Finite Group Databasebeta

← Group #13155696

Character table — Group #13155696

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222222444444444444444444888888888888881212121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363636363636108108
order1222333446666666663336666666661212121212123666121212121212121212124444441212121212121212444412121212121212121212121212121212121212121212121288881212242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111111
χ511111111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1
χ611111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ711111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ911-1-11111-1-1-1-1-111-11-1111-1-1-1-1-11-11111-1-1-111-1-111-111-1-111-1-11-11-1i−i11-1-1ii−i−ii−ii−iii−i−ii−i1-11-11-1ii−i−i11-1-111-1-11-1i−ii−i11-1-1ii−i−ii−i
χ1011-1-11111-1-1-1-1-111-11-1111-1-1-1-1-11-11111-1-1-111-1-111-111-1-111-1-11-11-1−ii11-1-1−i−iii−ii−ii−i−iii−ii1-11-11-1−i−iii11-1-111-1-11-1−ii−ii11-1-1−i−iii−ii
χ1111-1-11111-1-1-1-1-111-11-1111-1-1-1-1-11-11111-1-1-111-1-111-111-1-111-1-11-1-11i−i11-1-1ii−i−ii−ii−iii−i−ii−i-111-1-11ii−i−i11-1-1-1-111-11−iii−i-1-111−i−iii−ii
χ1211-1-11111-1-1-1-1-111-11-1111-1-1-1-1-11-11111-1-1-111-1-111-111-1-111-1-11-1-11−ii11-1-1−i−iii−ii−ii−i−iii−ii-111-1-11−i−iii11-1-1-1-111-11i−i−ii-1-111ii−i−ii−i
χ1311-1-11111-1-1-1-1-111-11-1111-1-1-1-1-11-11111-1-1-111-1-111-111-1-111-1-1-111-1i−i-1-111ii−i−i−ii−ii−i−iiii−i1-1-111-1ii−i−i-1-11111-1-1-11i−i−ii-1-111ii−i−i−ii
χ1411-1-11111-1-1-1-1-111-11-1111-1-1-1-1-11-11111-1-1-111-1-111-111-1-111-1-1-111-1−ii-1-111−i−iiii−ii−iii−i−i−ii1-1-111-1−i−iii-1-11111-1-1-11−iii−i-1-111−i−iiii−i
χ1511-1-11111-1-1-1-1-111-11-1111-1-1-1-1-11-11111-1-1-111-1-111-111-1-111-1-1-11-11i−i-1-111ii−i−i−ii−ii−i−iiii−i-11-11-11ii−i−i-1-111-1-1111-1−ii−ii11-1-1−i−iiii−i
χ1611-1-11111-1-1-1-1-111-11-1111-1-1-1-1-11-11111-1-1-111-1-111-111-1-111-1-1-11-11−ii-1-111−i−iiii−ii−iii−i−i−ii-11-11-11−i−iii-1-111-1-1111-1i−ii−i11-1-1ii−i−i−ii
χ172222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-20000000000000022-2-2-2-2-2-2000000000000000000000000220000000000
χ182222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-200000000000000-2-2222222000000000000000000000000-2-20000000000
χ19222222-12222222-1-12-12-1-122-1-1-1-1-12-12-1-1222-1-1-1-1-1-12-12-1-1-1-1-1220022-1-1-1-1-1-1-1-12222-1-1-1-122002200-1-1-1-1-1-1-1-100000000-1-10000000000
χ20222222-12222222-1-12-12-1-122-1-1-1-1-12-12-1-1222-1-1-1-1-1-12-12-1-1-1-1-12200-2-2-1-1-1-11111-2-2-2-21111-2-20022001111-1-1-1-100000000110000000000
χ21222222-12222222-1-12-12-1-122-1-1-1-1-12-12-1-1222-1-1-1-1-1-12-12-1-1-1-1-1-2-200221111-1-1-1-1-2-2-2-211112200-2-200-1-1-1-1111100000000110000000000
χ22222222-12222222-1-12-12-1-122-1-1-1-1-12-12-1-1222-1-1-1-1-1-12-12-1-1-1-1-1-2-200-2-2111111112222-1-1-1-1-2-200-2-2001111111100000000-1-10000000000
χ23222222-1-2-222222-1-12-12-1-122-1-1-1-1-12-1-211-2-2-2-1-1-1-111-21-211111000000−i3i3−i3i3−i3i3−i3i322-2-2111100000000−i3i3−i3i3−i3i3−i3i300000000-1-10000000000
χ24222222-1-2-222222-1-12-12-1-122-1-1-1-1-12-1-211-2-2-2-1-1-1-111-21-211111000000−i3i3−i3i3i3−i3i3−i3-2-222-1-1-1-100000000i3−i3i3−i3−i3i3−i3i300000000110000000000
χ25222222-1-2-222222-1-12-12-1-122-1-1-1-1-12-1-211-2-2-2-1-1-1-111-21-211111000000i3−i3i3−i3−i3i3−i3i3-2-222-1-1-1-100000000−i3i3−i3i3i3−i3i3−i300000000110000000000
