Finite Group Databasebeta

← Group #13170655

Character table — Group #13170655

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222222444444444444444444888888888888881212121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363636363636108108
order12442333466612121212121233366666612121212121212121236666661212121212121222244466661212121222446612126666666666121212121212121212126888812242424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-111-1111111111111111111-1-11111-1-111-1-11111-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-111-1111-1-111-1-1-1-1-1-1-1-1-1-11-11111-1-1111-11111-1-111-111-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111-1-11-1-111-1-111-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-11-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1111111
χ511111111111111111111111111111111111111111111111111-111-111-1-111-1-111-1-1-1-1-1-1-1-1-1111-1-11111-1111-1-11111-1-1-111-1-1-1-1-11111-1-1
χ611111111111111111111111111111111111111111111111111-11-1-11-1-1-111-1-111-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-11-1-1-1-111-1-1-111-1-1-11111-1-1-1-111
χ711111111111111111111111111111111111111111111111111-1-11-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-111
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
χ911-1-1-11111111-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1111111-1-1111-1-1-11111-1-1-1-11-11-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-11-1111-1-111-1-1-11
χ1011-1-1-11111111-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1111111-1-111-1-1-111111-1-1-1-11-11-111-1-111-1-11111-1-1-1-111-1-1-1-111-1-11-111-1-111-1-1111-1
χ1111-1-1-11111111-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1111111-1-11-11-11-111-1-1-1-111-11-11-1-1111-11111-1-111-11-1-1-1-111-1-111-1-11-111-1-1-1-1111-1
χ1211-1-1-11111111-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1111111-1-11-1-1-11111-1-1-1-111-11-11-1-1111-1-1-111-1-1-1-1-1111-1-111111-111-1-1-1-11111-1-1-11
χ1311-1-1-11111111-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1111-1-1-1-11111-1-1-11-11-1-111-1111-1-111111-1-1-111-1-1-1-11-111-1-1-1-11111-1-11-1
χ1411-1-1-11111111-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-11-11-11-1-11111-1-1-11-11-1-111-11-1-1-1-111-1-11-11111-1-11111-1-11-111-1-1-1-111-11
χ1511-1-1-11111111-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-1111-1-1-1-1-111111-11-111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11-111-1-111-1-111-11
χ1611-1-1-11111111-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1111-1-1-1-111111-11-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-11-11-1111-1-111-1-11-1
χ172222222-1222-12222-1-12-1-122-12-1-1-122-1-1-1-122-12-1-1-1-1-12-1-1-1-1-1-1220220-1-1-1-1-1-1-1-12222-1-1-1-12200-1-1-1-1002200-1-1-1-100-10000-10000000000
