Finite Group Databasebeta

← Group #72220740

Character table — Group #72220740

Order 5184.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size112444444448888888888889999121216161616161616161616161618182424242424242424242436363636363636364848484848484848727272728181108108108108108108162162162162162162162162162216216216216216216
order12233336666333366666666222224336666666666226666612121212126666666666661212121266662224444424444444461212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111111-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111-1-1-1-1-1-1
χ51111111111111111111111111-1-1111111111111111-111111111111111-1-1-1-111111111-111-1-1-1-1-1ii−i−i-1iiii−i−i−i−i-1-1ii−i−i
χ61111111111111111111111111-1-1111111111111111-111111111111111-1-1-1-111111111-111-1-1-1-1-1−i−iii-1−i−i−i−iiiii-1-1−i−iii
χ71111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111ii−i−i-1−i−i−i−iiiii11ii−i−i
χ81111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111−i−iii-1iiii−i−i−i−i11−i−iii
χ911-1111111111111-1-1-1-1111111111-111-1-1-1-111-1-1-1-1-1-111111-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111-11-11-1-111-1-111-1-11-11-11-1
χ1011-1111111111111-1-1-1-1111111111-111-1-1-1-111-1-1-1-1-1-111111-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111-1-11-11-1-1-111-1-1111-1-11-11
χ1111-1111111111111-1-1-1-111111111-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-111-111-11-1-1-1-111-1-111-111-11-1
χ1211-1111111111111-1-1-1-111111111-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-111-11-11-11-111-1-111-1-1-11-11-11
χ1311-1111111111111-1-1-1-1111111-1-11-111-1-1-1-111-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11-1-1-11i−i−ii1ii−i−i−i−iii-11i−i−ii
χ1411-1111111111111-1-1-1-1111111-1-11-111-1-1-1-111-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11-1-1-11−iii−i1−i−iiiii−i−i-11−iii−i
χ1511-1111111111111-1-1-1-1111111-1-1-1111-1-1-1-111-1-1-1-1-11-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111-1-11-1-11-1i−i−ii1−i−iiiii−i−i1-1i−i−ii
χ1611-1111111111111-1-1-1-1111111-1-1-1111-1-1-1-111-1-1-1-1-11-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111-1-11-1-11-1−iii−i1ii−i−i−i−iii1-1−iii−i
χ1722222222222222222222222-2-22200222222222222-220000000000-2-2-2-22222000000002-2-22-2-2000000-200000000000000
χ1822222222222222222222222-2-2-2-200222222222222-2-20000000000-2-2-2-2-2-2-2-200000000-2-2-2-222000000200000000000000
χ1922-2222222222222-2-2-2-22222-2-2220022-2-2-2-222-2-2-2-22-20000000000-2-2-2-2222200000000-222-2-2-2000000200000000000000
χ2022-2222222222222-2-2-2-22222-2-2-2-20022-2-2-2-222-2-2-2-2220000000000-2-2-2-2-2-2-2-200000000222222000000-200000000000000
χ212-202222-2-2-2-222220000-2-2-2-22-22-200220000-2-2000000000000000022-2-22-22-20000000000002-20000000002i−2i002i−2i000000
χ222-202222-2-2-2-222220000-2-2-2-22-22-200220000-2-2000000000000000022-2-22-22-20000000000002-2000000000−2i2i00−2i2i000000
χ232-202222-2-2-2-222220000-2-2-2-22-2-2200220000-2-2000000000000000022-2-2-22-22000000000000-220000000002-200-22000000
