Finite Group Databasebeta

← Group #13155733

Character table — Group #13155733

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222224444444444444444444444666688888888888812121212121212121212121212121212121212121818181824242424242424242424242424242424272727273636363636363636545472727272
order1244233346661212121212123336666666612121212121212121212128888366666121212121212248824242424242424242424242424242424444466661212121224242424242424248888248812121212886122424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111
χ911-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-11-1-1-1-11111-1-111-1-11-1-1-1-111111-1-11-1i−i11111111-1-1-1-1-1-1-1-1ii−i−i1111-1-1-1-1i−ii−iii−i−iii−i−i1-1i−iii−i−ii−i1-1i−i
χ1011-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-11-1-1-1-11111-1-111-1-11-1-1-1-111111-1-11-1−ii11111111-1-1-1-1-1-1-1-1−i−iii1111-1-1-1-1−ii−ii−i−iii−i−iii1-1−ii−i−iii−ii1-1−ii
χ1111-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-11-1-1-1-11111-1-111-1-11-1-1-1-111111-1-1-11i−i11111111-1-1-1-1-1-1-1-1−i−iii-1-1-1-11111i−ii−iii−i−i−i−iii-11i−i−i−iii−ii-11i−i
χ1211-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-11-1-1-1-11111-1-111-1-11-1-1-1-111111-1-1-11−ii11111111-1-1-1-1-1-1-1-1ii−i−i-1-1-1-11111−ii−ii−i−iiiii−i−i-11−iiii−i−ii−i-11−ii
χ1311-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-11-1-1-1-11111-1-1-1-1111-1-1-1-111111-1-11-1i−i-1-1-1-1-1-1-1-111111111ii−i−i1111-1-1-1-1i−ii−iii−i−i−i−iii-11−iiii−i−i−ii-11−ii
χ1411-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-11-1-1-1-11111-1-1-1-1111-1-1-1-111111-1-11-1−ii-1-1-1-1-1-1-1-111111111−i−iii1111-1-1-1-1−ii−ii−i−iiiii−i−i-11i−i−i−iiii−i-11i−i
χ1511-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-11-1-1-1-11111-1-1-1-1111-1-1-1-111111-1-1-11i−i-1-1-1-1-1-1-1-111111111−i−iii-1-1-1-11111i−ii−iii−i−iii−i−i1-1−ii−i−iiii−i1-1−ii
χ1611-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-11-1-1-1-11111-1-1-1-1111-1-1-1-111111-1-1-11−ii-1-1-1-1-1-1-1-111111111ii−i−i-1-1-1-11111−ii−ii−i−iii−i−iii1-1i−iii−i−i−ii1-1i−i
χ172222222-1222-1-1-122222-1-12-1-1-12-1-122-1-1-1-12-1-1-1222222-12-1-1-1-12-1-1-1-1-1220022-1-1-1-1-1-122-1-1-1-1-1-100002-1-1-12-1-1-10000000000002200000000-1-100
χ182222222-1222-1-1-122222-1-12-1-1-12-1-122-1-1-1-12-1-1-1222222-12-1-1-1-12-1-1-1-1-1-2-20022-1-1-1-1-1-122-1-1-1-1-1-10000-2111-2111000000000000-2-2000000001100
χ192222222-1222-1-1-122222-1-12-1-1-12-1-122-1-1-1-12-1-1-122-2-2-2-2-12-1-1-1-12-1-1-1-1-12200-2-2111111-2-211111100002-1-1-12-1-1-1000000000000-2-2000000001100
χ202222222-1222-1-1-122222-1-12-1-1-12-1-122-1-1-1-12-1-1-122-2-2-2-2-12-1-1-1-12-1-1-1-1-1-2-200-2-2111111-2-21111110000-2111-21110000000000002200000000-1-100
