Finite Group Databasebeta

← Group #72260324

Character table — Group #72260324

Order 4800.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size13445588812121515161616162020242425323232324040606075808080801501501501501501501501502001344558881212151516161616202024242532323232404060607580808080150150150150150150150150200
order125522355101022151515151010101021515151566101023030303044444444622101022610101010223030303010101010230303030661010230303030444444446
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-11
χ311111-1111111-111111-111-111111-11-1-111-1-1ii−i−iii−i−i-111111-1111111-111111-111-111111-11-1-111-1-1ii−i−iii−i−i-1
χ411111-1111111-111111-111-111111-11-1-111-1-1−i−iii−i−iii-111111-1111111-111111-111-111111-11-1-111-1-1−i−iii−i−iii-1
χ51111-1111111-111111-1111-11111-11-11-1-1-111i−ii−ii−ii−i-11111-1111111-111111-1111-11111-11-11-1-1-111i−ii−ii−ii−i-1
χ61111-1111111-111111-1111-11111-11-11-1-1-111−ii−ii−ii−ii-11111-1111111-111111-1111-11111-11-11-1-1-111−ii−ii−ii−ii-1
χ71111-1-111111-1-11111-1-11111111-1-1-1-11-1-1-1-11-1-111-1-1111111-1-111111-1-11111-1-11111111-1-1-1-11-1-1-1-11-1-111-1-111
χ81111-1-111111-1-11111-1-11111111-1-1-1-11-1-1-1-1-111-1-111-111111-1-111111-1-11111-1-11111111-1-1-1-11-1-1-1-1-111-1-111-11
χ9222222-1222222-1-1-1-122222-1-1-1-1-1-1222-1-1-1-100000000-1222222-1222222-1-1-1-122222-1-1-1-1-1-1222-1-1-1-100000000-1
χ1022222-2-122222-2-1-1-1-12-222-2-1-1-1-1-112-2-2-1-11100000000122222-2-122222-2-1-1-1-12-222-2-1-1-1-1-112-2-2-1-111000000001
χ112222-22-12222-22-1-1-1-1-2222-2-1-1-1-11-1-22-211-1-10000000012222-22-12222-22-1-1-1-1-2222-2-1-1-1-11-1-22-211-1-1000000001
χ122222-2-2-12222-2-2-1-1-1-1-2-2222-1-1-1-111-2-22111100000000-12222-2-2-12222-2-2-1-1-1-1-2-2222-1-1-1-111-2-22111100000000-1
χ133-13333033-1-1-1-1000033-1-13000000-1-1-100001111-1-1-1-103-13333033-1-1-1-1000033-1-13000000-1-1-100001111-1-1-1-10
χ143-13333033-1-1-1-1000033-1-13000000-1-1-10000-1-1-1-1111103-13333033-1-1-1-1000033-1-13000000-1-1-10000-1-1-1-111110
χ153-1333-3033-1-1-1100003-3-1-1-3000000-1110000ii−i−i−i−iii03-1333-3033-1-1-1100003-3-1-1-3000000-1110000ii−i−i−i−iii0
χ163-1333-3033-1-1-1100003-3-1-1-3000000-1110000−i−iiiii−i−i03-1333-3033-1-1-1100003-3-1-1-3000000-1110000−i−iiiii−i−i0
χ173-133-33033-1-11-10000-33-1-1-30000001-110000i−ii−i−ii−ii03-133-33033-1-11-10000-33-1-1-30000001-110000i−ii−i−ii−ii0
χ183-133-33033-1-11-10000-33-1-1-30000001-110000−ii−iii−ii−i03-133-33033-1-11-10000-33-1-1-30000001-110000−ii−iii−ii−i0
χ193-133-3-3033-1-1110000-3-3-1-1300000011-100001-1-11-111-103-133-3-3033-1-1110000-3-3-1-1300000011-100001-1-11-111-10
χ203-133-3-3033-1-1110000-3-3-1-1300000011-10000-111-11-1-1103-133-3-3033-1-1110000-3-3-1-1300000011-10000-111-11-1-110
χ21444-1044-1-14-10444-1-10-1-1-10-1-1-1-1040-1000-1-1000000000444-1044-1-14-10444-1-10-1-1-10-1-1-1-1040-1000-1-1000000000
χ22444-104-2-1-14-104-2-21−i1521+i1520-1-1-101−i1521−i1521+i1521+i1520-20-10001−i1521+i152000000000444-104-2-1-14-104-2-21−i1521+i1520-1-1-101−i1521−i1521+i1521+i1520-20-10001−i1521+i152000000000