χ182222222-1222-12222-1-12-1-122-12-1-1-122-1-1-1-122-12-1-1-1-1-12-1-1-1-1-1-12-202-20-1-111-1-111-2-2-2-211112-200-1-111002-200-1-111001000010000000000
χ192222222-1222-12222-1-12-1-122-12-1-1-122-1-1-1-122-12-1-1-1-1-12-1-1-1-1-1-1-220-22011-1-111-1-1-2-2-2-21111-220011-1-100-220011-1-1001000010000000000
χ202222222-1222-12222-1-12-1-122-12-1-1-122-1-1-1-122-12-1-1-1-1-12-1-1-1-1-1-1-2-20-2-20111111112222-1-1-1-1-2-200111100-2-200111100-10000-10000000000
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χ22222222-1222-1222-1-122-12-12-12-12-12-1-122-1-12-1-1-12-1-1-1-1-12-1-1-1-1-102-202-200220022000000000-1-2100-1-1110-1-2100-1-111000-2-200000111100
χ23222222-1222-1222-1-122-12-12-12-12-12-1-122-1-12-1-1-12-1-1-1-1-12-1-1-1-1-10-220-2200-2-200-2-200000000012-10011-1-1012-10011-1-1000-2-200000111100
χ24222222-1222-1222-1-122-12-12-12-12-12-1-122-1-12-1-1-12-1-1-1-1-12-1-1-1-1-10-2-20-2-200-2-200-2-20000000001-2100111101-210011110002200000-1-1-1-100
χ2522222-1222-122-1-12222-1-12-122-1-122-1-1-1-122-12-1-1-12-1-1-1-1-12-1-1-1-12022022200220000000000-10-12-1-100-1-1-10-12-1-100-1-1022000-1-1-1-1000000
χ2622222-1222-122-1-12222-1-12-122-1-122-1-1-1-122-12-1-1-12-1-1-1-1-12-1-1-1-120-220-22200220000000000-101-2-1-10011-101-2-1-100110-2-20001111000000
χ2722222-1222-122-1-12222-1-12-122-1-122-1-1-1-122-12-1-1-12-1-1-1-1-12-1-1-1-1-202-202-2-200-2-2000000000010-121100-1-110-121100-1-10-2-20001111000000
χ2822222-1222-122-1-12222-1-12-122-1-122-1-1-1-122-12-1-1-12-1-1-1-1-12-1-1-1-1-20-2-20-2-2-200-2-20000000000101-2110011101-2110011022000-1-1-1-1000000
χ292222-2222-2222222222222-2-2-2222-2222222-2-22-2-2-2-2-22-2-2-2-2-222000000000000002-2-22222200000000000000000000-20000-20000000000
χ302222-2222-2222222222222-2-2-2222-2222222-2-22-2-2-2-2-22-2-2-2-2-22200000000000000-222-2-2-2-2-2000000000000000000002000020000000000
χ312222-222-1-222-12222-1-12-1-1-2-212-1-1122-1-1-1-1-2-2-1-21111-1-21111-1-1000000−i3i3−i3i3−i3i3−i3i32-2-22-1-1-1-10000−i3i3−i3i3000000−i3i3−i3i3001000010000000000
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χ3522-2-22222-2222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-20000000000000022-2-222-2-20000000000000000000020000-20000000000
χ3622-2-22222-2222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-200000000000000-2-222-2-22200000000000000000000-2000020000000000
χ3722-2-2222-1-222-1-2-2-2-2112-1-122-12-1-11-2-21111-2-2-12-1-1-1-1-1-2111111000000−i3i3−i3i3i3−i3i3−i322-2-2-1-1110000−i3i3−i3i3000000i3−i3i3−i300-1000010000000000
χ3822-2-2222-1-222-1-2-2-2-2112-1-122-12-1-11-2-21111-2-2-12-1-1-1-1-1-2111111000000−i3i3i3−i3i3−i3−i3i3-2-22211-1-10000−i3i3i3−i3000000i3−i3−i3i30010000-10000000000
