Finite Group Databasebeta

← Group #72260342

Character table — Group #72260342

Order 4800.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size1133444488888810101212121216161616161616162020202024242424252530303232323232323232404040406060606075758080808080808080200200300300300300300300300300
order1222551010355610104410101010151515153030303020202020101010102244151515153030303012121212202020202260606060606060606644444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111-111111111111111-1-11111-1-11-11111111111-1-111-1-1-1-11111-1-1-1-1-1-1ii−i−iii−i−i
χ4111111111111111-111111111111111-1-11111-1-11-11111111111-1-111-1-1-1-11111-1-1-1-1-1-1−i−iii−i−iii
χ511111111111111-11111111111111-1-1111111-1-1-1111111111-1-111-1-111-1-1-1-1-1-11111-1-1i−ii−ii−ii−i
χ611111111111111-11111111111111-1-1111111-1-1-1111111111-1-111-1-111-1-1-1-1-1-11111-1-1−ii−ii−ii−ii
χ711111111111111-1-1111111111111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-111-1-11
χ811111111111111-1-1111111111111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-111-1-111-1
χ922222222-122-122222222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-100000000
χ1022222222-122-1222-22222-1-1-1-1-1-1-1-122-2-22222-2-22-2-1-1-1-1-1-1-1-1-1-11122-2-2-2-2-1-1-1-111111100000000
χ1122222222-122-122-222222-1-1-1-1-1-1-1-1-2-2222222-2-2-22-1-1-1-1-1-1-1-111-1-1-2-222-2-21111-1-1-1-11100000000
χ1222222222-122-122-2-22222-1-1-1-1-1-1-1-1-2-2-2-2222222-2-2-1-1-1-1-1-1-1-11111-2-2-2-22211111111-1-100000000
χ132-22-222-2-2222-2-2-20022-2-22222-2-2-2-2000022-2-22-2002222-2-2-2-2000000002-2000000002-200000000
χ142-22-222-2-2222-2-2-20022-2-22222-2-2-2-2000022-2-2-22002222-2-2-2-200000000-2200000000-2200000000
χ152-22-222-2-2-1221-2-20022-2-2-1-1-1-11111000022-2-22-200-1-1-1-111113−33−300002-233−3−333−3−3-1100000000
χ162-22-222-2-2-1221-2-20022-2-2-1-1-1-11111000022-2-22-200-1-1-1-11111−33−3300002-2−3−333−3−333-1100000000
χ172-22-222-2-2-1221-2-20022-2-2-1-1-1-11111000022-2-2-2200-1-1-1-111113−3−330000-2233−3−3−3−3331-100000000
χ182-22-222-2-2-1221-2-20022-2-2-1-1-1-11111000022-2-2-2200-1-1-1-11111−333−30000-22−3−33333−3−31-100000000
χ1933-1-1333303303333-1-1-1-1000000003333-1-1-1-133-1-1000000000000-1-1-1-1-1-100000000001111-1-1-1-1
χ2033-1-1333303303333-1-1-1-1000000003333-1-1-1-133-1-1000000000000-1-1-1-1-1-10000000000-1-1-1-11111
χ2133-1-133330330333-3-1-1-1-10000000033-3-3-1-1-1-1-3-3-11000000000000-1-111110000000000ii−i−i−i−iii
χ2233-1-133330330333-3-1-1-1-10000000033-3-3-1-1-1-1-3-3-11000000000000-1-111110000000000−i−iiiii−i−i
χ2333-1-13333033033-33-1-1-1-100000000-3-333-1-1-1-1-3-31-100000000000011-1-1110000000000i−ii−i−ii−ii
χ2433-1-13333033033-33-1-1-1-100000000-3-333-1-1-1-1-3-31-100000000000011-1-1110000000000−ii−iii−ii−i
χ2533-1-13333033033-3-3-1-1-1-100000000-3-3-3-3-1-1-1-133110000000000001111-1-100000000001-1-11-111-1
χ2633-1-13333033033-3-3-1-1-1-100000000-3-3-3-3-1-1-1-133110000000000001111-1-10000000000-111-11-1-11
χ2744444-14-14-1-14-1-1044-14-144-1-144-1-100-1-1-1-1-1-10004-1-1-1-1-1-1-1-1004400-1-1000000-1-1-1-10000000000
χ2844444-14-14-1-14-1-10-44-14-144-1-144-1-10011-1-1-1-1000-4-1-1-1-1-1-1-1-100-4-4001100000011110000000000
χ2944444-14-1-2-1-1-2-1-1044-14-1-2-21−i1521+i152-2-21−i1521+i15200-1-1-1-1-1-100041−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i15200-2-200-1-10000001−i1521+i1521−i1521+i1520000000000
χ3044444-14-1-2-1-1-2-1-1044-14-1-2-21+i1521−i152-2-21+i1521−i15200-1-1-1-1-1-100041+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i15200-2-200-1-10000001+i1521−i1521+i1521−i1520000000000
χ3144444-14-1-2-1-1-2-1-10-44-14-1-2-21−i1521+i152-2-21−i1521+i1520011-1-1-1-1000-41−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i15200220011000000−1+i152−1−i152−1+i152−1−i1520000000000
χ3244444-14-1-2-1-1-2-1-10-44-14-1-2-21+i1521−i152-2-21+i1521−i1520011-1-1-1-1000-41+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i15200220011000000−1−i152−1+i152−1−i152−1+i1520000000000
