Finite Group Databasebeta

← Group #13170580

Character table — Group #13170580

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1122222224444444444466888888121212121212121212121818242424242424242427273636363654727211222222244444444444668888881212121212121212121218182424242424242424272736363636547272
order123334666333666121212121288361212121224242424242424242488666612121212222424244612226664666666666121212121288661212121224242424242424242488666612121212222424244612
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-111111111-1-11111-1-1-1-1-1-1-11-1-1-1-1111111111111111111111111111111-111111111-1-11111-1-1-1-1-1-1-11-1-1-1-11
χ31111111111111111111111111111-1111111111-1-1-1-1-1-11111-1-11-1-1-1-11-11111111111111111111111111111-1111111111-1-1-1-1-1-11111-1-11-1-1-1-11-1
χ41111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-111-1-1111-1-11111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-111-1-1111-1-1
χ511111111111111111111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-111111111111111111111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1
χ611111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-111-111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-111-1
χ711111111111111111111-1-1111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-11-1111111111111111111111-1-1111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-11-11
χ811111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-111
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χ112222-122-12-1-12-12-1-12-1-1222-1-12-1-1-10222-1-1-1-1-1-10000002-1-1-10020000-102222-122-12-1-12-12-1-12-1-1222-1-12-1-1-10222-1-1-1-1-1-10000002-1-1-10020000-10
χ122222-122-12-1-12-12-1-12-1-1222-1-12-1-1-10-222-1-1-1-1-1-1000000-211100-20000102222-122-12-1-12-12-1-12-1-1222-1-12-1-1-10-222-1-1-1-1-1-1000000-211100-2000010
χ132222-122-12-1-12-12-1-12-1-12-2-2-1-12-1-1-102-2-21111110000002-1-1-100-20000102222-122-12-1-12-12-1-12-1-12-2-2-1-12-1-1-102-2-21111110000002-1-1-100-2000010
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χ28444-24-444-24-2-2-2-24-4222-400-2-22-42200000000000000000000000000000444-24-444-24-2-2-2-24-4222-400-2-22-42200000000000000000000000000000
χ29444-2-244-2-2-21-21-2-2-2-21144411-2-21100-2-2-2-211110000000000000000000444-2-244-2-2-21-21-2-2-2-21144411-2-21100-2-2-2-211110000000000000000000
χ30444-2-244-2-2-21-21-2-2-2-2114-4-411-2-211002222-1-1-1-10000000000000000000444-2-244-2-2-21-21-2-2-2-2114-4-411-2-211002222-1-1-1-10000000000000000000
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χ3644-24-2-4-2-241-2-2-2-212-422200112-1-1-10000000000000000003-300000000044-24-2-4-2-241-2-2-2-212-422200112-1-1-10000000000000000003-3000000000
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χ4144-2-24-4-24-2-2-21-21-2-422220011-12-1-100000000000000-33000000000000044-2-24-4-24-2-2-21-21-2-422220011-12-1-100000000000000-330000000000000
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χ454-44-240-4-424-2-222-400000−2i22i2-22000000i2−i2−2i22i2i2i2−i2−i200000000000000000004-44-240-4-424-2-222-400000−2i22i2-22000000i2−i2−2i22i2i2i2−i2−i20000000000000000000
χ464-44-2-20-422-21-2-122003i−3i02i2−2i21-1003i−3i00−i2i2−i2i22ζ−ζ3−ζ+2ζ3−2ζ+ζ3ζ−2ζ300000000000000000004-44-2-20-422-21-2-122003i−3i02i2−2i21-1003i−3i00−i2i2−i2i22ζ−ζ3−ζ+2ζ3−2ζ+ζ3ζ−2ζ30000000000000000000