χ3922-2-2222-1-222-1-2-2-2-2112-1-122-12-1-11-2-21111-2-2-12-1-1-1-1-1-2111111000000i3−i3−i3i3−i3i3i3−i3-2-22211-1-10000i3−i3−i3i3000000−i3i3i3−i30010000-10000000000
χ4022-2-2222-1-222-1-2-2-2-2112-1-122-12-1-11-2-21111-2-2-12-1-1-1-1-1-2111111000000i3−i3i3−i3−i3i3−i3i322-2-2-1-1110000i3−i3i3−i3000000−i3i3−i3i300-1000010000000000
χ4122-2-2-222-1222-1-2-2-2-2112-1-1-2-212-1-1-1-2-2111122-1-21111-12-1-1-1-111220-2-20-1-1-1-111112-22-2-1-1112200-1-1-1-100-2-20011110010000-10000000000
χ4222-2-2-222-1222-1-2-2-2-2112-1-1-2-212-1-1-1-2-2111122-1-21111-12-1-1-1-1112-20-220-1-11111-1-1-22-2211-1-12-200-1-11100-220011-1-100-1000010000000000
χ4322-2-2-222-1222-1-2-2-2-2112-1-1-2-212-1-1-1-2-2111122-1-21111-12-1-1-1-111-2202-2011-1-1-1-111-22-2211-1-1-220011-1-1002-200-1-11100-1000010000000000
χ4422-2-2-222-1222-1-2-2-2-2112-1-1-2-212-1-1-1-2-2111122-1-21111-12-1-1-1-111-2-202201111-1-1-1-12-22-2-1-111-2-2001111002200-1-1-1-10010000-10000000000
χ4522-2-2-22-1222-12-2-211-2-2-12-1-21-2-12-1211-2-2112-1-11-2111-1-12-1-1-1110220-2-2002200-2-2000000000-12-100-1-1-1-101-210011110002-200000-1-11100
χ4622-2-2-22-1222-12-2-211-2-2-12-1-21-2-12-1211-2-2112-1-11-2111-1-12-1-1-11102-20-22002200-2-2000000000-1-2100-1-111012-10011-1-1000-220000011-1-100
χ4722-2-2-22-1222-12-2-211-2-2-12-1-21-2-12-1211-2-2112-1-11-2111-1-12-1-1-1110-2202-200-2-2002200000000012-10011-1-10-1-2100-1-111000-220000011-1-100
χ4822-2-2-22-1222-12-2-211-2-2-12-1-21-2-12-1211-2-2112-1-11-2111-1-12-1-1-1110-2-202200-2-200220000000001-210011110-12-100-1-1-1-10002-200000-1-11100
χ4922-2-2-2-1222-12211-2-2-2-2-1-121-2-2-1-1221111-2-2-12-111-211-1-1-12-1-111202-20-22200-2-20000000000-10-12-1-100-1-1101-211001102-2000-1-111000000
χ5022-2-2-2-1222-12211-2-2-2-2-1-121-2-2-1-1221111-2-2-12-111-211-1-1-12-1-11120-2-2022200-2-20000000000-101-2-1-1001110-121100-1-10-2200011-1-1000000
χ5122-2-2-2-1222-12211-2-2-2-2-1-121-2-2-1-1221111-2-2-12-111-211-1-1-12-1-111-20220-2-2-20022000000000010-121100-1-1-101-2-1-100110-2200011-1-1000000
χ5222-2-2-2-1222-12211-2-2-2-2-1-121-2-2-1-1221111-2-2-12-111-211-1-1-12-1-111-20-2202-2-200220000000000101-2110011-10-12-1-100-1-102-2000-1-111000000
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χ864-44i−4i0-24402-4-4−2i2i4i−4i4i−4i-2-2400022-40−2i2i−2i2i4i−4i00-200000200000−2i2i000000000000000000000000000000000000000000000000i6−i66−6000000
χ874-44i−4i0-24402-4-4−2i2i4i−4i4i−4i-2-2400022-40−2i2i−2i2i4i−4i00-200000200000−2i2i000000000000000000000000000000000000000000000000−i6i6−66000000
χ884-4−4i4i04440-4-4-4−4i4i−4i4i−4i4i444000-4-4-40−4i4i−4i4i−4i4i00400000-400000−4i4i0000000000000000000000000000000000000000000000000000000000
χ894-4−4i4i044-20-4-42−4i4i−4i4i2i−2i4-2-2000-4220−4i4i2i−2i2i−2i00-2000002000002i−2i000000000000000000−2i32i3−2323000000000000000000000000000000000000
