Finite Group Databasebeta

← Group #13155657

Character table — Group #13155657

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222224444444444444444444444666688888888888812121212121212121212121212121212121212121818181824242424242424242424242424242424272727273636363636363636545472727272
order1222333446666666663336666666661212121212121212121288883666121212121212121244442424242424242424242424242424242488881212121212121212121212121212121244444444242424244412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ311111111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1
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
χ61111111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-111-1-1-1-11111-1-1
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-111
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
χ911-1-11111-1-1-1-1-11-11-11111-1-1-1-1-111-11-11-1-1-11111-111-1-11-1-111-11-111-1-11-1i−i11111111-1-1-1-1-1-1-1-1ii−i−ii−i1-1i−i1-1ii−i−i11-1-1ii−i−i1-1i−iii−i−ii−ii−i1-1
χ1011-1-11111-1-1-1-1-11-11-11111-1-1-1-1-111-11-11-1-1-11111-111-1-11-1-111-11-111-1-11-1−ii11111111-1-1-1-1-1-1-1-1−i−iii−ii1-1−ii1-1−i−iii11-1-1−i−iii1-1−ii−i−iii−ii−ii1-1
χ1111-1-11111-1-1-1-1-11-11-11111-1-1-1-1-111-11-11-1-1-11111-111-1-11-1-111-11-111-1-1-11i−i11111111-1-1-1-1-1-1-1-1−i−iiii−i-11i−i-11ii−i−i-1-111−i−iii-11i−i−i−iii−iii−i-11
χ1211-1-11111-1-1-1-1-11-11-11111-1-1-1-1-111-11-11-1-1-11111-111-1-11-1-111-11-111-1-1-11−ii11111111-1-1-1-1-1-1-1-1ii−i−i−ii-11−ii-11−i−iii-1-111ii−i−i-11−iiii−i−ii−i−ii-11
χ1311-1-11111-1-1-1-1-11-11-11111-1-1-1-1-111-11-11-1-1-11111-1-1-1111-1-111-11-111-1-11-1i−i-1-1-1-1-1-1-1-111111111ii−i−ii−i1-1i−i1-1ii−i−i11-1-1−i−iii-11−iiii−i−i−ii−ii-11
χ1411-1-11111-1-1-1-1-11-11-11111-1-1-1-1-111-11-11-1-1-11111-1-1-1111-1-111-11-111-1-11-1−ii-1-1-1-1-1-1-1-111111111−i−iii−ii1-1−ii1-1−i−iii11-1-1ii−i−i-11i−i−i−iiii−ii−i-11
χ1511-1-11111-1-1-1-1-11-11-11111-1-1-1-1-111-11-11-1-1-11111-1-1-1111-1-111-11-111-1-1-11i−i-1-1-1-1-1-1-1-111111111−i−iiii−i-11i−i-11ii−i−i-1-111ii−i−i1-1−ii−i−iiii−i−ii1-1
χ1611-1-11111-1-1-1-1-11-11-11111-1-1-1-1-111-11-11-1-1-11111-1-1-1111-1-111-11-111-1-1-11−ii-1-1-1-1-1-1-1-111111111ii−i−i−ii-11−ii-11−i−iii-1-111−i−iii1-1i−iii−i−i−iii−i1-1
χ172222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-200002222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000222200000000-2-20000
χ182222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-200002222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-2-2-200000000220000
χ19222222-122222-12-1-1222-1-122-1-1-12-1-1-12-12222222-10000-1-1-1-1-1-1-1-1-1-1-1-1222200000000000000002222-1-1-1-12222-1-1-1-1-1-1-1-100000000-1-1-1-1000000
χ20222222-122222-12-1-1222-1-122-1-1-12-1-1-12-12222222-10000-1-1-1-1-1-1-1-1-1-1-1-122-2-20000000000000000-2-2-2-211-1-1-2-2221111-1-1-1-1000000001111000000
χ21222222-122222-12-1-1222-1-122-1-1-12-1-1-12-12222222-10000-1-1-1-1-1-1-1-1-1-1-1-1-2-2220000000000000000-2-2-2-2-1-11122-2-2-1-1-1-11111000000001111000000
χ22222222-122222-12-1-1222-1-122-1-1-12-1-1-12-12222222-10000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000000000000022221111-2-2-2-21111111100000000-1-1-1-1000000
