Finite Group Databasebeta

← Group #13155668

Character table — Group #13155668

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222222444444444444444444888888888888881212121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363636363636108108
order122233344666666666333666666666121212121212366612121212121212121212224444666612121212444412121212666666121212121212121212121212121288881212242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ511111111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-11111-1-1
χ611111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ711111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111
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
χ911-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-111-11-11-11-1-1111-1-11-111-1-11-11-1i−i11-1-1ii−i−ii−ii−iii−i−i1-111-1-1i−i11-1-1ii−i−i11-1-11-1i−ii−i11-1-1ii−i−ii−i
χ1011-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-111-11-11-11-1-1111-1-11-111-1-11-11-1−ii11-1-1−i−iii−ii−ii−i−iii1-111-1-1−ii11-1-1−i−iii11-1-11-1−ii−ii11-1-1−i−iii−ii
χ1111-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-111-11-11-11-1-1111-1-11-111-1-11-1-11i−i11-1-1ii−i−ii−ii−iii−i−i1-111-1-1i−i-1-111ii−i−i-1-111-11−iii−i-1-111−i−iii−ii
χ1211-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-111-11-11-11-1-1111-1-11-111-1-11-1-11−ii11-1-1−i−iii−ii−ii−i−iii1-111-1-1−ii-1-111−i−iii-1-111-11i−i−ii-1-111ii−i−ii−i
χ1311-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-111-11-11-11-1-1111-1-11-111-1-1-111-1i−i-1-111ii−i−i−ii−ii−i−iii-11-1-111i−i11-1-1ii−i−i11-1-1-11i−i−ii-1-111ii−i−i−ii
χ1411-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-111-11-11-11-1-1111-1-11-111-1-1-111-1−ii-1-111−i−iiii−ii−iii−i−i-11-1-111−ii11-1-1−i−iii11-1-1-11−iii−i-1-111−i−iiii−i
χ1511-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-111-11-11-11-1-1111-1-11-111-1-1-11-11i−i-1-111ii−i−i−ii−ii−i−iii-11-1-111i−i-1-111ii−i−i-1-1111-1−ii−ii11-1-1−i−iiii−i
χ1611-1-11111-1-1-1-11-111-1-1111-1-1-1-1-111-111-11-11-11-1-1111-1-11-111-1-1-11-11−ii-1-111−i−iiii−ii−iii−i−i-11-1-111−ii-1-111−i−iii-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
χ19222222-122222-1222-1-12-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-1220022-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-1220000-1-1-1-100000000-1-10000000000
χ20222222-122222-1222-1-12-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-12200-2-2-1-1-1-11111-2-2-2-2111122-1-1-1-1-2-20000111100000000110000000000
χ21222222-122222-1222-1-12-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-200221111-1-1-1-1-2-2-2-21111-2-21111220000-1-1-1-100000000110000000000
χ22222222-122222-1222-1-12-1-122-1-1-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-200-2-2111111112222-1-1-1-1-2-21111-2-20000111100000000-1-10000000000
χ23222222-1-2-2222-1222-1-12-1-122-1-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-21111000000−i3i3−i3i3−i3i3−i3i322-2-2111100−i3i3−i3i3000000−i3i3−i3i300000000-1-10000000000
χ24222222-1-2-2222-1222-1-12-1-122-1-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-21111000000−i3i3−i3i3i3−i3i3−i3-2-222-1-1-1-100−i3i3−i3i3000000i3−i3i3−i300000000110000000000