χ904-4−4i4i044-20-4-42−4i4i−4i4i2i−2i4-2-2000-4220−4i4i2i−2i2i−2i00-2000002000002i−2i0000000000000000002i3−2i323−23000000000000000000000000000000000000
χ914-4−4i4i04-240-42-4−4i4i2i−2i−4i4i-24-20002-4202i−2i−4i4i2i−2i00-2000002000002i−2i0000000000000000000000000000000000000000000000000000i6−i6−6600
χ924-4−4i4i04-240-42-4−4i4i2i−2i−4i4i-24-20002-4202i−2i−4i4i2i−2i00-2000002000002i−2i0000000000000000000000000000000000000000000000000000−i6i66−600
χ934-4−4i4i0-24402-4-42i−2i−4i4i−4i4i-2-2400022-402i−2i2i−2i−4i4i00-2000002000002i−2i000000000000000000000000000000000000000000000000i6−i6−66000000
χ944-4−4i4i0-24402-4-42i−2i−4i4i−4i4i-2-2400022-402i−2i2i−2i−4i4i00-2000002000002i−2i000000000000000000000000000000000000000000000000−i6i66−6000000
χ9588888-4-4-48-4-4-4-4-4-4-4-4-4222-4-4-4222-4222222-4-4-1222-1-1-1222-1-1-1-10000000000000000000000000000000000000000000000000000000000
χ968888-8-4-4-4-8-4-4-4-4-4-4-4-4-4222444222422222244-1-2-2-211-1-2-2-211-1-10000000000000000000000000000000000000000000000000000000000
χ9788-8-88-4-4-4-8-4-4-4444444222-4-4-42224-2-2-2-2-2-244-1222-1-1-1-2-2-211110000000000000000000000000000000000000000000000000000000000
χ9888-8-8-8-4-4-48-4-4-4444444222444222-4-2-2-2-2-2-2-4-4-1-2-2-211-1222-1-1110000000000000000000000000000000000000000000000000000000000
χ998-88i−8i08-4-40-8448i−8i−4i4i−4i4i-4-4200044-20−4i4i−4i4i2i−2i00200000-2000002i−2i0000000000000000000000000000000000000000000000000000000000
χ1008-88i−8i0-48-404-84−4i4i8i−8i−4i4i-42-40004-240−4i4i2i−2i−4i4i00200000-2000002i−2i0000000000000000000000000000000000000000000000000000000000
χ1018-88i−8i0-4-48044-8−4i4i−4i4i8i−8i2-4-4000-24402i−2i−4i4i−4i4i00200000-2000002i−2i0000000000000000000000000000000000000000000000000000000000
χ1028-88i−8i0-4-4-40444−4i4i−4i4i−4i4i222000-2-2-202i−2i2i−2i2i−2i00-1000−3i33i3100033−33−ii0000000000000000000000000000000000000000000000000000000000
χ1038-88i−8i0-4-4-40444−4i4i−4i4i−4i4i222000-2-2-202i−2i2i−2i2i−2i00-10003i3−3i31000−3333−ii0000000000000000000000000000000000000000000000000000000000
χ1048-8−8i8i08-4-40-844−8i8i4i−4i4i−4i-4-4200044-204i−4i4i−4i−2i2i00200000-200000−2i2i0000000000000000000000000000000000000000000000000000000000
χ1058-8−8i8i0-48-404-844i−4i−8i8i4i−4i-42-40004-2404i−4i−2i2i4i−4i00200000-200000−2i2i0000000000000000000000000000000000000000000000000000000000
χ1068-8−8i8i0-4-48044-84i−4i4i−4i−8i8i2-4-4000-2440−2i2i4i−4i4i−4i00200000-200000−2i2i0000000000000000000000000000000000000000000000000000000000
χ1078-8−8i8i0-4-4-404444i−4i4i−4i4i−4i222000-2-2-20−2i2i−2i2i−2i2i00-1000−3i33i31000−3333i−i0000000000000000000000000000000000000000000000000000000000
χ1088-8−8i8i0-4-4-404444i−4i4i−4i4i−4i222000-2-2-20−2i2i−2i2i−2i2i00-10003i3−3i3100033−33i−i0000000000000000000000000000000000000000000000000000000000

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