χ26222222-1-2-222222-1-12-12-1-122-1-1-1-1-12-1-211-2-2-2-1-1-1-111-21-211111000000i3−i3i3−i3i3−i3i3−i322-2-2111100000000i3−i3i3−i3i3−i3i3−i300000000-1-10000000000
χ2722222-122222-1-1-12222-12-1-1-122-1-1-1-12-1222-12-1-1-1-1-1-1-12-12-1-1-1-10022220000222200000000-1-1-1-10022-1-1-1-10000-1-1-1-10022000000-1-1-1-100
χ2822222-122222-1-1-12222-12-1-1-122-1-1-1-12-1222-12-1-1-1-1-1-1-12-12-1-1-1-10022-2-20000-2-2-2-20000000011-1-1002211110000-1-1-1-100-2-2000000111100
χ2922222-122222-1-1-12222-12-1-1-122-1-1-1-12-1222-12-1-1-1-1-1-1-12-12-1-1-1-100-2-2220000222200000000-1-11100-2-2-1-1-1-10000111100-2-2000000111100
χ3022222-122222-1-1-12222-12-1-1-122-1-1-1-12-1222-12-1-1-1-1-1-1-12-12-1-1-1-100-2-2-2-20000-2-2-2-200000000111100-2-21111000011110022000000-1-1-1-100
χ312222-12222-1-122222-12-1-12-1-1-1-1222-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-122220022220000000000000022-1-1-1-10000-1-1-1-1-1-1-1-1220000-1-1-1-1000000
χ322222-12222-1-122222-12-1-12-1-1-1-1222-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-122-2-200222200000000000000-2-2-1-1110000-1-1-1-11111-2-200001111000000
χ332222-12222-1-122222-12-1-12-1-1-1-1222-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-1-2-22200-2-2-2-2000000000000002211-1-100001111-1-1-1-1-2-200001111000000
χ342222-12222-1-122222-12-1-12-1-1-1-1222-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-200-2-2-2-200000000000000-2-21111000011111111220000-1-1-1-1000000
χ3522-2-2222-22-2-2-2-222-22-2222-2-2-2-2-22-222-2-2222-22-2-22-22-2-222-2-222000000000000002i−2i−2i2i−2i−2i2i2i0000000000000000000000002i−2i0000000000
χ3622-2-2222-22-2-2-2-222-22-2222-2-2-2-2-22-222-2-2222-22-2-22-22-2-222-2-22200000000000000−2i2i2i−2i2i2i−2i−2i000000000000000000000000−2i2i0000000000
χ3722-2-222-12-2-2-2-2-22-11212-1-1-2-2111-112-12-11-2-22-111-1-112-1-21-1-1112-2002i−2i-1-111−i−iii2i−2i2i−2i−i−iii2i−2i002-200−i−iii-1-11100000000−ii0000000000
χ3822-2-222-12-2-2-2-2-22-11212-1-1-2-2111-112-12-11-2-22-111-1-112-1-21-1-1112-200−2i2i-1-111ii−i−i−2i2i−2i2iii−i−i−2i2i002-200ii−i−i-1-11100000000i−i0000000000
χ3922-2-222-12-2-2-2-2-22-11212-1-1-2-2111-112-12-11-2-22-111-1-112-1-21-1-111-22002i−2i11-1-1−i−iii−2i2i−2i2iii−i−i2i−2i00-2200−i−iii11-1-100000000i−i0000000000
χ4022-2-222-12-2-2-2-2-22-11212-1-1-2-2111-112-12-11-2-22-111-1-112-1-21-1-111-2200−2i2i11-1-1ii−i−i2i−2i2i−2i−i−iii−2i2i00-2200ii−i−i11-1-100000000−ii0000000000
χ4122-2-222-1-22-2-2-2-22-11212-1-1-2-2111-112-1-21-122-2-111-11-1-212-111-1-1000000−i3i3i3−i33−3−332i−2i−2i2iii−i−i000000003−3−33−i3i3i3−i300000000−ii0000000000
χ4222-2-222-1-22-2-2-2-22-11212-1-1-2-2111-112-1-21-122-2-111-11-1-212-111-1-1000000−i3i3i3−i3−333−3−2i2i2i−2i−i−iii00000000−333−3−i3i3i3−i300000000i−i0000000000
χ4322-2-222-1-22-2-2-2-22-11212-1-1-2-2111-112-1-21-122-2-111-11-1-212-111-1-1000000i3−i3−i3i33−3−33−2i2i2i−2i−i−iii000000003−3−33i3−i3−i3i300000000i−i0000000000
χ4422-2-222-1-22-2-2-2-22-11212-1-1-2-2111-112-1-21-122-2-111-11-1-212-111-1-1000000i3−i3−i3i3−333−32i−2i−2i2iii−i−i00000000−333−3i3−i3−i3i300000000−ii0000000000
χ4522-2-22-122-2-2-211-12-22-2-12-111-2-21-11-12-12-2-212-111-1-11-121-2-1-111002-22i−2i00002i2i−2i−2i00000000−ii-11002-2−i−iii0000-1-111002i−2i000000−i−iii00
χ4622-2-22-122-2-2-211-12-22-2-12-111-2-21-11-12-12-2-212-111-1-11-121-2-1-111002-2−2i2i0000−2i−2i2i2i00000000i−i-11002-2ii−i−i0000-1-11100−2i2i000000ii−i−i00