χ2322222-122222-12-122-12-12-1-1-122-1-1-1-12-122-1-1-12-1-122222-1-1-1-1-1-122-1-1-1-1002222-1-1-1-1-1-122-1-1-1-1-1-100002200-1-100-1-1-1-1000000000022000000-1-100
χ2422222-122222-12-122-12-12-1-1-122-1-1-1-12-122-1-1-12-1-122222-1-1-1-1-1-122-1-1-1-100-2-222-1-1-1-1-1-122-1-1-1-1-1-10000-2-200110011110000000000-2-20000001100
χ2522222-122222-12-122-12-12-1-1-122-1-1-1-12-122-1-1-12-1-12-2-2-2-2-1-1-1-1-1-122-1-1-1-10022-2-2111111-2-211111100002200-1-100-1-1-1-10000000000-2-20000001100
χ2622222-122222-12-122-12-12-1-1-122-1-1-1-12-122-1-1-12-1-12-2-2-2-2-1-1-1-1-1-122-1-1-1-100-2-2-2-2111111-2-21111110000-2-20011001111000000000022000000-1-100
χ272222-12222-1-1222222-1-1-12-1-1-1-12-122-122-1-1-12-1-1-122222-1-1-1-122-1-1-1-1-1-12200-1-122-1-1-1-1-1-122-1-1-1-10000002200-1-10000-1-1-1-10000220000000000-1-1
χ282222-12222-1-1222222-1-1-12-1-1-1-12-122-122-1-1-12-1-1-122222-1-1-1-122-1-1-1-1-1-1-2-200-1-122-1-1-1-1-1-122-1-1-1-1000000-2-20011000011110000-2-2000000000011
χ292222-12222-1-1222222-1-1-12-1-1-1-12-122-122-1-1-12-1-1-12-2-2-2-2-1-1-1-122-1-1-1-1-1-1220011-2-2111111-2-211110000002200-1-10000-1-1-1-10000-2-2000000000011
χ302222-12222-1-1222222-1-1-12-1-1-1-12-122-122-1-1-12-1-1-12-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-20011-2-2111111-2-21111000000-2-20011000011110000220000000000-1-1
χ3122-2-2222-22-2-2-2-22-22-22222-2-2-2-2-222-222-2222-2-2-2-2200002-2-22-22-22-2-22200000000000000000000000000000000000000002i2i−2i−2i00000000−2i2i0000
χ3222-2-2222-22-2-2-2-22-22-22222-2-2-2-2-222-222-2222-2-2-2-2200002-2-22-22-22-2-2220000000000000000000000000000000000000000−2i−2i2i2i000000002i−2i0000
χ3322-2-222-12-2-2-2-2121-1-222-1-1-2-21112-11-1-2-1-2-2-2222210000-111-1-11-11-1-1112-22i−2i00000000000000002i2i−2i−2i−ii-112i−2i2-2−i−iii-1-11100000000−i−iii000000
χ3422-2-222-12-2-2-2-2121-1-222-1-1-2-21112-11-1-2-1-2-2-2222210000-111-1-11-11-1-1112-2−2i2i0000000000000000−2i−2i2i2ii−i-11−2i2i2-2ii−i−i-1-11100000000ii−i−i000000
χ3522-2-222-12-2-2-2-2121-1-222-1-1-2-21112-11-1-2-1-2-2-2222210000-111-1-11-11-1-111-222i−2i0000000000000000−2i−2i2i2i−ii1-12i−2i-22−i−iii11-1-100000000ii−i−i000000
χ3622-2-222-12-2-2-2-2121-1-222-1-1-2-21112-11-1-2-1-2-2-2222210000-111-1-11-11-1-111-22−2i2i00000000000000002i2i−2i−2ii−i1-1−2i2i-22ii−i−i11-1-100000000−i−iii000000
χ3722-2-22-122-2-2-21-2-1-2212-12-111-2-21-1-11212-211-12-1-1-222-2-2-111-1-112-2-1-111002i−2i22-1-1-1-1-1-1-2-211111100002i−2i00−ii00−i−iii00000000002i−2i000000−ii00
χ3822-2-22-122-2-2-21-2-1-2212-12-111-2-21-1-11212-211-12-1-1-222-2-2-111-1-112-2-1-11100−2i2i22-1-1-1-1-1-1-2-21111110000−2i2i00i−i00ii−i−i0000000000−2i2i000000i−i00
χ3922-2-22-122-2-2-21-2-1-2212-12-111-2-21-1-11212-211-12-1-1-2-2-222-111-1-112-2-1-111002i−2i-2-211111122-1-1-1-1-1-100002i−2i00−ii00−i−iii0000000000−2i2i000000i−i00
χ4022-2-22-122-2-2-21-2-1-2212-12-111-2-21-1-11212-211-12-1-1-2-2-222-111-1-112-2-1-11100−2i2i-2-211111122-1-1-1-1-1-10000−2i2i00i−i00ii−i−i00000000002i−2i000000−ii00
χ4122-2-2-1222-211-2-22-22-2-1-1-121111-2-12-2-1-221112-1-1-1-222-2-2-111-12-2-11-1-1112-200-1-122-1-1-1-111-2-211110000002-200-110000-1-11100002-20000000000-11
χ4222-2-2-1222-211-2-22-22-2-1-1-121111-2-12-2-1-221112-1-1-1-222-2-2-111-12-2-11-1-111-2200-1-122-1-1-1-111-2-21111000000-22001-1000011-1-10000-2200000000001-1