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χ494-44-2-20-422-21-2-12200−3i3i0−2i22i21-100−3i3i00i2−i2i2−i2ζ−2ζ3−2ζ+ζ3−ζ+2ζ32ζ−ζ300000000000000000004-44-2-20-422-21-2-12200−3i3i0−2i22i21-100−3i3i00i2−i2i2−i2ζ−2ζ3−2ζ+ζ3−ζ+2ζ32ζ−ζ30000000000000000000
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χ5288-4-4-48-4-4-4222222-4-422-400-1-122-1-10000000000000000000000000000088-4-4-48-4-4-4222222-4-422-400-1-122-1-100000000000000000000000000000
χ5388-4-4-4-8-4-4-422222244-2-2400-1-1-2-2110000000000000000000000000000088-4-4-4-8-4-4-422222244-2-2400-1-1-2-21100000000000000000000000000000
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χ58111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ5911111111111111111111111111111-111111111-1-11111-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111111-11111-1
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χ611111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-111
χ6211111111111111111111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1111
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χ6411111111111111111111-1-1111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111111111111111-1-1-1-1-1-11-111-11-1
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χ822-22220-2-2-2222-2-2-200000−i2i22-2000000−i2i2−i2i2−i2−i2i2i2i2−i200000000-2200i2−i2000-22-2-2-20222-2-2-222200000i2−i2-22000000i2−i2i2−i2i2i2−i2−i2−i2i2000000002-200−i2i2000
χ832-22220-2-2-2222-2-2-200000−i2i22-2000000−i2i2−i2i2−i2−i2i2i2−i2i2000000002-200−i2i2000-22-2-2-20222-2-2-222200000i2−i2-22000000i2−i2i2−i2i2i2−i2−i2i2−i200000000-2200i2−i2000
χ844444-2-44-24-2-24-24-22-422-400-2-2-422200000000000000000000000000000-4-4-4-424-42-422-42-42-24-2-2400224-2-2-200000000000000000000000000000
χ85444-24-444-24-2-2-2-24-4222-400-2-22-42200000000000000000000000000000-4-4-42-44-4-42-42222-44-2-2-240022-24-2-200000000000000000000000000000
χ86444-2-244-2-2-21-21-2-2-2-21144411-2-21100-2-2-2-211110000000000000000000-4-4-422-4-4222-12-12222-1-1-4-4-4-1-122-1-1002222-1-1-1-10000000000000000000
χ87444-2-244-2-2-21-21-2-2-2-2114-4-411-2-211002222-1-1-1-10000000000000000000-4-4-422-4-4222-12-12222-1-1-444-1-122-1-100-2-2-2-211110000000000000000000
χ88444-2-2-44-2-2-21-21-2-222-1-1-4001122-1-10000003i−3i3i−3i0000000000000000000-4-4-4224-4222-12-122-2-211400-1-1-2-211000000−3i3i−3i3i0000000000000000000
χ89444-2-2-44-2-2-21-21-2-222-1-1-4001122-1-1000000−3i3i−3i3i0000000000000000000-4-4-4224-4222-12-122-2-211400-1-1-2-2110000003i−3i3i−3i0000000000000000000
χ9044-244-4-244-24-24-2-2-4-4-4-4200-2-2222200000000000000000000000000000-4-42-4-442-4-42-42-4224444-20022-2-2-2-200000000000000000000000000000
χ9144-24-24-2-241-2-2-2-21-24-2-2-20011-21110400000000000000-2-211000000000-4-42-42-422-4-12222-12-422200-1-12-1-1-10-40000000000000022-1-1000000000
χ9244-24-24-2-241-2-2-2-21-24-2-2-20011-21110-40000000000000022-1-1000000000-4-42-42-422-4-12222-12-422200-1-12-1-1-10400000000000000-2-211000000000
χ9344-24-2-4-2-241-2-2-2-212-422200112-1-1-10000000000000000003-3000000000-4-42-42422-4-12222-1-24-2-2-200-1-1-2111000000000000000000-33000000000
χ9444-24-2-4-2-241-2-2-2-212-422200112-1-1-1000000000000000000-33000000000-4-42-42422-4-12222-1-24-2-2-200-1-1-21110000000000000000003-3000000000
