Finite Group Databasebeta

← Group #72220332

Character table — Group #72220332

Order 5184.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111444444444444444488888888888888881616161616161616181818181818181818181818363636363636363636363636363636363636363636363636363636367272727272727272727272727272727272727272727272727272727281818181324324324324
order122233336666666666663333666666666666336666664444444444442222121212121212121212121212121212121212121212121212666666666666666612121212121212121212121222224444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ611111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1
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χ1011-1-11111-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−i-11-111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111-1-111-1-11111-1-1ii−i−iii−i−i11-1-1−ii−ii
χ1111-1-11111-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii1-11-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-111-1-111-1-111-1-1−i−iii−i−iii11-1-1−ii−ii
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χ1311-1-11111-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111ii−i−i−i−iii1-1-11-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-11111-1-1-1-111-1-111ii−i−i−i−iii11-1-1i−i−ii
χ1411-1-11111-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111ii−i−i−i−iii-111-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1-1-11111-1-1-1-111ii−i−i−i−iii11-1-1−iii−i
χ1511-1-11111-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111−i−iiiii−i−i1-1-11-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-11111-1-1-1-111-1-111−i−iiiii−i−i11-1-1−iii−i
χ1611-1-11111-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111−i−iiiii−i−i-111-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1-1-11111-1-1-1-111−i−iiiii−i−i11-1-1i−i−ii
χ17222222222222222222222222222222222222222222222-22-200000000000022-2-222-2-2000000000000000000000000000000002-22-200000000-2-2-2-20000
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χ2022-2-22222-2-2-2-222-2-2-2-222222222-2-222-2-2-2-2-2-22222-2-2-2-2-222-2000000000000-2-22222-2-200000000000000000000000000000000-222-200000000-2-2220000
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χ252-2-222222-2-222-2-2-2-222-2-22222-2-2-22-2-2-2-222-2222-2-2-2-222000000002-2-220000000000000000000022-2-2-2-2220000000000000000000000002-2-222-2-220000
χ262-2-222222-2-222-2-2-2-222-2-22222-2-2-22-2-2-2-222-2222-2-2-2-22200000000-222-200000000000000000000-2-22222-2-2000000000000000000000000-222-22-2-220000
χ272-2-222222-2-222-2-2-2-222-2-22222-2-2-22-2-2-2-222-2222-2-2-2-22200002i−2i−2i2i00000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000002i−2i−2i2i0000-222-20000
χ282-2-222222-2-222-2-2-2-222-2-22222-2-2-22-2-2-2-222-2222-2-2-2-2220000−2i2i2i−2i0000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000−2i2i2i−2i0000-222-20000
χ294444144-24-24-21414144-211-2-21111-2-2-2-2-2-2111-21-21-21-20404222222220000001100112-12-12-12-12-12-12-12-100000000000000000-20-2-1-1-1-1-1-1-1-100000000
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χ33444441-24-24-24414141-2411-2-21111-2-2-2-2-2-211-21-21-21-21404022222222000011001100-12-12-12-12-12-12-12-120000000000000000-20-20-1-1-1-1-1-1-1-100000000
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χ35444441-24-24-24414141-2411-2-21111-2-2-2-2-2-211-21-21-21-21-40-402222-2-2-2-20000-1-100-1-100-12-12-12-121-21-21-21-200000000000000002020-1-1-1-1111100000000