χ4322-2-2-1222-211-2-22-22-2-1-1-121111-2-12-2-1-221112-1-1-1-2-2-222-111-12-2-11-1-1112-20011-2-21111-1-122-1-1-1-10000002-200-110000-1-1110000-2200000000001-1
χ4422-2-2-1222-211-2-22-22-2-1-1-121111-2-12-2-1-221112-1-1-1-2-2-222-111-12-2-11-1-111-220011-2-21111-1-122-1-1-1-1000000-22001-1000011-1-100002-20000000000-11
χ452-22-2222002-222-2-2-2-2-22222-22-22-2-2-2-200000000002−22−222-2-20000000000002−22−222−2−22−22−222−2−22−22−200000000000000002-22-200002−22−2000000
χ462-22-2222002-222-2-2-2-2-22222-22-22-2-2-2-200000000002−22−222-2-20000000000002−22−222−2−22−22−222−2−2−22−220000000000000000-22-220000−22−22000000
χ472-22-2222002-222-2-2-2-2-22222-22-22-2-2-2-20000000000−22−2222-2-2000000000000−22−22−2−222−22−22−2−2222−22−20000000000000000-22-2200002−22−2000000
χ482-22-2222002-222-2-2-2-2-22222-22-22-2-2-2-20000000000−22−2222-2-2000000000000−22−22−2−222−22−22−2−222−22−2200000000000000002-22-20000−22−22000000
χ492-2-2222200-22-2-2-22-22-2222-22-22-2-2-22-200000000002−2−222-22-20000000000002−22−222−2−2−22−22−2−222i2−i2−i2i200000000000000002i−2i−2i2i0000i2−i2−i2i2000000
χ502-2-2222200-22-2-2-22-22-2222-22-22-2-2-22-200000000002−2−222-22-20000000000002−22−222−2−2−22−22−2−222−i2i2i2−i20000000000000000−2i2i2i−2i0000−i2i2i2−i2000000
χ512-2-2222200-22-2-2-22-22-2222-22-22-2-2-22-20000000000−222−22-22-2000000000000−22−22−2−2222−22−222−2−2i2−i2−i2i20000000000000000−2i2i2i−2i0000i2−i2−i2i2000000
χ522-2-2222200-22-2-2-22-22-2222-22-22-2-2-22-20000000000−222−22-22-2000000000000−22−22−2−2222−22−222−2−2−i2i2i2−i200000000000000002i−2i−2i2i0000−i2i2i2−i2000000
χ53444444-2-4-4444-24-2-2444-2-244-2-2-24-2-2-2-42-4-4-4-4-4-4-420000-2-2-2-2222222220000000000000000000000000000000000000000000000000000000000
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χ864-44-44-24004-4-242-4-42-4-24-2-224-4-2222-40000000000−2222−2222-2-222000000000000−22222−222−2−2−22222−222−2−200000000000000000000000000000000000000
χ874-44-4-24400-2244-4-4-4-42-2-24-22-2242-4-42000000000022−2222−22-2-222000000000000−2222−22−2−222−2222−22−2−22200000000000000000000000000000000000000
χ884-44-4-24400-2244-4-4-4-42-2-24-22-2242-4-420000000000−2222−2222-2-2220000000000002−2−222222−2−22−2−222222−2−200000000000000000000000000000000000000
χ894-44-4-2-2400-22-242-4-4221-2-21-1-22-2-12220003i−3i003i−3i022−2222−2211-1-100003i−3i3i−3i0000−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ300000000000000000000000000000000000000
χ904-44-4-2-2400-22-242-4-4221-2-21-1-22-2-12220003i−3i003i−3i0−2222−222211-1-100003i−3i3i−3i00002−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ32−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ300000000000000000000000000000000000000
χ914-44-4-2-2400-22-242-4-4221-2-21-1-22-2-1222000−3i3i00−3i3i022−2222−2211-1-10000−3i3i−3i3i0000−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ300000000000000000000000000000000000000
χ924-44-4-2-2400-22-242-4-4221-2-21-1-22-2-1222000−3i3i00−3i3i0−2222−222211-1-10000−3i3i−3i3i00002−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ32−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ300000000000000000000000000000000000000
