Finite Group Databasebeta

← Group #13155742

Character table — Group #13155742

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222224444444444444444444444666688888888888812121212121212121212121212121212121212121818181824242424242424242424242424242424272727273636363636363636545472727272
order1244233346661212121212123336666666612121212121212121212124444366666121212121212888812121212121212121212121212121212888824242424242424242424242424242424888822442424242488661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-11-11-1
χ311111111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-11-11-1-1-1-1-1-1-11-11
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
χ61111111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-11-11-1-1-1-111-11-11
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111111-11-1-1-1-1-1111-11-1
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
χ911-1-1-11111111-1-1-1-1-1-1111-1111-1-1-1-11111-1-1-1-1-1-11ii−i−i1-1-1-1-111111-1-1i−ii−iiiiiiiii−i−i−i−i−i−i−i−i11-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−i11-1-111-1-1i−i11-1-1
χ1011-1-1-11111111-1-1-1-1-1-1111-1111-1-1-1-11111-1-1-1-1-1-11ii−i−i1-1-1-1-111111-1-1i−i−iiiiiiiiii−i−i−i−i−i−i−i−i-1-111i−i−iii−i−iiii−i−i−i−iii−i−iii1-1-11-1-111−ii1-1-11
χ1111-1-1-11111111-1-1-1-1-1-1111-1111-1-1-1-11111-1-1-1-1-1-11ii−i−i1-1-1-1-111111-1-1−iii−iiiiiiiii−i−i−i−i−i−i−i−i-1-111−iii−i−iii−i−i−iiiii−i−i−i−iii-111-1-1-111−ii-111-1
χ1211-1-1-11111111-1-1-1-1-1-1111-1111-1-1-1-11111-1-1-1-1-1-11ii−i−i1-1-1-1-111111-1-1−ii−iiiiiiiiii−i−i−i−i−i−i−i−i11-1-1−ii−ii−ii−ii−i−iii−i−iiiii−i−i-1-11111-1-1i−i-1-111
χ1311-1-1-11111111-1-1-1-1-1-1111-1111-1-1-1-11111-1-1-1-1-1-11−i−iii1-1-1-1-111111-1-1i−ii−i−i−i−i−i−i−i−i−iiiiiiiii11-1-1i−ii−ii−ii−iii−i−iii−i−i−i−iii-1-11111-1-1−ii-1-111
χ1411-1-1-11111111-1-1-1-1-1-1111-1111-1-1-1-11111-1-1-1-1-1-11−i−iii1-1-1-1-111111-1-1i−i−ii−i−i−i−i−i−i−i−iiiiiiiii-1-111i−i−iii−i−iiii−i−i−i−iiiii−i−i-111-1-1-111i−i-111-1
χ1511-1-1-11111111-1-1-1-1-1-1111-1111-1-1-1-11111-1-1-1-1-1-11−i−iii1-1-1-1-111111-1-1−iii−i−i−i−i−i−i−i−i−iiiiiiiii-1-111−iii−i−iii−i−i−iiiii−i−iii−i−i1-1-11-1-111i−i1-1-11
χ1611-1-1-11111111-1-1-1-1-1-1111-1111-1-1-1-11111-1-1-1-1-1-11−i−iii1-1-1-1-111111-1-1−ii−ii−i−i−i−i−i−i−i−iiiiiiiii11-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii11-1-111-1-1−ii11-1-1
χ172222222-1222-122-1-1222-1-122-1-12-1-1-12-1-1-1-1-122-1-122222-12-1-1-1-12-1-1-1-1-1002222-1-1-1-1-1-122-1-1-1-1-1-1000000-1-100220000-1-1-1-1000002020000000-10-1
χ182222222-1222-122-1-1222-1-122-1-12-1-1-12-1-1-1-1-122-1-122222-12-1-1-1-12-1-1-1-1-100-2-222-1-1-1-1-1-122-1-1-1-1-1-10000001100-2-20000111100000-20-20000000101
χ192222222-1222-122-1-1222-1-122-1-12-1-1-12-1-1-1-1-122-1-12-2-2-2-2-12-1-1-1-12-1-1-1-1-10022-2-2111111-2-2111111000000-1-100220000-1-1-1-100000-20-20000000101
χ202222222-1222-122-1-1222-1-122-1-12-1-1-12-1-1-1-1-122-1-12-2-2-2-2-12-1-1-1-12-1-1-1-1-100-2-2-2-2111111-2-21111110000001100-2-200001111000002020000000-10-1
χ21222222-1222-12-1-12222-12-12-12-1-12-1-1-12-1-1-1-1-1-12222222-1-12-1-1-1-12-1-1-1-12200-1-122-1-1-1-1-1-122-1-1-1-10000-1-1002200-1-1-1-1000000002020000000-10-10