χ36444441-24-24-24414141-2411-2-21111-2-2-2-2-2-211-21-21-21-21-40-40-2-2-2-222220000-1-100-1-1001-21-21-21-2-12-12-12-12000000000000000020201111-1-1-1-100000000
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χ3944444-21414144-24-24-214-2-211-2-2-2-2111111-2-21-21-21-21-2-40-400000000022-2-2220022000000000000000000-12-121-21-2-1-1-1-11111-10-100000000000000000
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χ424444-24414141-24-24-2441-2-211-2-2-2-2111111-2-2-21-21-21-21040400000000-2-2-2-200-2-200-2-20000000000000000-21-21-21-211111111101010000000000000000
χ434444-24414141-24-24-2441-2-211-2-2-2-2111111-2-2-21-21-21-210-40-40000000022-2-20022002200000000000000002-12-1-21-21-1-1-1-111110-10-10000000000000000
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χ4544-4-4144-2-42-4214-1-4-1-44-211-2-211-1-1-2-22222-1-11-21-2-12-12040-42i2i−2i−2i2i2i−2i−2i0000001100-1-12i−i2i−i−2ii−2ii2i−i2i−i−2ii−2ii00000000000000000-202−i−iii−i−iii00000000
χ4644-4-4144-2-42-4214-1-4-1-44-211-2-211-1-1-2-22222-1-11-21-2-12-12040-4−2i−2i2i2i−2i−2i2i2i0000001100-1-1−2ii−2ii2i−i2i−i−2ii−2ii2i−i2i−i00000000000000000-202ii−i−iii−i−i00000000
χ4744-4-4144-2-42-4214-1-4-1-44-211-2-211-1-1-2-22222-1-11-21-2-12-120-4042i2i−2i−2i−2i−2i2i2i000000-1-100112i−i2i−i−2ii−2ii−2ii−2ii2i−i2i−i0000000000000000020-2−i−iiiii−i−i00000000
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χ734-4-4441-242-4-24-4-1-4-1412-411-2-2-1-1-112222-2-2-11-212-12-1-2100002i−2i−2i2i2-2-220000−3i3i003i−3i00−i2ii−2ii−2i−i2i-121-21-2-1200000000000000000000−iii−i-111-100000000
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χ79888822-4-4-4-4-4-4222222-4-4-4522-45-452222225-4-1-1-1-1-1-1-1-1000044440000000000000000-2-2-2-2-2-2-2-200000000000000000000000000001111000000000000
χ80888822-4-4-4-4-4-4222222-4-4-4522-45-452222225-4-1-1-1-1-1-1-1-10000-4-4-4-40000000000000000222222220000000000000000000000000000-1-1-1-1000000000000
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χ8588-8-822-4-4444422-2-2-2-2-4-45-4225-4-5422-2-2-2-24-5-1-1-1-11111000000004i4i−4i−4i00000000000000000000−2i−2i−2i−2i2i2i2i2i000000000000000000000000ii−i−i00000000
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χ8788-8-822-4-4444422-2-2-2-2-4-4-4522-454-522-2-2-2-2-54-1-1-1-1111100004i4i−4i−4i0000000000000000−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000ii−i−i000000000000
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χ8988-8-8-4-422-2-2-2-2-4-4444422225-422-2-25-4-54-54-2-2-1-1-1-11111000000000000004-40000000000000000000000000000-2-222000011-1-100000000000000000000
χ9088-8-8-4-422-2-2-2-2-4-4444422225-422-2-25-4-54-54-2-2-1-1-1-1111100000000000000-44000000000000000000000000000022-2-20000-1-11100000000000000000000
χ9188-8-8-4-422-2-2-2-2-4-444442222-4522-2-2-454-54-5-2-2-1-1-1-111110000000000004-400000000000000000000000000-2-222000011-1-1000000000000000000000000
χ9288-8-8-4-422-2-2-2-2-4-444442222-4522-2-2-454-54-5-2-2-1-1-1-11111000000000000-440000000000000000000000000022-2-20000-1-111000000000000000000000000
χ938-88-822-4-4-4-444-2-222-2-2445-422-5454-2-222-2-2-4-5-1-111-1-111000000004i−4i4i−4i00000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000i−ii−i00000000
χ948-88-822-4-4-4-444-2-222-2-2445-422-5454-2-222-2-2-4-5-1-111-1-11100000000−4i4i−4i4i000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000−ii−ii00000000