χ4722-2-22-122-2-2-211-12-22-2-12-111-2-21-11-12-12-2-212-111-1-11-121-2-1-11100-222i−2i00002i2i−2i−2i00000000−ii1-100-22−i−iii000011-1-100−2i2i000000ii−i−i00
χ4822-2-22-122-2-2-211-12-22-2-12-111-2-21-11-12-12-2-212-111-1-11-121-2-1-11100-22−2i2i0000−2i−2i2i2i00000000i−i1-100-22ii−i−i000011-1-1002i−2i000000−i−iii00
χ4922-2-2-1222-211-2-222-2-1-2-1-121111-22-2-1-122-21-2-1-111-12-2-1-111-1-1112-22-20022-2-2000000000000002-2-11-110000-1-111-1-1112-20000-1-111000000
χ5022-2-2-1222-211-2-222-2-1-2-1-121111-22-2-1-122-21-2-1-111-12-2-1-111-1-1112-2-220022-2-200000000000000-22-111-10000-1-11111-1-1-22000011-1-1000000
χ5122-2-2-1222-211-2-222-2-1-2-1-121111-22-2-1-122-21-2-1-111-12-2-1-111-1-111-222-200-2-222000000000000002-21-1-11000011-1-1-1-111-22000011-1-1000000
χ5222-2-2-1222-211-2-222-2-1-2-1-121111-22-2-1-122-21-2-1-111-12-2-1-111-1-111-22-2200-2-22200000000000000-221-11-1000011-1-111-1-12-20000-1-111000000
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χ894-4-4444-200-444-4-42-2-424-2-2-442-2-222-42000000-22-220000000000000000000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ904-4-4444-200-444-4-42-2-424-2-2-442-2-222-42000000-22-2200000000000000000000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ914-4-444-2400-44-222-44-4-4-24-22-2-44-2222-4000000-22-2200000000000000000000000000000000000000000000000000000000000000i6−i6−i6i600
χ924-4-444-2400-44-222-44-4-4-24-22-2-44-2222-4000000-22-2200000000000000000000000000000000000000000000000000000000000000−i6i6i6−i600
χ934-4-44-244002-24-4-4-442-4-2-242-22-24-4-422000000-22-220000000000000000000000000000000000000000000000000000000000i6−i6−i6i6000000
χ944-4-44-244002-24-4-4-442-4-2-242-22-24-4-422000000-22-220000000000000000000000000000000000000000000000000000000000−i6i6i6−i6000000
χ958888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-4-1-1-1-1222222-1-1-1-10000000000000000000000000000000000000000000000000000000000
χ968888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-1-1-1-1-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-4-48-84444-4-44-44222-2-2-2-2-22-222-4-4444-4-111-12-222-2-2-1-1110000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-4-884444-4-44-44222-2-2-2-2-22-22244-4-4-44-111-1-22-2-22211-1-10000000000000000000000000000000000000000000000000000000000
χ998-88-88-4-4008-84-4444-8-4-4-42-44-44-2-224400000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ1008-88-8-48-400-44-88-8444-4-42-4-442-244-44-200000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4800-444-44-8-8482-4-42-2-4444-4-2400000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-400-444-44444-42222-22-2-2-22-2-2000000-1-11100000033−3333−330000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-400-444-44444-42222-22-2-2-22-2-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000000000000000
χ1048-8-888-4-400-88-4444-4-84-4-424-44-42-2-2440000002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-4004-48-8-84-444-42-44-4-22-4444-20000002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-48004-4-444-884-82-4-4-224-4-444-240000002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4004-4-4444-444222-22-222-2-2-2-2000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4004-4-4444-444222-22-222-2-2-2-2000000-11-11000000−333333−330000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).