χ23444-104-2-1-14-104-2-21+i1521−i1520-1-1-101+i1521+i1521−i1521−i1520-20-10001+i1521−i152000000000444-104-2-1-14-104-2-21+i1521−i1520-1-1-101+i1521+i1521−i1521−i1520-20-10001+i1521−i152000000000
χ24444-10-44-1-14-10-444-1-101-1-10-1-1-1-10-40100011000000000444-10-44-1-14-10-444-1-101-1-10-1-1-1-10-40100011000000000
χ25444-10-4-2-1-14-10-4-2-21−i1521+i15201-1-101−i1521−i1521+i1521+i1520201000−1+i152−1−i152000000000444-10-4-2-1-14-10-4-2-21−i1521+i15201-1-101−i1521−i1521+i1521+i1520201000−1+i152−1−i152000000000
χ26444-10-4-2-1-14-10-4-2-21+i1521−i15201-1-101+i1521+i1521−i1521−i1520201000−1−i152−1+i152000000000444-10-4-2-1-14-10-4-2-21+i1521−i15201-1-101+i1521+i1521−i1521−i1520201000−1−i152−1+i152000000000
χ2744-14404-1-1-1440-1-144-10-1-10-1-1-1-140-100-1-10000000000044-14404-1-1-1440-1-144-10-1-10-1-1-1-140-100-1-100000000000
χ2844-1440-2-1-1-14401−i1521+i152-2-2-10-1-101−i1521+i1521−i1521+i152-20-1001−i1521+i1520000000000044-1440-2-1-1-14401−i1521+i152-2-2-10-1-101−i1521+i1521−i1521+i152-20-1001−i1521+i15200000000000
χ2944-1440-2-1-1-14401+i1521−i152-2-2-10-1-101+i1521−i1521+i1521−i152-20-1001+i1521−i1520000000000044-1440-2-1-1-14401+i1521−i152-2-2-10-1-101+i1521−i1521+i1521−i152-20-1001+i1521−i15200000000000
χ3044-14-404-1-1-14-40-1-14410-1-10-1-1-1-1-40100110000000000044-14-404-1-1-14-40-1-14410-1-10-1-1-1-1-401001100000000000
χ3144-14-40-2-1-1-14-401−i1521+i152-2-210-1-101−i1521+i1521−i1521+i15220100−1+i152−1−i1520000000000044-14-40-2-1-1-14-401−i1521+i152-2-210-1-101−i1521+i1521−i1521+i15220100−1+i152−1−i15200000000000
χ3244-14-40-2-1-1-14-401+i1521−i152-2-210-1-101+i1521−i1521+i1521−i15220100−1−i152−1+i1520000000000044-14-40-2-1-1-14-401+i1521−i152-2-210-1-101+i1521−i1521+i1521−i15220100−1−i152−1+i15200000000000
χ3388-2-20083-2-2-200-2-2-2-2003-203-2-2300000000000000000088-2-20083-2-2-200-2-2-2-2003-203-2-23000000000000000000
χ3488-2-2008-23-2-200-2-2-2-200-230-233-200000000000000000088-2-2008-23-2-200-2-2-2-200-230-233-2000000000000000000
χ3588-2-200-43-2-2-2001−i151+i151−i151+i15003-20−3+i15211−3−i15200000000000000000088-2-200-43-2-2-2001−i151+i151−i151+i15003-20−3+i15211−3−i152000000000000000000
χ3688-2-200-43-2-2-2001+i151−i151+i151−i15003-20−3−i15211−3+i15200000000000000000088-2-200-43-2-2-2001+i151−i151+i151−i15003-20−3−i15211−3+i152000000000000000000
χ3788-2-200-4-23-2-2001−i151+i151+i151−i1500-2301−3−i152−3+i152100000000000000000088-2-200-4-23-2-2001−i151+i151+i151−i1500-2301−3−i152−3+i1521000000000000000000
χ3888-2-200-4-23-2-2001+i151−i151−i151+i1500-2301−3+i152−3−i152100000000000000000088-2-200-4-23-2-2001+i151−i151−i151+i1500-2301−3+i152−3−i1521000000000000000000
χ3912-412-30120-3-3-410-400000-3110000000010000000000000012-412-30120-3-3-410-400000-31100000000100000000000000
χ4012-412-30-120-3-3-41040000031100000000-10000000000000012-412-30-120-3-3-41040000031100000000-100000000000000
χ4112-4-3121200-3-31-4-400000-30110000000100000000000000012-4-3121200-3-31-4-400000-301100000001000000000000000
χ4212-4-312-1200-3-31-440000030110000000-100000000000000012-4-312-1200-3-31-440000030110000000-1000000000000000
χ4324-8-6-60009-62200000000-320000000000000000000000024-8-6-60009-62200000000-3200000000000000000000000