χ958-88-822-4-4-4-444-2-222-2-244-45224-5-4-5-2-222-2-254-1-111-1-11100004-44-40000000000000000-2-222-2-22200000000000000000000000000001-11-1000000000000
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χ988-88-8-488282-8-24-8-484-8-8-2-4-42244-44-2-222-2-2-44-424-2-424-20000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1008-88-8-4-42222-2-244-4-444-2-2225-4-2-22-2-545-4-542-2-1-111-1-1110000000000000000000000000000000000000000000000000000-33-3300000000000000000000
χ1018-88-8-4-42222-2-244-4-444-2-222-45-2-22-24-5-454-52-2-1-111-1-1110000000000000000000000000000000000000000000000003-33-3000000000000000000000000
χ1028-88-8-4-42222-2-244-4-444-2-222-45-2-22-24-5-454-52-2-1-111-1-111000000000000000000000000000000000000000000000000-33-33000000000000000000000000
χ1038-8-8822-4-444-4-4-2-2-2-222445-422-54-5-4-2-2-2-22245-1-11111-1-1000000004-4-4400000000000000000000-2-22222-2-20000000000000000000000001-1-1100000000
χ1048-8-8822-4-444-4-4-2-2-2-222445-422-54-5-4-2-2-2-22245-1-11111-1-100000000-444-40000000000000000000022-2-2-2-222000000000000000000000000-111-100000000
χ1058-8-8822-4-444-4-4-2-2-2-22244-45224-545-2-2-2-222-5-4-1-11111-1-100004i−4i−4i4i0000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000i−i−ii000000000000
χ1068-8-8822-4-444-4-4-2-2-2-22244-45224-545-2-2-2-222-5-4-1-11111-1-10000−4i4i4i−4i00000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000−iii−i000000000000
χ1078-8-888-428-2-828-84-848-4-2-8-4-422444-4-2-2-2-2224-42-4-24-242-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4882-8-2824-84-8-48-8-2-4-422444-4-2-2-2-2224-4-424-24-2-420000000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-422-2-2224444-4-4-2-2225-4-2-2-22-54-545-4-22-1-11111-1-100000000000000000000000000000000000000000000000000003-3-3300000000000000000000
χ1108-8-88-4-422-2-2224444-4-4-2-2225-4-2-2-22-54-545-4-22-1-11111-1-10000000000000000000000000000000000000000000000000000-333-300000000000000000000
χ1118-8-88-4-422-2-2224444-4-4-2-222-45-2-2-224-54-5-45-22-1-11111-1-10000000000000000000000000000000000000000000000003-3-33000000000000000000000000
χ1128-8-88-4-422-2-2224444-4-4-2-222-45-2-2-224-54-5-45-22-1-11111-1-1000000000000000000000000000000000000000000000000-333-3000000000000000000000000
χ113161616164-84-84-84-84-84-84-84-8-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2141414140000000000000000000000000000000000000000000000000000000000000000000000000000
χ11416161616-84-84-84-84-84-84-84-84-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2414141410000000000000000000000000000000000000000000000000000000000000000000000000000
χ1151616-16-164-84-8-48-484-8-48-484-8-2-2-2-2-2-222-2-22222221414-1-4-1-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ1161616-16-16-84-848-48-4-848-48-4-84-2-2-2-2-2-222-2-22222224141-4-1-4-10000000000000000000000000000000000000000000000000000000000000000000000000000
χ11716-1616-164-84-84-8-48-484-8-48-48-2-2-2-222-2222-2-222-2214-1-414-1-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ11816-1616-16-84-84-848-48-4-848-48-4-2-2-2-222-2222-2-222-2241-4-141-4-10000000000000000000000000000000000000000000000000000000000000000000000000000
χ11916-16-16164-84-8-484-8-48-484-8-48-2-2-2-2222-22222-2-22-214-1-4-1-4140000000000000000000000000000000000000000000000000000000000000000000000000000
χ12016-16-1616-84-848-4-848-48-4-848-4-2-2-2-2222-22222-2-22-241-4-1-4-1410000000000000000000000000000000000000000000000000000000000000000000000000000

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