χ25222222-1-2-2222-1222-1-12-1-122-1-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-21111000000i3−i3i3−i3−i3i3−i3i3-2-222-1-1-1-100i3−i3i3−i3000000−i3i3−i3i300000000110000000000
χ26222222-1-2-2222-1222-1-12-1-122-1-1-1-1-1-1211-2-2-2-2-1-1-1-11111-2-21111000000i3−i3i3−i3i3−i3i3−i322-2-2111100i3−i3i3−i3000000i3−i3i3−i300000000-1-10000000000
χ2722222-12222-1-1222-122-12-1-1-12-1-12-12-1222-1-12-1-1-1-12-12-1-1-1-1-1-1-12222002222000000000000-1-1-1-1-1-1002-12-10000-1-1-1-1220000-1-1-1-1000000
χ2822222-12222-1-1222-122-12-1-1-12-1-12-12-1222-1-12-1-1-1-12-12-1-1-1-1-1-1-122-2-2002222000000000000-1-1-1-1-1-100-21-2100001111-2-200001111000000
χ2922222-12222-1-1222-122-12-1-1-12-1-12-12-1222-1-12-1-1-1-12-12-1-1-1-1-1-1-1-2-22200-2-2-2-2000000000000111111002-12-10000-1-1-1-1-2-200001111000000
χ3022222-12222-1-1222-122-12-1-1-12-1-12-12-1222-1-12-1-1-1-12-12-1-1-1-1-1-1-1-2-2-2-200-2-2-2-200000000000011111100-21-2100001111220000-1-1-1-1000000
χ312222-12222-1222-1-1222-1-12-1-1-122-12-1-122-122-1-1-1-1-1-12-12-1-1-1-1-1-10022220000222200000000000000-1-1-12-12-1-1-1-1-1-1-1-10022000000-1-1-1-100
χ322222-12222-1222-1-1222-1-12-1-1-122-12-1-122-122-1-1-1-1-1-12-12-1-1-1-1-1-10022-2-20000-2-2-2-20000000000000011-12-121111-1-1-1-100-2-2000000111100
χ332222-12222-1222-1-1222-1-12-1-1-122-12-1-122-122-1-1-1-1-1-12-12-1-1-1-1-1-100-2-2220000222200000000000000-1-11-21-2-1-1-1-1111100-2-2000000111100
χ342222-12222-1222-1-1222-1-12-1-1-122-12-1-122-122-1-1-1-1-1-12-12-1-1-1-1-1-100-2-2-2-20000-2-2-2-200000000000000111-21-2111111110022000000-1-1-1-100
χ3522-2-2222-22-2-2-22-222-2-2222-2-2-2-2-222-22-22-22-222-2-22-2-222-22-2-222000000000000002i−2i−2i2i−2i−2i2i2i0000000000000000000000002i−2i0000000000
χ3622-2-2222-22-2-2-22-222-2-2222-2-2-2-2-222-22-22-22-222-2-22-2-222-22-2-22200000000000000−2i2i2i−2i2i2i−2i−2i000000000000000000000000−2i2i0000000000
χ3722-2-222-12-2-2-2-2-1-222112-1-1-2-2111-1-112-112-22-2-111-1-1-1112-2-1-1112-2002i−2i-1-111−i−iii2i−2i2i−2i−i−iii2-2-1-1112i−2i0000−i−iii00000000−ii0000000000
χ3822-2-222-12-2-2-2-2-1-222112-1-1-2-2111-1-112-112-22-2-111-1-1-1112-2-1-1112-200−2i2i-1-111ii−i−i−2i2i−2i2iii−i−i2-2-1-111−2i2i0000ii−i−i00000000i−i0000000000
χ3922-2-222-12-2-2-2-2-1-222112-1-1-2-2111-1-112-112-22-2-111-1-1-1112-2-1-111-22002i−2i11-1-1−i−iii−2i2i−2i2iii−i−i-2211-1-12i−2i0000−i−iii00000000i−i0000000000
χ4022-2-222-12-2-2-2-2-1-222112-1-1-2-2111-1-112-112-22-2-111-1-1-1112-2-1-111-2200−2i2i11-1-1ii−i−i2i−2i2i−2i−i−iii-2211-1-1−2i2i0000ii−i−i00000000−ii0000000000
χ4122-2-222-1-22-2-2-2-1-222112-1-1-2-2111-1-1121-1-22-22-111-111-1-1-2211-1-1000000−i3i3i3−i33−3−332i−2i−2i2iii−i−i00−i3i3i3−i30000003−3−3300000000−ii0000000000
χ4222-2-222-1-22-2-2-2-1-222112-1-1-2-2111-1-1121-1-22-22-111-111-1-1-2211-1-1000000−i3i3i3−i3−333−3−2i2i2i−2i−i−iii00−i3i3i3−i3000000−333−300000000i−i0000000000
χ4322-2-222-1-22-2-2-2-1-222112-1-1-2-2111-1-1121-1-22-22-111-111-1-1-2211-1-1000000i3−i3−i3i33−3−33−2i2i2i−2i−i−iii00i3−i3−i3i30000003−3−3300000000i−i0000000000
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χ4522-2-22-122-2-2112-22-1-2-2-12-111-2112-1-2-12-221-1-2-111-12-1-21-11-1-1112-22-20022-2-2000000000000-11-1-111002-1-210000-1-1112-20000-1-111000000