χ22222222-1222-12-1-12222-12-12-12-1-12-1-1-12-1-1-1-1-1-12222222-1-12-1-1-1-12-1-1-1-1-2-200-1-122-1-1-1-1-1-122-1-1-1-100001100-2-200111100000000-20-200000001010
χ23222222-1222-12-1-12222-12-12-12-1-12-1-1-12-1-1-1-1-1-1222-2-2-2-2-1-12-1-1-1-12-1-1-1-1220011-2-2111111-2-211110000-1-1002200-1-1-1-100000000-20-200000001010
χ24222222-1222-12-1-12222-12-12-12-1-12-1-1-12-1-1-1-1-1-1222-2-2-2-2-1-12-1-1-1-12-1-1-1-1-2-20011-2-2111111-2-2111100001100-2-2001111000000002020000000-10-10
χ2522222-1222-1222222-1-1-1-12-1-1-122222222222-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000022222222-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1000000
χ2622222-1222-1222222-1-1-1-12-1-1-122222222222-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-122-2-20000000000000000-2-2-2-222-2-2-1-111-1-1-1-11111000000001111000000
χ2722222-1222-1222222-1-1-1-12-1-1-122222222222-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-2-2220000000000000000-2-2-2-2-2-22211-1-11111-1-1-1-1000000001111000000
χ2822222-1222-1222222-1-1-1-12-1-1-122222222222-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000000000002222-2-2-2-211111111111100000000-1-1-1-1000000
χ292222-2222-2222222222222-2222-2-2-2-2-2-2-2-2222222-200002-2-2-2-22-2-2-2-2220000000000000000000000000000000000000000222200000000-2-20000
χ302222-2222-2222222222222-2222-2-2-2-2-2-2-2-2222222-200002-2-2-2-22-2-2-2-2220000000000000000000000000000000000000000-2-2-2-200000000220000
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
χ3322-2-2-222-1222-1-2-211-2-22-1-1-22-1-1-21112-1-1-111-2-21122i2i−2i−2i-1-2111-12-1-1-111002i−2i2i2i−i−i−i−i−i−i−2i−2iiiiiii000000−ii002i−2i0000−i−iii0000020-20000000-101
χ3422-2-2-222-1222-1-2-211-2-22-1-1-22-1-1-21112-1-1-111-2-21122i2i−2i−2i-1-2111-12-1-1-11100−2i2i2i2i−i−i−i−i−i−i−2i−2iiiiiii000000i−i00−2i2i0000ii−i−i00000-202000000010-1
χ3522-2-2-222-1222-1-2-211-2-22-1-1-22-1-1-21112-1-1-111-2-2112−2i−2i2i2i-1-2111-12-1-1-111002i−2i−2i−2iiiiiii2i2i−i−i−i−i−i−i000000−ii002i−2i0000−i−iii00000-202000000010-1
χ3622-2-2-222-1222-1-2-211-2-22-1-1-22-1-1-21112-1-1-111-2-2112−2i−2i2i2i-1-2111-12-1-1-11100−2i2i−2i−2iiiiiii2i2i−i−i−i−i−i−i000000i−i00−2i2i0000ii−i−i0000020-20000000-101
χ3722-2-2-22-1222-1211-2-2-2-2-12-1-2-12-11-211-12-1-11111-2-222i2i−2i−2i-11-211-1-12-1-1112i−2i00−i−i2i2i−i−i−i−iii−2i−2iiiii0000−ii002i−2i00−i−iii0000000020-20000000-1010
χ3822-2-2-22-1222-1211-2-2-2-2-12-1-2-12-11-211-12-1-11111-2-222i2i−2i−2i-11-211-1-12-1-111−2i2i00−i−i2i2i−i−i−i−iii−2i−2iiiii0000i−i00−2i2i00ii−i−i00000000-202000000010-10
χ3922-2-2-22-1222-1211-2-2-2-2-12-1-2-12-11-211-12-1-11111-2-22−2i−2i2i2i-11-211-1-12-1-1112i−2i00ii−2i−2iiiii−i−i2i2i−i−i−i−i0000−ii002i−2i00−i−iii00000000-202000000010-10
χ4022-2-2-22-1222-1211-2-2-2-2-12-1-2-12-11-211-12-1-11111-2-22−2i−2i2i2i-11-211-1-12-1-111−2i2i00ii−2i−2iiiii−i−i2i2i−i−i−i−i0000i−i00−2i2i00ii−i−i0000000020-20000000-1010
χ4122-2-2-2-1222-122-2-2-2-211-1-121-1-12-2-2-2-22222-2-21111-10000-11111-1-1-1-1-1112i−2i2i−2i000000000000000022-2-22i−2i2i−2i−ii−ii−i−iii−i−iii00000000-1-111000000