χ21222222-1222-1222-1-122-12-12222-12-1-1-122-1-12222-1-10000-1-1-1-1-1-1-1-1-1-1-1-1222200000000000000002222-12-1-1-12-1-1-1-122-1-1-1-100000000-1-1-1-1000000
χ22222222-1222-1222-1-122-12-12222-12-1-1-122-1-12222-1-10000-1-1-1-1-1-1-1-1-1-1-1-122-2-20000000000000000-2-2-2-2-12-1-1-12-1-111-2-21111000000001111000000
χ23222222-1222-1222-1-122-12-12222-12-1-1-122-1-12222-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-2-2220000000000000000-2-2-2-21-2111-211-1-122-1-1-1-1000000001111000000
χ24222222-1222-1222-1-122-12-12222-12-1-1-122-1-12222-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000000000000022221-2111-21111-2-2111100000000-1-1-1-1000000
χ2522222-1222-1222222-1-1-1-12-12-1-1-1-1222-1-122-12-1-1-1-12222-1-12-1-1-1-12-1-1-1-10022-1-122-1-1-1-1-1-122-1-1-1-100000000000022-1-1-1-1-1-10000002200000000-1-1
χ2622222-1222-1222222-1-1-1-12-12-1-1-1-1222-1-122-12-1-1-1-12222-1-12-1-1-1-12-1-1-1-100-2-2-1-122-1-1-1-1-1-122-1-1-1-1000000000000-2-2111111000000-2-20000000011
χ2722222-1222-1222222-1-1-1-12-12-1-1-1-1222-1-122-12-1-1-1-1-2-2-2-2-1-12-1-1-1-12-1-1-1-1002211-2-2111111-2-2111100000000000022-1-1-1-1-1-1000000-2-20000000011
χ2822222-1222-1222222-1-1-1-12-12-1-1-1-1222-1-122-12-1-1-1-1-2-2-2-2-1-12-1-1-1-12-1-1-1-100-2-211-2-2111111-2-21111000000000000-2-21111110000002200000000-1-1
χ292222-2222-2222222222222-2-2-2-2222-2-22222-2-2-2-22200002-2-2-2-22-2-2-2-2220000000000000000000000000000000000000000222200000000-2-20000
χ302222-2222-2222222222222-2-2-2-2222-2-22222-2-2-2-22200002-2-2-2-22-2-2-2-2220000000000000000000000000000000000000000-2-2-2-200000000220000
χ3122-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-20000222222-2-2-2-2-2-200000000000000000000000000000000000000002i2i−2i−2i00000000−2i2i0000
χ3222-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-20000222222-2-2-2-2-2-20000000000000000000000000000000000000000−2i−2i2i2i000000002i−2i0000
χ3322-2-2-222-1222-111-2-2-2-22-1-1-21112-1-1-2211112-1-1-1-2-222-2-2-1-2111-12-1-1-1112-20022-1-1-1-1-1-1-2-211111100002-1-1-1-21110000000000002-200000000-1100
χ3422-2-2-222-1222-111-2-2-2-22-1-1-21112-1-1-2211112-1-1-1-2-222-2-2-1-2111-12-1-1-111-220022-1-1-1-1-1-1-2-21111110000-21112-1-1-1000000000000-22000000001-100
χ3522-2-2-222-1222-111-2-2-2-22-1-1-21112-1-1-2211112-1-1-1-2-2-2-222-1-2111-12-1-1-1112-200-2-211111122-1-1-1-1-1-100002-1-1-1-2111000000000000-22000000001-100
χ3622-2-2-222-1222-111-2-2-2-22-1-1-21112-1-1-2211112-1-1-1-2-2-2-222-1-2111-12-1-1-111-2200-2-211111122-1-1-1-1-1-10000-21112-1-1-10000000000002-200000000-1100