χ934-4-4444-200-44-42-4-224-44-2-2-442-22-42-2200000000000000-22-2200000000000000000000000000002i2−2i2−2i22i2000000000000000000000000−i2i2i2−i2000000
χ944-4-4444-200-44-42-4-224-44-2-2-442-22-42-2200000000000000-22-220000000000000000000000000000−2i22i22i2−2i2000000000000000000000000i2−i2−i2i2000000
χ954-4-444-2400-442-424-4-2-4-24-22-2-44222-2-4000000000022−22−2222-22-2200000000000022−22−22−2−222−22222−222−2−200000000000000000000000000000000000000
χ964-4-444-2400-442-424-4-2-4-24-22-2-44222-2-40000000000−222222−22-22-22000000000000−22222−222−2−222−22−22−2−22200000000000000000000000000000000000000
χ974-4-44-244002-2-4-4-44-442-2-242-22-2-42-442000000000022−22−2222-22-22000000000000−2222−22−2−2222−2−222222−2−200000000000000000000000000000000000000
χ984-4-44-244002-2-4-4-44-442-2-242-22-2-42-4420000000000−222222−22-22-220000000000002−2−222222−2−2−2222−22−2−22200000000000000000000000000000000000000
χ994-4-44-2-24002-22-424-4-221-2-2-112-22-12-220003i−3i00−3i3i022−22−22221-11-10000−3i3i3i−3i0000−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ32−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ300000000000000000000000000000000000000
χ1004-4-44-2-24002-22-424-4-221-2-2-112-22-12-220003i−3i00−3i3i0−222222−221-11-10000−3i3i3i−3i00002−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ300000000000000000000000000000000000000
χ1014-4-44-2-24002-22-424-4-221-2-2-112-22-12-22000−3i3i003i−3i022−22−22221-11-100003i−3i−3i3i0000−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ300000000000000000000000000000000000000
χ1024-4-44-2-24002-22-424-4-221-2-2-112-22-12-22000−3i3i003i−3i0−222222−221-11-100003i−3i−3i3i00002−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ300000000000000000000000000000000000000
χ1038888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-422-4-422-40000-1-1-1-12222-1-1-1-10000000000000000000000000000000000000000000000000000000000
χ1048888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444-2-244-2-240000-1-1-1-1-2-2-2-211110000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-48-84444-44-44-4222-2-2-2-2-222-224-44-2-2-4-42240000-111-12-22-2-1-1110000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-4-884444-44-44-4222-2-2-2-2-222-22-44-42244-2-2-40000-111-1-22-2211-1-10000000000000000000000000000000000000000000000000000000000
χ1078-88-88-4-4008-8-4-44444-8-4-42-44-4424-2-240000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-48-400-448-4-844-84-42-4-442-2-4444-20000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-400-44-4-4444442222-22-22-2-2-2-20006i−6i006i−6i00000-1-1110000−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-400-44-4-4444442222-22-22-2-2-2-2000−6i6i00−6i6i00000-1-11100003i−3i3i−3i0000000000000000000000000000000000000000000000000000000000
χ1118-8-888-4-400-88444-44-4-8-4-424-44-4-24-224000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-48-4004-4-84-8-4484-42-44-4-22444-4-2000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4004-4444-44-44222-22-22-2-2-22-20006i−6i00−6i6i00000-11-1100003i−3i−3i3i0000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4004-4444-44-44222-22-22-2-2-22-2000−6i6i006i−6i00000-11-110000−3i3i3i−3i0000000000000000000000000000000000000000000000000000000000

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