χ242-202222-2-2-2-222220000-2-2-2-22-2-2200220000-2-2000000000000000022-2-2-22-22000000000000-22000000000-22002-2000000
χ252-202222-2-2-2-222220000-2-2-2-2-222-200220000-2-20000000000000000-2-2222-22-2000000000000-2200000002-2002-200000000
χ262-202222-2-2-2-222220000-2-2-2-2-222-200220000-2-20000000000000000-2-2222-22-2000000000000-220000000-2200-2200000000
χ272-202222-2-2-2-222220000-2-2-2-2-22-2200220000-2-20000000000000000-2-222-22-220000000000002-200000002i−2i00−2i2i00000000
χ282-202222-2-2-2-222220000-2-2-2-2-22-2200220000-2-20000000000000000-2-222-22-220000000000002-20000000−2i2i002i−2i00000000
χ29444144-2144-2-2-2-2-2144-2-2-2-2-200440011-2-2-2-21111110400000000000000-2-21100000000100-20000222200000000000-1-1-1-1
χ30444144-2144-2-2-2-2-2144-2-2-2-2-200440011-2-2-2-21111110400000000000000-2-21100000000100-20000-2-2-2-2000000000001111
χ31444144-2144-2-2-2-2-2144-2-2-2-2-200-4-40011-2-2-2-21111110-40000000000000022-1-100000000-100200002i2i−2i−2i00000000000−i−iii
χ32444144-2144-2-2-2-2-2144-2-2-2-2-200-4-40011-2-2-2-21111110-40000000000000022-1-100000000-10020000−2i−2i2i2i00000000000ii−i−i
χ3344441-2441-2411-2-241-2411-2-24400441-211-2-21-211-2-24011-2-2411-2-241-21-2000011-2-211-2-201-2000000000000000000000000
χ3444441-2441-2411-2-241-2411-2-24400-4-41-211-2-21-211-2-240-1-122-4-1-122-41-21-20000-1-122-1-12201-2000000000000000000000000
χ3544441-2441-2411-2-241-2411-2-2-4-400001-211-2-21-211-2-2-403-30003-3000-12-1200003-3003-3000-12000000000000000000000000
χ3644441-2441-2411-2-241-2411-2-2-4-400001-211-2-21-211-2-2-40-33000-33000-12-120000-3300-33000-12000000000000000000000000
χ374444-2144-214-2-2114-214-2-211440044-21-2-211-21-2-21140-2-2114-2-2114-21-210000-2-211-2-2110-21000000000000000000000000
χ384444-2144-214-2-2114-214-2-2114400-4-4-21-2-211-21-2-2114022-1-1-422-1-1-4-21-21000022-1-122-1-10-21000000000000000000000000
χ394444-2144-214-2-2114-214-2-211-4-40000-21-2-211-21-2-211-40003-30003-302-12-10000003-3003-302-1000000000000000000000000
χ404444-2144-214-2-2114-214-2-211-4-40000-21-2-211-21-2-211-4000-33000-3302-12-1000000-3300-3302-1000000000000000000000000
χ41444-2441-24411111-24411111004422-2-21111-2-2-2-2-2-2042222-12222-1000011-2-2-1-1-1-1-1-1-1-1-200100220000000000000-1-10000
χ42444-2441-24411111-244111110044-2-2-2-21111-2-2-2-2-2-204-2-2-2-21-2-2-2-21000011-2-211111111-200100-2-20000000000000110000
χ43444-2441-24411111-2441111100-4-422-2-21111-2-2-2-2-2-20-42222-12222-10000-1-122-1-1-1-1-1-1-1-1200-100-2-20000000000000110000
χ44444-2441-24411111-2441111100-4-4-2-2-2-21111-2-2-2-2-2-20-4-2-2-2-21-2-2-2-210000-1-12211111111200-100220000000000000-1-10000
χ4544-4144-2144-2-2-2-2-2-1-4-42-2-2-2-200440011222211-1-1-1-10-400000000000000-2-21100000000-100200002-22-200000000000-11-11
χ4644-4144-2144-2-2-2-2-2-1-4-42-2-2-2-200440011222211-1-1-1-10-400000000000000-2-21100000000-10020000-22-22000000000001-11-1
χ4744-4144-2144-2-2-2-2-2-1-4-42-2-2-2-200-4-40011222211-1-1-1-1040000000000000022-1-100000000100-200002i−2i−2i2i00000000000−iii−i