χ3722-2-2-22-1222-12-2-211-2-2-12-1-2-2-2-2-12-11-1-2-2112222110000-11111-1-1-1-1-1112-22i−2i00000000000000002i2i−2i−2i-12-1-11-211−ii2i−2i−i−iii00000000−i−iii000000
χ3822-2-2-22-1222-12-2-211-2-2-12-1-2-2-2-2-12-11-1-2-2112222110000-11111-1-1-1-1-1112-2−2i2i0000000000000000−2i−2i2i2i-12-1-11-211i−i−2i2iii−i−i00000000ii−i−i000000
χ3922-2-2-22-1222-12-2-211-2-2-12-1-2-2-2-2-12-11-1-2-2112222110000-11111-1-1-1-1-111-222i−2i0000000000000000−2i−2i2i2i1-211-12-1-1−ii2i−2i−i−iii00000000ii−i−i000000
χ4022-2-2-22-1222-12-2-211-2-2-12-1-2-2-2-2-12-11-1-2-2112222110000-11111-1-1-1-1-111-22−2i2i00000000000000002i2i−2i−2i1-211-12-1-1i−i−2i2iii−i−i00000000−i−iii000000
χ4122-2-2-2-1222-122-2-2-2-211-1-121-211-1-12-2211-2-2-12-1-11122-2-2-11-211-1-12-1-111002i−2i-1-122-1-1-1-111-2-211110000000000002i−2i−ii−i−iii0000002i−2i00000000−ii
χ4222-2-2-2-1222-122-2-2-2-211-1-121-211-1-12-2211-2-2-12-1-11122-2-2-11-211-1-12-1-11100−2i2i-1-122-1-1-1-111-2-21111000000000000−2i2ii−iii−i−i000000−2i2i00000000i−i
χ4322-2-2-2-1222-122-2-2-2-211-1-121-211-1-12-2211-2-2-12-1-111-2-222-11-211-1-12-1-111002i−2i11-2-21111-1-122-1-1-1-10000000000002i−2i−ii−i−iii000000−2i2i00000000i−i
χ4422-2-2-2-1222-122-2-2-2-211-1-121-211-1-12-2211-2-2-12-1-111-2-222-11-211-1-12-1-11100−2i2i11-2-21111-1-122-1-1-1-1000000000000−2i2ii−iii−i−i0000002i−2i00000000−ii
χ452-22i−2i02220-2-2-22i−2i2i−2i2i−2i2220000-2-2-2002i−2i2i−2i00002i−2i2−2i2−i220000-200002i−2i00002−22−222−2−2i2−i2i2−i2i2i2−i2−i21+i−1−i1−i−1+i00000000000000002ζ−2ζ2ζ3−2ζ300001+i−1−i1−i−1+i000000
χ462-22i−2i02220-2-2-22i−2i2i−2i2i−2i2220000-2-2-2002i−2i2i−2i00002i−2i2−2i2−i220000-200002i−2i00002−22−222−2−2i2−i2i2−i2i2i2−i2−i2−1−i1+i−1+i1−i0000000000000000−2ζ2ζ−2ζ32ζ30000−1−i1+i−1+i1−i000000
χ472-22i−2i02220-2-2-22i−2i2i−2i2i−2i2220000-2-2-2002i−2i2i−2i00002i−2i−22−i2i220000-200002i−2i0000−22−22−2−222−i2i2−i2i2−i2−i2i2i21+i−1−i1−i−1+i0000000000000000−2ζ2ζ−2ζ32ζ300001+i−1−i1−i−1+i000000
χ482-22i−2i02220-2-2-22i−2i2i−2i2i−2i2220000-2-2-2002i−2i2i−2i00002i−2i−22−i2i220000-200002i−2i0000−22−22−2−222−i2i2−i2i2−i2−i2i2i2−1−i1+i−1+i1−i00000000000000002ζ−2ζ2ζ3−2ζ30000−1−i1+i−1+i1−i000000
χ492-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i2220000-2-2-200−2i2i−2i2i0000−2i2i2−2−i2i220000-20000−2i2i00002−22−222−2−2−i2i2−i2i2−i2−i2i2i21−i−1+i1+i−1−i0000000000000000−2ζ32ζ3−2ζ2ζ00001−i−1+i1+i−1−i000000
χ502-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i2220000-2-2-200−2i2i−2i2i0000−2i2i2−2−i2i220000-20000−2i2i00002−22−222−2−2−i2i2−i2i2−i2−i2i2i2−1+i1−i−1−i1+i00000000000000002ζ3−2ζ32ζ−2ζ0000−1+i1−i−1−i1+i000000
