii−2i−i−i−i−i2i2i−i−i−i−iiiii−2i−2iiiii0000000020-202i−2i000000−i−iii00000000-1010
χ5022-2-2-2-1222-12211-2-2-2-2-1-12-1-1-2-1-12-1-11-22i−2i-1221111-2-211112i2i−2i−2i11-211-1-12-1-1−i2ii−2i−i−i−i−i2i2i−i−i−i−iiiii−2i−2iiiii00000000-2020−2i2i000000ii−i−i0000000010-10
χ5122-2-2-2-1222-12211-2-2-2-2-1-12-1-1-2-1-12-1-11-2−2i2i-1221111-2-21111−2i−2i2i2i11-211-1-12-1-1i−2i−i2iiiii−2i−2iiiii−i−i−i−i2i2i−i−i−i−i0000000020-20−2i2i000000ii−i−i00000000-1010
χ5222-2-2-2-1222-12211-2-2-2-2-1-12-1-1-2-1-12-1-11-2−2i2i-1221111-2-21111−2i−2i2i2i11-211-1-12-1-1i−2i−i2iiiii−2i−2iiiii−i−i−i−i2i2i−i−i−i−i00000000-20202i−2i000000−i−iii0000000010-10
χ53444444-2-244-2-244-2-2-2-2-2-2111-2-2-21114-2444-2-2-2-2-2-2111111-2-2-2-2-2-2111-2-21114-24-2-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000000000
χ54444444-2-244-2-244-2-2-2-2-2-2111-2-2-21114-2-4-44-2-2-2-2-2-21111112222-2-2111-2-2111-42-422222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000000000000000
χ5544444-24-24-24-2-2-244-2-2-21-211-2-21-211-2444-24-2-2-211-2-21111-2-2-2-2-21-211-21-211-24-24-2-211-2-21111-2-211-2-21111000000000000000000000000000000000000
χ5644444-24-24-24-2-2-244-2-2-21-211-2-21-211-24-4-4-24-2-2-211-2-211112222-21-211-21-2112-42-422-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000000000000000000000
χ5744444-2-244-2-24-2-2-2-2441-2-21141-2-211-2-244-2-2411-2-2-2-2111144441-2-2111-2-211-2-2-2-211-2-2-2-2111111-2-2-2-21111000000000000000000000000000000000000
χ5844444-2-244-2-24-2-2-2-2441-2-21141-2-211-2-2-4-4-2-2411-2-2-2-21111-4-4-4-41-2-2111-2-2112222-1-12222-1-1-1-1-1-12222-1-1-1-1000000000000000000000000000000000000
χ5944444-2-2-24-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32-2111−1−3i32−1+3i32-2-244-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2-2-2-2111−1−3i32−1+3i32111−1−3i32−1+3i32-2-2-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000000000000000
χ6044444-2-2-24-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32-2111−1−3i32−1+3i32-2-2-4-4-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i322222111−1−3i32−1+3i32111−1−3i32−1+3i322222-1-1-1-1-1-11+3i321−3i321+3i321−3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000000000000
χ6144444-2-2-24-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32-2111−1+3i32−1−3i32-2-244-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-2-2-2111−1+3i32−1−3i32111−1+3i32−1−3i32-2-2-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000000000000000
χ6244444-2-2-24-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32-2111−1+3i32−1−3i32-2-2-4-4-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i322222111−1+3i32−1−3i32111−1+3i32−1−3i322222-1-1-1-1-1-11−3i321+3i321−3i321+3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000000000000000000
χ634444-44-24-44-2444-2-244-24-2-2-2-4-24-2-2-2-4200-42-4-2-244-2-2-2-2-2-200002-42222-4222000000000000000000000000000000000000000000000000000000000000
χ644444-44-2-2-44-2-244-2-2-2-2-2-21112-2-2111-4200-422-2-2-2-2111111−2i32i3−2i32i322-1-1-122-1-1-1000000−2i32i3i3−i3i3i3−i3−i300−2i32i3i3−i3i3i3−i3−i3000000000000000000000000000000000000
χ654444-44-2-2-44-2-244-2-2-2-2-2-21112-2-2111-4200-422-2-2-2-21111112i3−2i32i3−2i322-1-1-122-1-1-10000002i3−2i3−i3i3−i3−i3i3i3002i3−2i3−i3i3−i3−i3i3i3000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.