χ4424-8-6-6000-6922000000002-30000000000000000000000024-8-6-6000-6922000000002-300000000000000000000000
χ4511111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4611111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1
χ4711111-1111111-111111-111-111111-11-1-111-1-1ii−i−iii−i−i-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-1-11-1-11-1-1-1-1-11-111-1-111−i−iii−i−iii1
χ4811111-1111111-111111-111-111111-11-1-111-1-1−i−iii−i−iii-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-1-11-1-11-1-1-1-1-11-111-1-111ii−i−iii−i−i1
χ491111-1111111-111111-1111-11111-11-11-1-1-111i−ii−ii−ii−i-1-1-1-1-11-1-1-1-1-1-11-1-1-1-1-11-1-1-11-1-1-1-11-11-1111-1-1−ii−ii−ii−ii1
χ501111-1111111-111111-1111-11111-11-11-1-1-111−ii−ii−ii−ii-1-1-1-1-11-1-1-1-1-1-11-1-1-1-1-11-1-1-11-1-1-1-11-11-1111-1-1i−ii−ii−ii−i1
χ511111-1-111111-1-11111-1-11111111-1-1-1-11-1-1-1-11-1-111-1-111-1-1-1-111-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-11111-11111-111-1-111-1-1
χ521111-1-111111-1-11111-1-11111111-1-1-1-11-1-1-1-1-111-1-111-11-1-1-1-111-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-11111-111111-1-111-1-11-1
χ53222222-1222222-1-1-1-122222-1-1-1-1-1-1222-1-1-1-100000000-1-2-2-2-2-2-21-2-2-2-2-2-21111-2-2-2-2-2111111-2-2-21111000000001
χ5422222-2-122222-2-1-1-1-12-222-2-1-1-1-1-112-2-2-1-111000000001-2-2-2-2-221-2-2-2-2-221111-22-2-2211111-1-22211-1-100000000-1
χ552222-22-12222-22-1-1-1-1-2222-2-1-1-1-11-1-22-211-1-1000000001-2-2-2-22-21-2-2-2-22-211112-2-2-221111-112-22-1-11100000000-1
χ562222-2-2-12222-2-2-1-1-1-1-2-2222-1-1-1-111-2-22111100000000-1-2-2-2-2221-2-2-2-222111122-2-2-21111-1-122-2-1-1-1-1000000001
χ573-13333033-1-1-1-1000033-1-13000000-1-1-100001111-1-1-1-10-31-3-3-3-30-3-311110000-3-311-30000001110000-1-1-1-111110
χ583-13333033-1-1-1-1000033-1-13000000-1-1-10000-1-1-1-111110-31-3-3-3-30-3-311110000-3-311-300000011100001111-1-1-1-10
χ593-1333-3033-1-1-1100003-3-1-1-3000000-1110000ii−i−i−i−iii0-31-3-3-330-3-3111-10000-331130000001-1-10000−i−iiiii−i−i0
χ603-1333-3033-1-1-1100003-3-1-1-3000000-1110000−i−iiiii−i−i0-31-3-3-330-3-3111-10000-331130000001-1-10000ii−i−i−i−iii0
χ613-133-33033-1-11-10000-33-1-1-30000001-110000i−ii−i−ii−ii0-31-3-33-30-3-311-1100003-3113000000-11-10000−ii−iii−ii−i0
χ623-133-33033-1-11-10000-33-1-1-30000001-110000−ii−iii−ii−i0-31-3-33-30-3-311-1100003-3113000000-11-10000i−ii−i−ii−ii0
χ633-133-3-3033-1-1110000-3-3-1-1300000011-100001-1-11-111-10-31-3-3330-3-311-1-100003311-3000000-1-110000-111-11-1-110
χ643-133-3-3033-1-1110000-3-3-1-1300000011-10000-111-11-1-110-31-3-3330-3-311-1-100003311-3000000-1-1100001-1-11-111-10
χ65444-1044-1-14-10444-1-10-1-1-10-1-1-1-1040-1000-1-1000000000-4-4-410-4-411-410-4-4-4110111011110-40100011000000000
χ66444-104-2-1-14-104-2-21−i1521+i1520-1-1-101−i1521−i1521+i1521+i1520-20-10001−i1521+i152000000000-4-4-410-4211-410-422−1+i152−1−i15201110−1+i152−1+i152−1−i152−1−i1520201000−1+i152−1−i152000000000
χ67444-104-2-1-14-104-2-21+i1521−i1520-1-1-101+i1521+i1521−i1521−i1520-20-10001+i1521−i152000000000-4-4-410-4211-410-422−1−i152−1+i15201110−1−i152−1−i152−1+i152−1+i1520201000−1−i152−1+i152000000000
