Finite Group Databasebeta

← Group #13155729

Character table — Group #13155729

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222224444444444444444444444666688888888888812121212121212121212121212121212121212121818181824242424242424242424242424242424272727273636363636363636545472727272
order1244233346661212121212123336666666612121212121212121212124444366666121212121212224412121212121212121212121212121212888866666666121212121212121288888888242424248824242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-11-11111111111111111-1-1-1-11-11-111-1-11-11-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1
χ311111111111111111111111111111111111111111111111111111111-11-111111111111111111-1-1-1-1-11-11-1-111-11-11-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111
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
χ61111111111111111111111111111111111111111-1-1-1-11111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11-11-111-1-11111-1-111-1-1-1-111-1-111
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-11-11-1-111111111-1-1-1-1-1-11111-1-1
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
χ911-1-1-11111111-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-1-1-11ii−i−i1-1-1-1-111111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111111111-1-1-1-1-1-1-1-1ii−i−ii−ii−i11-1-1i−ii−ii−i
χ1011-1-1-11111111-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-1-1-11ii−i−i1-1-1-1-111111-1-11-1-11iiiiiiii−i−i−i−i−i−i−i−i-1-1111-11-111-1-1-11-11-1-111−i−iiii−i−ii-1-111−iii−i−ii
χ1111-1-1-11111111-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-1-1-11ii−i−i1-1-1-1-111111-1-1-111-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-11-11-1-1111-11-111-1-1−i−iii−iii−i-1-111−ii−iii−i
χ1211-1-1-11111111-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-1-1-11ii−i−i1-1-1-1-111111-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-1-1-1-1-1-1-111111111ii−i−i−ii−ii11-1-1i−i−ii−ii
χ1311-1-1-11111111-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-1-1-11−i−iii1-1-1-1-111111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111111111-1-1-1-1-1-1-1-1−i−iii−ii−ii11-1-1−ii−ii−ii
χ1411-1-1-11111111-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-1-1-11−i−iii1-1-1-1-111111-1-11-1-11−i−i−i−i−i−i−i−iiiiiiiii-1-1111-11-111-1-1-11-11-1-111ii−i−i−iii−i-1-111i−i−iii−i
χ1511-1-1-11111111-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-1-1-11−i−iii1-1-1-1-111111-1-1-111-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-11-11-1-1111-11-111-1-1ii−i−ii−i−ii-1-111i−ii−i−ii
χ1611-1-1-11111111-1-1-1-1-1-1111-11-1-1-1-1111111-1-1-1-1-1-11−i−iii1-1-1-1-111111-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-1-1-1-1-1-1-111111111−i−iiii−ii−i11-1-1−iii−ii−i
χ172222222-1222-1-1-122222-1-1-122222-1-1222222-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-122220000000000000000222222-1-1-1-1-1-122-1-1-1-1-1-100000000-1-1-1-1000000