χ4222-2-2-2-1222-122-2-2-2-211-1-121-1-12-2-2-2-22222-2-21111-10000-11111-1-1-1-1-1112i−2i−2i2i0000000000000000-2-2222i−2i−2i2i−iii−i−i−iiiii−i−i0000000011-1-1000000
χ4322-2-2-2-1222-122-2-2-2-211-1-121-1-12-2-2-2-22222-2-21111-10000-11111-1-1-1-1-111−2i2i2i−2i0000000000000000-2-222−2i2i2i−2ii−i−iiii−i−i−i−iii0000000011-1-1000000
χ4422-2-2-2-1222-122-2-2-2-211-1-121-1-12-2-2-2-22222-2-21111-10000-11111-1-1-1-1-111−2i2i−2i2i000000000000000022-2-2−2i2i−2i2ii−ii−iii−i−iii−i−i00000000-1-111000000
χ452-22i−2i02220-2-2-22i−2i2i−2i2i−2i2220-2-2-2000000002i−2i2i−2i2i−2i01+i−1−i1−i−1+i20000-200002i−2i00001+i−1−i1+i−1−i1+i1+i−1−i−1−i1−i−1+i1−i−1+i1−i1−i−1+i−1+i2−2i2−i200000000000000002ζ−2ζ2ζ3−2ζ300002−2i2−i2000000
χ462-22i−2i02220-2-2-22i−2i2i−2i2i−2i2220-2-2-2000000002i−2i2i−2i2i−2i01+i−1−i1−i−1+i20000-200002i−2i00001+i−1−i1+i−1−i1+i1+i−1−i−1−i1−i−1+i1−i−1+i1−i1−i−1+i−1+i−22−i2i20000000000000000−2ζ2ζ−2ζ32ζ30000−22−i2i2000000
χ472-22i−2i02220-2-2-22i−2i2i−2i2i−2i2220-2-2-2000000002i−2i2i−2i2i−2i0−1−i1+i−1+i1−i20000-200002i−2i0000−1−i1+i−1−i1+i−1−i−1−i1+i1+i−1+i1−i−1+i1−i−1+i−1+i1−i1−i2−2i2−i20000000000000000−2ζ2ζ−2ζ32ζ300002−2i2−i2000000
χ482-22i−2i02220-2-2-22i−2i2i−2i2i−2i2220-2-2-2000000002i−2i2i−2i2i−2i0−1−i1+i−1+i1−i20000-200002i−2i0000−1−i1+i−1−i1+i−1−i−1−i1+i1+i−1+i1−i−1+i1−i−1+i−1+i1−i1−i−22−i2i200000000000000002ζ−2ζ2ζ3−2ζ30000−22−i2i2000000
χ492-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i2220-2-2-200000000−2i2i−2i2i−2i2i01−i−1+i1+i−1−i20000-20000−2i2i00001−i−1+i1−i−1+i1−i1−i−1+i−1+i1+i−1−i1+i−1−i1+i1+i−1−i−1−i2−2−i2i20000000000000000−2ζ32ζ3−2ζ2ζ00002−2−i2i2000000
χ502-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i2220-2-2-200000000−2i2i−2i2i−2i2i01−i−1+i1+i−1−i20000-20000−2i2i00001−i−1+i1−i−1+i1−i1−i−1+i−1+i1+i−1−i1+i−1−i1+i1+i−1−i−1−i−22i2−i200000000000000002ζ3−2ζ32ζ−2ζ0000−22i2−i2000000
χ512-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i2220-2-2-200000000−2i2i−2i2i−2i2i0−1+i1−i−1−i1+i20000-20000−2i2i0000−1+i1−i−1+i1−i−1+i−1+i1−i1−i−1−i1+i−1−i1+i−1−i−1−i1+i1+i2−2−i2i200000000000000002ζ3−2ζ32ζ−2ζ00002−2−i2i2000000
χ522-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i2220-2-2-200000000−2i2i−2i2i−2i2i0−1+i1−i−1−i1+i20000-20000−2i2i0000−1+i1−i−1+i1−i−1+i−1+i1−i1−i−1−i1+i−1−i1+i−1−i−1−i1+i1+i−22i2−i20000000000000000−2ζ32ζ3−2ζ2ζ0000−22i2−i2000000
χ53444444-2-244-2-2-2-2-2-244-2-214-2-21-2-211-2-21111-2-2-2-2444441-2-2111-2-211110000-2-2-2-21111-2-2-2-2111100000000000000000000000000000000000000
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χ5544444-24-24-24-244-2-2-2-2-21-2-2-21-24-2-2-24-2-2-2-2-2-2-211-200001-21111-21111100440000000000000000000000-2-200-2-200001111000000000000000000
χ5644444-24-24-24-244-2-2-2-2-21-2-2-21-24-2-2-24-2-2-2-2-2-2-211-200001-21111-21111100-4-400000000000000000000002200220000-1-1-1-1000000000000000000
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χ7344-4-44-24-2-4-24-2-4-42222-21-2-2-21-24-2-2-2-42222222-1-1200001-211112-1-1-1-1-10000000000000000000000000000000000003i−3i−3i3i000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.