χ4844-4144-2144-2-2-2-2-2-1-4-42-2-2-2-200-4-40011222211-1-1-1-1040000000000000022-1-100000000100-20000−2i2i2i−2i00000000000i−i−ii
χ4944-441-2441-2411-2-2-4-12-411-2-244004-41-2-1-1221-2-1-122-4011-2-24-1-122-41-21-2000011-2-2-1-1220-12000000000000000000000000
χ5044-441-2441-2411-2-2-4-12-411-2-24400-441-2-1-1221-2-1-122-40-1-122-411-2-241-21-20000-1-12211-2-20-12000000000000000000000000
χ5144-441-2441-2411-2-2-4-12-411-2-2-4-400001-2-1-1221-2-1-122403-3000-33000-12-1200003-300-330001-2000000000000000000000000
χ5244-441-2441-2411-2-2-4-12-411-2-2-4-400001-2-1-1221-2-1-12240-330003-3000-12-120000-33003-30001-2000000000000000000000000
χ5344-44-2144-214-2-211-42-1-4-2-21144004-4-2122-1-1-2122-1-1-40-2-211422-1-1-4-21-210000-2-21122-1-102-1000000000000000000000000
χ5444-44-2144-214-2-211-42-1-4-2-2114400-44-2122-1-1-2122-1-1-4022-1-1-4-2-2114-21-21000022-1-1-2-21102-1000000000000000000000000
χ5544-44-2144-214-2-211-42-1-4-2-211-4-40000-2122-1-1-2122-1-140003-3000-3302-12-10000003-300-330-21000000000000000000000000
χ5644-44-2144-214-2-211-42-1-4-2-211-4-40000-2122-1-1-2122-1-14000-330003-302-12-1000000-33003-30-21000000000000000000000000
χ5744-4-2441-244111112-4-4-1111100442-2-2-2-1-1-1-1-2-222220-42222-1-2-2-2-21000011-2-2-1-1-1-11111200-1002-20000000000000-110000
χ5844-4-2441-244111112-4-4-111110044-22-2-2-1-1-1-1-2-222220-4-2-2-2-212222-1000011-2-21111-1-1-1-1200-100-2200000000000001-10000
χ5944-4-2441-244111112-4-4-1111100-4-42-2-2-2-1-1-1-1-2-22222042222-1-2-2-2-210000-1-122-1-1-1-11111-200100-2200000000000001-10000
χ6044-4-2441-244111112-4-4-1111100-4-4-22-2-2-1-1-1-1-2-2222204-2-2-2-212222-10000-1-1221111-1-1-1-1-2001002-20000000000000-110000
χ61888-42-42-42-425-4-1-1-42-425-4-1-1000044-125-4-1-1-12-1-122004-2-2-2-24-2-2-2-200000000-2111-2111000000000000000000000000000
χ62888-42-42-42-425-4-1-1-42-425-4-1-10000-4-4-125-4-1-1-12-1-12200-42222-42222000000002-1-1-12-1-1-1000000000000000000000000000
χ63888-42-42-42-42-45-1-1-42-42-45-1-1000044-12-45-1-1-12-1-12200-24-2-2-2-24-2-2-2000000001-2111-211000000000000000000000000000
χ64888-42-42-42-42-45-1-1-42-42-45-1-10000-4-4-12-45-1-1-12-1-122002-42222-422200000000-12-1-1-12-1-1000000000000000000000000000
χ65888-4-422-4-422-1-15-4-4-422-1-15-40000442-1-1-15-42-122-1-100-2-24-2-2-2-24-2-20000000011-2111-21000000000000000000000000000
χ66888-4-422-4-422-1-15-4-4-422-1-15-40000-4-42-1-1-15-42-122-1-10022-42222-42200000000-1-12-1-1-12-1000000000000000000000000000
χ67888-4-422-4-422-1-1-45-4-422-1-1-450000442-1-1-1-452-122-1-100-2-2-24-2-2-2-24-200000000111-2111-2000000000000000000000000000
χ68888-4-422-4-422-1-1-45-4-422-1-1-450000-4-42-1-1-1-452-122-1-100222-42222-4200000000-1-1-12-1-1-12000000000000000000000000000
χ6988-8-42-42-42-425-4-1-14-24-25-4-1-100004-4-12-5411-1211-2-2004-2-2-2-2-4222200000000-21112-1-1-1000000000000000000000000000
χ7088-8-42-42-42-425-4-1-14-24-25-4-1-10000-44-12-5411-1211-2-200-422224-2-2-2-2000000002-1-1-1-2111000000000000000000000000000
χ7188-8-42-42-42-42-45-1-14-24-2-45-1-100004-4-124-511-1211-2-200-24-2-2-22-4222000000001-211-12-1-1000000000000000000000000000