χ182222222-1222-1-1-122222-1-1-122222-1-1222222-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-12-22-20000000000000000-2-2-2-22-2-11-1-1112-2-11-1-111000000001111000000
χ192222222-1222-1-1-122222-1-1-122222-1-1222222-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-22-220000000000000000-2-2-2-2-221-111-1-1-221-111-1-1000000001111000000
χ202222222-1222-1-1-122222-1-1-122222-1-1222222-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000000000002222-2-2111111-2-211111100000000-1-1-1-1000000
χ21222222-1222-122222-1-1-12-12-12-1-1-12-12-1-1-1-1-122-1-122222-12-1-1-1-12-1-1-1-1-1020222-1-1-1-1-1-122-1-1-1-1-1-100000-10200-1-10-10200-1-10000002200000000-1-1
χ22222222-1222-122222-1-1-12-12-12-1-1-12-12-1-1-1-1-122-1-122222-12-1-1-1-12-1-1-1-1-10-20-222-1-1-1-1-1-122-1-1-1-1-1-10000010-20011010-20011000000-2-20000000011
χ23222222-1222-122222-1-1-12-12-12-1-1-12-12-1-1-1-1-122-1-12-2-2-2-2-12-1-1-1-12-1-1-1-1-10202-2-2111111-2-211111100000-10200-1-10-10200-1-1000000-2-20000000011
χ24222222-1222-122222-1-1-12-12-12-1-1-12-12-1-1-1-1-122-1-12-2-2-2-2-12-1-1-1-12-1-1-1-1-10-20-2-2-2111111-2-21111110000010-20011010-200110000002200000000-1-1
χ2522222-1222-12222-1-122-1-122-1-12-1-1-12-12-1-1-1-1-1-12222222-1-12-1-1-1-12-1-1-1-12020-1-122-1-1-1-1-1-122-1-1-1-10000-1020-1-100-1020-1-10000002200000000-1-100
χ2622222-1222-12222-1-122-1-122-1-12-1-1-12-12-1-1-1-1-1-12222222-1-12-1-1-1-12-1-1-1-1-20-20-1-122-1-1-1-1-1-122-1-1-1-1000010-20110010-2011000000-2-2000000001100
χ2722222-1222-12222-1-122-1-122-1-12-1-1-12-12-1-1-1-1-1-1222-2-2-2-2-1-12-1-1-1-12-1-1-1-1202011-2-2111111-2-211110000-1020-1-100-1020-1-1000000-2-2000000001100
χ2822222-1222-12222-1-122-1-122-1-12-1-1-12-12-1-1-1-1-1-1222-2-2-2-2-1-12-1-1-1-12-1-1-1-1-20-2011-2-2111111-2-21111000010-20110010-20110000002200000000-1-100
χ292222-2222-2222222222222-22-2-2-2-222-2-2-2-2222222-200002-2-2-2-22-2-2-2-2220000000000000000000000000000000000000000222200000000-2-20000
χ302222-2222-2222222222222-22-2-2-2-222-2-2-2-2222222-200002-2-2-2-22-2-2-2-2220000000000000000000000000000000000000000-2-2-2-200000000220000
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
χ3322-2-2-222-1222-111-2-2-2-22-1-112-2-2-2-2-1-12222-2-21111-10000-11111-1-1-1-1-11122-2-2000000000000000022-2-222-1-1-1-1-1-1-2-211111100000000-1-111000000
χ3422-2-2-222-1222-111-2-2-2-22-1-112-2-2-2-2-1-12222-2-21111-10000-11111-1-1-1-1-1112-2-220000000000000000-2-2222-2-11-1-111-221-111-1-10000000011-1-1000000
χ3522-2-2-222-1222-111-2-2-2-22-1-112-2-2-2-2-1-12222-2-21111-10000-11111-1-1-1-1-111-222-20000000000000000-2-222-221-111-1-12-2-11-1-1110000000011-1-1000000
χ3622-2-2-222-1222-111-2-2-2-22-1-112-2-2-2-2-1-12222-2-21111-10000-11111-1-1-1-1-111-2-222000000000000000022-2-2-2-211111122-1-1-1-1-1-100000000-1-111000000
χ3722-2-2-22-1222-12-2-2-2-211-12-1-2-1-21112-12-1-1-111-2-21122i2i−2i−2i-1-2111-12-1-1-111020-22i2i−i−i−i−i−i−i−2i−2iiiiiii00000-10200-1-1010-200110000002i−2i00000000−ii