χ4622-2-22-122-2-2112-22-1-2-2-12-111-2112-1-2-12-221-1-2-111-12-1-21-11-1-1112-2-220022-2-2000000000000-11-1-11100-212-1000011-1-1-22000011-1-1000000
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χ4822-2-22-122-2-2112-22-1-2-2-12-111-2112-1-2-12-221-1-2-111-12-1-21-11-1-111-22-2200-2-2220000000000001-111-1-100-212-1000011-1-12-20000-1-111000000
χ4922-2-2-1222-21-2-221-12-2-2-1-12111-2-2-121-12-2-1-221-111-1-121-2-11-1-111002-22i−2i00002i2i−2i−2i00000000000000−ii-121-2−i−iii-1-111002i−2i000000−i−iii00
χ5022-2-2-1222-21-2-221-12-2-2-1-12111-2-2-121-12-2-1-221-111-1-121-2-11-1-111002-2−2i2i0000−2i−2i2i2i00000000000000i−i-121-2ii−i−i-1-11100−2i2i000000ii−i−i00
χ5122-2-2-1222-21-2-221-12-2-2-1-12111-2-2-121-12-2-1-221-111-1-121-2-11-1-11100-222i−2i00002i2i−2i−2i00000000000000−ii1-2-12−i−iii11-1-100−2i2i000000ii−i−i00
χ5222-2-2-1222-21-2-221-12-2-2-1-12111-2-2-121-12-2-1-221-111-1-121-2-11-1-11100-22−2i2i0000−2i−2i2i2i00000000000000i−i1-2-12ii−i−i11-1-1002i−2i000000−i−iii00
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χ894-4-4444-200-4-4424-4-42-24-2-2-4422-222-2-4000000-22-220000000000000000000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ904-4-4444-200-4-4424-4-42-24-2-2-4422-222-2-4000000-22-2200000000000000000000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ914-4-444-2400-42-2-44-42-44-24-22-2-42-2-4242000000-22-2200000000000000000000000000000000000000000000000000000000006−6−66000000
χ924-4-444-2400-42-2-44-42-44-24-22-2-42-2-4242000000-22-220000000000000000000000000000000000000000000000000000000000−666−6000000
χ934-4-44-244002-44-4-22-4-44-2-242-22-442-4-22000000-22-22000000000000000000000000000000000000000000000000000000000000006−6−6600
χ944-4-44-244002-44-4-22-4-44-2-242-22-442-4-22000000-22-2200000000000000000000000000000000000000000000000000000000000000−666−600
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
χ9788-8-8-4-4-48-8444-44-4-444222-2-2-2-2-222-22-44-44-44-111-122-2-22-2-1-1110000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-4-88444-44-4-444222-2-2-2-2-222-224-44-44-4-111-1-2-222-2211-1-10000000000000000000000000000000000000000000000000000000000
χ998-88-88-4-4008-444-8-84-44-4-42-44-42-24-24400000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ1008-88-8-48-400-48-8444-8-44-42-4-442-44-24-2400000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4800-4-44-84448-82-4-42-2-4-44444-200000022-2-200000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-400-4-444444-442222-222-2-2-2-2-2000000-1-11100000033−3333−330000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-400-4-444444-442222-222-2-2-2-2-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000000000000000
χ1048-8-888-4-400-84-448-844-4-4-424-44-224-2-440000002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-4004-884-44-84-4-42-44-4-24-4-24240000002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-480044-4-8-444-882-4-4-2244-444-4-20000002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-40044-44-4444-4222-22-2-22-2-22-2000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-40044-44-4444-4222-22-2-22-2-22-2000000-11-11000000−333333−330000000000000000000000000000000000000000000000000000000000

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