χ7288-8-42-42-42-42-45-1-14-24-2-45-1-10000-44-124-511-1211-2-2002-4222-24-2-2-200000000-12-1-11-211000000000000000000000000000
χ7388-8-4-422-4-422-1-15-444-2-2-1-15-400004-42-111-542-1-2-21100-2-24-2-222-4220000000011-21-1-12-1000000000000000000000000000
χ7488-8-4-422-4-422-1-15-444-2-2-1-15-40000-442-111-542-1-2-2110022-422-2-24-2-200000000-1-12-111-21000000000000000000000000000
χ7588-8-4-422-4-422-1-1-4544-2-2-1-1-4500004-42-1114-52-1-2-21100-2-2-24-2222-4200000000111-2-1-1-12000000000000000000000000000
χ7688-8-4-422-4-422-1-1-4544-2-2-1-1-450000-442-1114-52-1-2-21100222-42-2-2-24-200000000-1-1-12111-2000000000000000000000000000
χ778-80288-4-2-8-84-4-4-4-400004444008-800220000-2-200000000000000000000-442-200000000000000000000000000000000000
χ788-80288-4-2-8-84-4-4-4-40000444400-8800220000-2-2000000000000000000004-4-2200000000000000000000000000000000000
χ798-8082-48-8-24-822-4-40000-2-2448-800002-40000-2400000000000000002-4-24000000000000000000000000000000000000000
χ808-8082-48-8-24-822-4-40000-2-244-8800002-40000-240000000000000000-242-4000000000000000000000000000000000000000
χ818-808-428-84-2-8-4-422000044-2-28-80000-4200004-20000000000000000-424-2000000000000000000000000000000000000000
χ828-808-428-84-2-8-4-422000044-2-2-880000-4200004-200000000000000004-2-42000000000000000000000000000000000000000
χ838-80-48824-8-8-222220000-2-2-2-2008-800-4-4000044000000000000000000002-2-4400000000000000000000000000000000000
χ848-80-48824-8-8-222220000-2-2-2-200-8800-4-400004400000000000000000000-224-400000000000000000000000000000000000
χ8516161644-8-844-8-8-2-24444-8-8-2-2440000001-2-2-2441-211-2-20000000000000000000000000000000000000000000000000000000
χ861616164-84-84-84-844-2-24-84-844-2-2000000-2144-2-2-21-2-2110000000000000000000000000000000000000000000000000000000
χ871616-1644-8-844-8-8-2-244-4-488-2-2440000001-222-4-41-2-1-1220000000000000000000000000000000000000000000000000000000
χ881616-164-84-84-84-844-2-2-48-4844-2-2000000-21-4-422-2122-1-10000000000000000000000000000000000000000000000000000000
χ8916-16044-8-8-4-488-2-244000022-4-40000001-20000-129-9000000000000000000000000000000000000000000000000000000000
χ9016-16044-8-8-4-488-2-244000022-4-40000001-20000-12-99000000000000000000000000000000000000000000000000000000000
χ9116-1604-84-8-48-4844-2-20000-4-422000000-2100002-1009-90000000000000000000000000000000000000000000000000000000
χ9216-1604-84-8-48-4844-2-20000-4-422000000-2100002-100-990000000000000000000000000000000000000000000000000000000
χ9316-160-84-848-48-410-8-2-20000-10822000000-2400002-400000000000000000000000000000000000000000000000000000000000
χ9416-160-84-848-48-4-810-2-200008-1022000000-2400002-400000000000000000000000000000000000000000000000000000000000
χ9516-160-8-84488-4-4-2-210-8000022-1080000004-20000-4200000000000000000000000000000000000000000000000000000000000
χ9616-160-8-84488-4-4-2-2-8100000228-100000004-20000-4200000000000000000000000000000000000000000000000000000000000

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