χ512-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i2220000-2-2-200−2i2i−2i2i0000−2i2i−22i2−i220000-20000−2i2i0000−22−22−2−222i2−i2i2−i2i2i2−i2−i21−i−1+i1+i−1−i00000000000000002ζ3−2ζ32ζ−2ζ00001−i−1+i1+i−1−i000000
χ522-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i2220000-2-2-200−2i2i−2i2i0000−2i2i−22i2−i220000-20000−2i2i0000−22−22−2−222i2−i2i2−i2i2i2−i2−i2−1+i1−i−1−i1+i0000000000000000−2ζ32ζ3−2ζ2ζ0000−1+i1−i−1−i1+i000000
χ53444444-2-244-2-2-2-2-2-244-2-214-2-2-2-2-21-2-2-2-2114-2-2-2-2-200001-21111-211111440000000000000000000000-2-211-2-21100000000000000000000000000
χ54444444-2-244-2-2-2-2-2-244-2-214-2-2-2-2-21-2-2-2-2114-2-2-2-2-200001-21111-211111-4-4000000000000000000000022-1-122-1-100000000000000000000000000
χ5544444-24-24-24-2-2-244-2-2-21-2-2-211-21-24411-2-2-2-211-2-244441-2-2111-2-211110000-2-2-2-21111-2-2-2-2111100000000000000000000000000000000000000
χ5644444-24-24-24-2-2-244-2-2-21-2-2-211-21-24411-2-2-2-211-2-2-4-4-4-41-2-2111-2-2111100002222-1-1-1-12222-1-1-1-100000000000000000000000000000000000000
χ5744444-2-244-2-2444-2-2-2-21-2-2-24-2-21-2-2-2-2-2-2-2-2-24-2-211000011-21111-2111100440000000000000000000000000000-2-2-2-21111000000000000000000
χ5844444-2-244-2-2444-2-2-2-21-2-2-24-2-21-2-2-2-2-2-2-2-2-24-2-211000011-21111-2111100-4-400000000000000000000000000002222-1-1-1-1000000000000000000
χ594444-444-2-444-2-2-244444-2-2-42224-2-2-4-4-2-2-2-2-4222440000-2-4222-2-4222-2-20000000000000000000000000000000000000000000000000000000000
χ604444-44-24-44-2444-2-244-24-2-4-4-4-4-24-22244-2-2-4-4-4-4-2-20000-22222-22222-2-20000000000000000000000000000000000000000000000000000000000
χ614444-44-2-2-44-2-2-2-2-2-244-2-21-4222-2-2122-2-211-4222-2-2000012-1-1-112-1-1-111000000000000000000000000003-3003-300000000000000000000000000
χ624444-44-2-2-44-2-2-2-2-2-244-2-21-4222-2-2122-2-211-4222-2-2000012-1-1-112-1-1-11100000000000000000000000000-3300-3300000000000000000000000000
χ634444-4-244-4-2444444-2-2-2-242-422-2-24-4-4-2-2442-422-2-20000-22-422-22-422-2-20000000000000000000000000000000000000000000000000000000000
χ644444-4-24-2-4-24-2-2-244-2-2-21-222-1-1-21-2-4-411-2-222-1-1-2-20000122-1-1122-1-111000000003i−3i3i−3i00003i−3i3i−3i00000000000000000000000000000000000000
χ654444-4-24-2-4-24-2-2-244-2-2-21-222-1-1-21-2-4-411-2-222-1-1-2-20000122-1-1122-1-11100000000−3i3i−3i3i0000−3i3i−3i3i00000000000000000000000000000000000000
χ664444-4-2-24-4-2-2444-2-2-2-21-2-22-4221-2-222-2-2-2-22-4221100001-12-1-11-12-1-1110000000000000000000000000000000000003-33-3000000000000000000
χ674444-4-2-24-4-2-2444-2-2-2-21-2-22-4221-2-222-2-2-2-22-4221100001-12-1-11-12-1-111000000000000000000000000000000000000-33-33000000000000000000