χ3822-2-2-22-1222-12-2-2-2-211-12-1-2-1-21112-12-1-1-111-2-21122i2i−2i−2i-1-2111-12-1-1-1110-2022i2i−i−i−i−i−i−i−2i−2iiiiiii0000010-200110-10200-1-1000000−2i2i00000000i−i
χ3922-2-2-22-1222-12-2-2-2-211-12-1-2-1-21112-12-1-1-111-2-2112−2i−2i2i2i-1-2111-12-1-1-111020-2−2i−2iiiiiii2i2i−i−i−i−i−i−i00000-10200-1-1010-20011000000−2i2i00000000i−i
χ4022-2-2-22-1222-12-2-2-2-211-12-1-2-1-21112-12-1-1-111-2-2112−2i−2i2i2i-1-2111-12-1-1-1110-202−2i−2iiiiiii2i2i−i−i−i−i−i−i0000010-200110-10200-1-10000002i−2i00000000−ii
χ4122-2-2-2-1222-122-2-211-2-2-1-12-2-11-211-12-12-1-11111-2-222i2i−2i−2i-11-211-1-12-1-11120-20−i−i2i2i−i−i−i−iii−2i−2iiiii0000-1020-1-10010-20110000002i−2i00000000−ii00
χ4222-2-2-2-1222-122-2-211-2-2-1-12-2-11-211-12-12-1-11111-2-222i2i−2i−2i-11-211-1-12-1-111-2020−i−i2i2i−i−i−i−iii−2i−2iiiii000010-201100-1020-1-1000000−2i2i00000000i−i00
χ4322-2-2-2-1222-122-2-211-2-2-1-12-2-11-211-12-12-1-11111-2-22−2i−2i2i2i-11-211-1-12-1-11120-20ii−2i−2iiiii−i−i2i2i−i−i−i−i0000-1020-1-10010-2011000000−2i2i00000000i−i00
χ4422-2-2-2-1222-122-2-211-2-2-1-12-2-11-211-12-12-1-11111-2-22−2i−2i2i2i-11-211-1-12-1-111-2020ii−2i−2iiiii−i−i2i2i−i−i−i−i000010-201100-1020-1-10000002i−2i00000000−ii00
χ452-22i−2i02220-2-2-22i−2i2i−2i2i−2i2220-20000-2-200002i−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−2i2220-20000-2-200002i−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−2i2220-20000-2-200002i−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−2i2220-20000-2-200002i−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−2i2i2220-20000-2-20000−2i2i−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−2i2i2220-20000-2-20000−2i2i−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−2i2i2220-20000-2-20000−2i2i−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−2i2i2220-20000-2-20000−2i2i−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
χ53444444-2-244-2-2-2-244-2-2-2-21-2-24-2-2-2-214-2-2-2-2-2-2-211-200001-21111-2111110404000000000000000000000-20-200110-20-20011000000000000000000
χ54444444-2-244-2-2-2-244-2-2-2-21-2-24-2-2-2-214-2-2-2-2-2-2-211-200001-21111-2111110-40-400000000000000000000020200-1-1020200-1-1000000000000000000
χ5544444-24-24-24-2-2-2-2-244-21-2-2-2-24-2-21-2-24-2-2-2-211-2-2-2000011-21111-21111404000000000000000000000-20-201100-20-201100000000000000000000
χ5644444-24-24-24-2-2-2-2-244-21-2-2-2-24-2-21-2-24-2-2-2-211-2-2-2000011-21111-21111-40-40000000000000000000002020-1-1002020-1-100000000000000000000
χ5744444-2-244-2-2444-2-2-2-21-2-241-2-211-2-2-2-21111-2-2-2-2444441-2-2111-2-211110000-2-2-2-21111-2-2-2-2111100000000000000000000000000000000000000
χ5844444-2-244-2-2444-2-2-2-21-2-241-2-211-2-2-2-21111-2-2-2-24-4-4-4-41-2-2111-2-2111100002222-1-1-1-12222-1-1-1-100000000000000000000000000000000000000
χ594444-444-2-444-2-2-244444-2-224-4-4-4-4-2-2-4-4-4-444-2-2-2-220000-22222-22222-2-20000000000000000000000000000000000000000000000000000000000