χ9544-2-244-24-2-2-21-21-24-2-2-2-200111-211400000000000-2-2110000000000000-4-422-4-42-4222-12-12-4222200-1-1-12-1-1-40000000000022-1-10000000000000
χ9644-2-244-24-2-2-21-21-24-2-2-2-200111-211-40000000000022-1-10000000000000-4-422-4-42-4222-12-12-4222200-1-1-12-1-1400000000000-2-2110000000000000
χ9744-2-24-4-24-2-2-21-21-2-422220011-12-1-1000000000000003-30000000000000-4-422-442-4222-12-124-2-2-2-200-1-11-21100000000000000-330000000000000
χ9844-2-24-4-24-2-2-21-21-2-422220011-12-1-100000000000000-330000000000000-4-422-442-4222-12-124-2-2-2-200-1-11-211000000000000003-30000000000000
χ994-444-20-42-4-2-242-42000002i2−2i2-220000002i2−2i2−i2i2−i2−i2i2i20000000000000000000-44-4-4204-2422-4-24-200000−2i22i22-2000000−2i22i2i2−i2i2i2−i2−i20000000000000000000
χ1004-444-20-42-4-2-242-4200000−2i22i2-22000000−2i22i2i2−i2i2i2−i2−i20000000000000000000-44-4-4204-2422-4-24-2000002i2−2i22-20000002i2−2i2−i2i2−i2−i2i2i20000000000000000000
χ1014-44-240-4-424-2-222-4000002i2−2i2-22000000−i2i22i2−2i2−i2−i2i2i20000000000000000000-44-42-4044-2-422-2-2400000−2i22i22-2000000i2−i2−2i22i2i2i2−i2−i20000000000000000000
χ1024-44-240-4-424-2-222-400000−2i22i2-22000000i2−i2−2i22i2i2i2−i2−i20000000000000000000-44-42-4044-2-422-2-24000002i2−2i22-2000000−i2i22i2−2i2−i2−i2i2i20000000000000000000
χ1034-44-2-20-422-21-2-122003i−3i02i2−2i21-1003i−3i00−i2i2−i2i22ζ−ζ3−ζ+2ζ3−2ζ+ζ3ζ−2ζ30000000000000000000-44-42204-2-22-121-2-200−3i3i0−2i22i2-1100−3i3i00i2−i2i2−i2−2ζ+ζ3ζ−2ζ32ζ−ζ3−ζ+2ζ30000000000000000000
χ1044-44-2-20-422-21-2-122003i−3i0−2i22i21-1003i−3i00i2−i2i2−i2−2ζ+ζ3ζ−2ζ32ζ−ζ3−ζ+2ζ30000000000000000000-44-42204-2-22-121-2-200−3i3i02i2−2i2-1100−3i3i00−i2i2−i2i22ζ−ζ3−ζ+2ζ3−2ζ+ζ3ζ−2ζ30000000000000000000
χ1054-44-2-20-422-21-2-12200−3i3i02i2−2i21-100−3i3i00−i2i2−i2i2−ζ+2ζ32ζ−ζ3ζ−2ζ3−2ζ+ζ30000000000000000000-44-42204-2-22-121-2-2003i−3i0−2i22i2-11003i−3i00i2−i2i2−i2ζ−2ζ3−2ζ+ζ3−ζ+2ζ32ζ−ζ30000000000000000000
χ1064-44-2-20-422-21-2-12200−3i3i0−2i22i21-100−3i3i00i2−i2i2−i2ζ−2ζ3−2ζ+ζ3−ζ+2ζ32ζ−ζ30000000000000000000-44-42204-2-22-121-2-2003i−3i02i2−2i2-11003i−3i00−i2i2−i2i2−ζ+2ζ32ζ−ζ3ζ−2ζ3−2ζ+ζ30000000000000000000
χ1074-4-24402-4-4-24-2-4220000000-22000000000000002i2−2i2000000000000−i2i2000-442-4-40-2442-424-2-200000002-200000000000000−2i22i2000000000000i2−i2000
χ1084-4-24402-4-4-24-2-4220000000-2200000000000000−2i22i2000000000000i2−i2000-442-4-40-2442-424-2-200000002-2000000000000002i2−2i2000000000000−i2i2000
χ10988-4-4-48-4-4-4222222-4-422-400-1-122-1-100000000000000000000000000000-8-8444-8444-2-2-2-2-2-244-2-240011-2-21100000000000000000000000000000
χ11088-4-4-4-8-4-4-422222244-2-2400-1-1-2-21100000000000000000000000000000-8-84448444-2-2-2-2-2-2-4-422-4001122-1-100000000000000000000000000000
χ1118-8-48-4044-82-4-444-200000002-2000000000000000000000000000000000-884-840-4-48-244-4-420000000-22000000000000000000000000000000000
χ1128-8-4-4804-84-4-424-2400000002-2000000000000000000000000000000000-8844-80-48-444-2-42-40000000-22000000000000000000000000000000000
χ1138-8-4-4-40444222-2-2-2006i−6i000-1100−3i3i00000000000000000000000000000-884440-4-4-4-2-2-222200−6i6i0001-1003i−3i00000000000000000000000000000
χ1148-8-4-4-40444222-2-2-200−6i6i000-11003i−3i00000000000000000000000000000-884440-4-4-4-2-2-2222006i−6i0001-100−3i3i00000000000000000000000000000

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