χ68444-10-44-1-14-10-444-1-101-1-10-1-1-1-10-40100011000000000-4-4-4104-411-4104-4-4110-11101111040-1000-1-1000000000
χ69444-10-4-2-1-14-10-4-2-21−i1521+i15201-1-101−i1521−i1521+i1521+i1520201000−1+i152−1−i152000000000-4-4-4104211-410422−1+i152−1−i1520-1110−1+i152−1+i152−1−i152−1−i1520-20-10001−i1521+i152000000000
χ70444-10-4-2-1-14-10-4-2-21+i1521−i15201-1-101+i1521+i1521−i1521−i1520201000−1−i152−1+i152000000000-4-4-4104211-410422−1−i152−1+i1520-1110−1−i152−1−i152−1+i152−1+i1520-20-10001+i1521−i152000000000
χ7144-14404-1-1-1440-1-144-10-1-10-1-1-1-140-100-1-100000000000-4-41-4-40-4111-4-4011-4-4101101111-401001100000000000
χ7244-1440-2-1-1-14401−i1521+i152-2-2-10-1-101−i1521+i1521−i1521+i152-20-1001−i1521+i15200000000000-4-41-4-402111-4-40−1+i152−1−i1522210110−1+i152−1−i152−1+i152−1−i15220100−1+i152−1−i15200000000000
χ7344-1440-2-1-1-14401+i1521−i152-2-2-10-1-101+i1521−i1521+i1521−i152-20-1001+i1521−i15200000000000-4-41-4-402111-4-40−1−i152−1+i1522210110−1−i152−1+i152−1−i152−1+i15220100−1−i152−1+i15200000000000
χ7444-14-404-1-1-14-40-1-14410-1-10-1-1-1-1-401001100000000000-4-41-440-4111-44011-4-4-10110111140-100-1-100000000000
χ7544-14-40-2-1-1-14-401−i1521+i152-2-210-1-101−i1521+i1521−i1521+i15220100−1+i152−1−i15200000000000-4-41-4402111-440−1+i152−1−i15222-10110−1+i152−1−i152−1+i152−1−i152-20-1001−i1521+i15200000000000
χ7644-14-40-2-1-1-14-401+i1521−i152-2-210-1-101+i1521−i1521+i1521−i15220100−1−i152−1+i15200000000000-4-41-4402111-440−1−i152−1+i15222-10110−1−i152−1+i152−1−i152−1+i152-20-1001+i1521−i15200000000000
χ7788-2-20083-2-2-200-2-2-2-2003-203-2-23000000000000000000-8-82200-8-322200222200-320-322-3000000000000000000
χ7888-2-2008-23-2-200-2-2-2-200-230-233-2000000000000000000-8-82200-82-322002222002-302-3-32000000000000000000
χ7988-2-200-43-2-2-2001−i151+i151−i151+i15003-20−3+i15211−3−i152000000000000000000-8-822004-322200−1+i15−1−i15−1+i15−1−i1500-3203−i152-1-13+i152000000000000000000
χ8088-2-200-43-2-2-2001+i151−i151+i151−i15003-20−3−i15211−3+i152000000000000000000-8-822004-322200−1−i15−1+i15−1−i15−1+i1500-3203+i152-1-13−i152000000000000000000
χ8188-2-200-4-23-2-2001−i151+i151+i151−i1500-2301−3−i152−3+i1521000000000000000000-8-8220042-32200−1+i15−1−i15−1−i15−1+i15002-30-13+i1523−i152-1000000000000000000
χ8288-2-200-4-23-2-2001+i151−i151−i151+i1500-2301−3+i152−3−i1521000000000000000000-8-8220042-32200−1−i15−1+i15−1+i15−1−i15002-30-13−i1523+i152-1000000000000000000
χ8312-412-30120-3-3-410-400000-31100000000100000000000000-124-1230-120334-104000003-1-100000000-100000000000000
χ8412-412-30-120-3-3-41040000031100000000-100000000000000-124-1230120334-10-400000-3-1-100000000100000000000000
χ8512-4-3121200-3-31-4-400000-301100000001000000000000000-1243-12-120033-1440000030-1-10000000-1000000000000000
χ8612-4-312-1200-3-31-440000030110000000-1000000000000000-1243-12120033-14-400000-30-1-100000001000000000000000
χ8724-8-6-60009-62200000000-3200000000000000000000000-24866000-96-2-2000000003-200000000000000000000000
χ8824-8-6-6000-6922000000002-300000000000000000000000-248660006-9-2-200000000-2300000000000000000000000

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