χ6844-4-4444-2-444-222-4-4-4-44-2-24-2-2-24-2-24-42222-4222-4-40000-24-2-2-2-2-4222220000000000000000000000000000000000000000000000000000000000
χ6944-4-444-24-44-24-4-422-4-4-24-24444-24-2-22-4-422-4-4-4-4220000-2-2-2-2-2-22222220000000000000000000000000000000000000000000000000000000000
χ7044-4-444-2-2-44-2-22222-4-4-2-214-2-2-2-2-21-2222-1-1-42222200001-211112-1-1-1-1-1000000000000000000000000003-300-3300000000000000000000000000
χ7144-4-444-2-2-44-2-22222-4-4-2-214-2-2-2-2-21-2222-1-1-42222200001-211112-1-1-1-1-100000000000000000000000000-33003-300000000000000000000000000
χ7244-4-44-244-4-244-4-4-4-422-2-24-24-2-2-2-244-422-4-42-422220000-2-24-2-2-22-422220000000000000000000000000000000000000000000000000000000000
χ7344-4-44-24-2-4-24-222-4-422-21-2-2-211-21-24-4-1-12222-1-12200001-2-211122-1-1-1-1000000003i−3i3i−3i0000−3i3i−3i3i00000000000000000000000000000000000000
χ7444-4-44-24-2-4-24-222-4-422-21-2-2-211-21-24-4-1-12222-1-12200001-2-211122-1-1-1-100000000−3i3i−3i3i00003i−3i3i−3i00000000000000000000000000000000000000
χ7544-4-44-2-24-4-2-24-4-422221-2-2-24-2-21-2-2-2222222-422-1-1000011-2111-12-1-1-1-10000000000000000000000000000000000003i−3i−3i3i000000000000000000
χ7644-4-44-2-24-4-2-24-4-422221-2-2-24-2-21-2-2-2222222-422-1-1000011-2111-12-1-1-1-1000000000000000000000000000000000000−3i3i3i−3i000000000000000000
χ7744-4-4-44-2-244-2-22222-4-4-2-21-4222-2-212-222-1-14-2-2-222000012-1-1-11-2111-1-14-40000000000000000000000-2-21122-1-100000000000000000000000000
χ7844-4-4-44-2-244-2-22222-4-4-2-21-4222-2-212-222-1-14-2-2-222000012-1-1-11-2111-1-1-44000000000000000000000022-1-1-2-21100000000000000000000000000
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χ8044-4-4-4-24-24-24-222-4-422-21-222-1-1-21-2-44-1-122-2-21122-4-444122-1-11-2-211-1-100002222-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000
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χ1108-88i−8i0-4-4-40444−4i4i−4i4i−4i4i22200-66-2-2-2002i−2i2i−2i00−6i6i2i−2i0000-1003-31003i−3i−ii0000000000000000000000000000000000000000000000000000000000
χ1118-8−8i8i08-4-40-8444i−4i4i−4i−8i8i-4-42000044-2004i−4i−2i2i00004i−4i000020000-20000−2i2i0000000000000000000000000000000000000000000000000000000000
χ1128-8−8i8i0-4-48044-8−8i8i4i−4i4i−4i2-4-40000-244004i−4i4i−4i0000−2i2i000020000-20000−2i2i0000000000000000000000000000000000000000000000000000000000
χ1138-8−8i8i0-4-4-404444i−4i4i−4i4i−4i222006-6-2-2-200−2i2i−2i2i00−6i6i−2i2i0000-100-331003i−3ii−i0000000000000000000000000000000000000000000000000000000000
χ1148-8−8i8i0-4-4-404444i−4i4i−4i4i−4i22200-66-2-2-200−2i2i−2i2i006i−6i−2i2i0000-1003-3100−3i3ii−i0000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.