χ604444-44-24-44-244444-2-2-24-2-4-2-42224-2-4222-2-244-2-2-40000-2-4222-2-4222-2-20000000000000000000000000000000000000000000000000000000000
χ614444-44-2-2-44-2-2-2-244-2-2-2-212-2-4222-21-4222-2-2-2-2112000012-1-1-112-1-1-1110000000000000000000000000000003-30000003-3000000000000000000
χ624444-44-2-2-44-2-2-2-244-2-2-2-212-2-4222-21-4222-2-2-2-2112000012-1-1-112-1-1-111000000000000000000000000000000-33000000-33000000000000000000
χ634444-4-244-4-24444-2-244-2-24-4-22-422-242-422-2-2-2-244-40000-22-422-22-422-2-20000000000000000000000000000000000000000000000000000000000
χ644444-4-24-2-4-24-2-2-2-2-244-21-22-22-4221-22-422-2-211-2-2200001-12-1-11-12-1-11100000000000000000000000000003-30000003-300000000000000000000
χ654444-4-24-2-4-24-2-2-2-2-244-21-22-22-4221-22-422-2-211-2-2200001-12-1-11-12-1-1110000000000000000000000000000-33000000-3300000000000000000000
χ664444-4-2-24-4-2-2444-2-2-2-21-2-2-4122-1-1-2-222-1-111-2-2-2-2-40000122-1-1122-1-111000000003i−3i3i−3i00003i−3i3i−3i00000000000000000000000000000000000000
χ674444-4-2-24-4-2-2444-2-2-2-21-2-2-4122-1-1-2-222-1-111-2-2-2-2-40000122-1-1122-1-11100000000−3i3i−3i3i0000−3i3i−3i3i00000000000000000000000000000000000000
χ6844-4-4444-2-444-222-4-4-4-44-2-2-244444-2-2-4-4-4-4-4-4222220000-2-2-2-2-2-22222220000000000000000000000000000000000000000000000000000000000
χ6944-4-444-24-44-24-4-4-4-422-24-24-24-2-2-24-2-422222-4-422-40000-24-2-2-2-2-4222220000000000000000000000000000000000000000000000000000000000
χ7044-4-444-2-2-44-2-222-4-422-2-21-2-24-2-2-2-21-42222222-1-1200001-211112-1-1-1-1-10000000000000000000000000000003-3000000-33000000000000000000
χ7144-4-444-2-2-44-2-222-4-422-2-21-2-24-2-2-2-21-42222222-1-1200001-211112-1-1-1-1-1000000000000000000000000000000-330000003-3000000000000000000
χ7244-4-44-244-4-244-4-422-4-4-2-244-2-24-2-2-242-4222222-4-4-40000-2-24-2-2-22-422220000000000000000000000000000000000000000000000000000000000
χ7344-4-44-24-2-4-24-22222-4-4-21-2-2-2-24-2-21-22-42222-1-1222000011-2111-12-1-1-1-100000000000000000000000000003-3000000-3300000000000000000000
χ7444-4-44-24-2-4-24-22222-4-4-21-2-2-2-24-2-21-22-42222-1-1222000011-2111-12-1-1-1-10000000000000000000000000000-330000003-300000000000000000000
χ7544-4-44-2-24-4-2-24-4-422221-2-241-2-211-2-222-1-1-1-12222-400001-2-211122-1-1-1-1000000003-33-30000-33-3300000000000000000000000000000000000000
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χ1078-88i−8i08-4-40-844−4i4i8i−8i−4i4i-4-420400004-20000−4i4i−4i4i2i−2i0000020000-200002i−2i0000000000000000000000000000000000000000000000000000000000
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χ1118-8−8i8i08-4-40-8444i−4i−8i8i4i−4i-4-420400004-200004i−4i4i−4i−2i2i0000020000-20000−2i2i0000000000000000000000000000000000000000000000000000000000
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χ1148-8−8i8i0-4-4-404444i−4i4i−4i4i−4i2220-200-66-2-2006i−6i−2i2i−2i2i−2i2i00000-1003-3100−3i3ii−i0000000000000000000000000000000000000000000000000000000000

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