χ334444-14-144-1-14-1-140-14-14-1-144-1-144-1-100-1-1-1-10040-1-1-1-1-1-1-1-14400-1-10000-1-1-1-100000000000000
χ344444-14-144-1-14-1-1-40-14-14-1-144-1-1441100-1-1-1-100-40-1-1-1-1-1-1-1-1-4-400110000111100000000000000
χ354444-14-14-2-1-1-2-1-140-14-141−i1521+i152-2-21−i1521+i152-2-2-1-100-1-1-1-100401−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152-2-200-1-100001−i1521+i1521−i1521+i15200000000000000
χ364444-14-14-2-1-1-2-1-140-14-141+i1521−i152-2-21+i1521−i152-2-2-1-100-1-1-1-100401+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152-2-200-1-100001+i1521−i1521+i1521−i15200000000000000
χ374444-14-14-2-1-1-2-1-1-40-14-141−i1521+i152-2-21−i1521+i152-2-21100-1-1-1-100-401−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1522200110000−1+i152−1−i152−1+i152−1−i15200000000000000
χ384444-14-14-2-1-1-2-1-1-40-14-141+i1521−i152-2-21+i1521−i152-2-21100-1-1-1-100-401+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1522200110000−1−i152−1+i152−1−i152−1+i15200000000000000
χ394-44-44-1-414-1-1-411004-1-4144-1-1-4-41100−i5i5-1-1110000-1-1-1-11111000000−i5i5000000−i5i5i5−i50000000000
χ404-44-44-1-414-1-1-411004-1-4144-1-1-4-41100i5−i5-1-1110000-1-1-1-11111000000i5−i5000000i5−i5−i5i50000000000
χ414-44-44-1-41-2-1-1211004-1-41-2-21−i1521+i15222−1+i152−1−i15200−i5i5-1-11100001−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i15200−232300−i5i5000000−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ47ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ470000000000
χ424-44-44-1-41-2-1-1211004-1-41-2-21−i1521+i15222−1+i152−1−i15200i5−i5-1-11100001−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i1520023−2300i5−i5000000ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ47−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ470000000000
χ434-44-44-1-41-2-1-1211004-1-41-2-21+i1521−i15222−1−i152−1+i15200−i5i5-1-11100001+i1521+i1521−i1521−i152−1−i152−1−i152−1+i152−1+i1520023−2300−i5i5000000ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ59−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ590000000000
χ444-44-44-1-41-2-1-1211004-1-41-2-21+i1521−i15222−1−i152−1+i15200i5−i5-1-11100001+i1521+i1521−i1521−i152−1−i152−1−i152−1+i152−1+i15200−232300i5−i5000000−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ59ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ590000000000
χ454-44-4-141-44-1-1-41100-141-4-1-14411-4-4−i5i500-1-1110000-1-1-1-111110000−i5i50000−i5i5i5−i500000000000000
χ464-44-4-141-44-1-1-41100-141-4-1-14411-4-4i5−i500-1-1110000-1-1-1-111110000i5−i50000i5−i5−i5i500000000000000
χ474-44-4-141-4-2-1-121100-141-41−i1521+i152-2-2−1+i152−1−i15222−i5i500-1-11100001−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152−232300−i5i50000−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ47ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ4700000000000000
χ484-44-4-141-4-2-1-121100-141-41−i1521+i152-2-2−1+i152−1−i15222i5−i500-1-11100001−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i15223−2300i5−i50000ζ7−ζ11+ζ43−ζ59ζ19−ζ23+ζ31−ζ47−ζ7+ζ11−ζ43+ζ59−ζ19+ζ23−ζ31+ζ4700000000000000
χ494-44-4-141-4-2-1-121100-141-41+i1521−i152-2-2−1−i152−1+i15222−i5i500-1-11100001+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i15223−2300−i5i50000ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ59−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ5900000000000000
χ504-44-4-141-4-2-1-121100-141-41+i1521−i152-2-2−1−i152−1+i15222i5−i500-1-11100001+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152−232300i5−i50000−ζ19+ζ23−ζ31+ζ47−ζ7+ζ11−ζ43+ζ59ζ19−ζ23+ζ31−ζ47ζ7−ζ11+ζ43−ζ5900000000000000
χ516-6-2266-6-60660-6-600-2-222000000000000-2-2226-6000000000000000000-22000000000000000000
χ526-6-2266-6-60660-6-600-2-222000000000000-2-222-660000000000000000002-2000000000000000000
χ538888-2-2-2-283-283-200-2-2-2-2-2-2-2-2-2-2-2-200003-23-200003-2-233-2-230000000000000000000000000000
χ548888-2-2-2-28-238-2300-2-2-2-2-2-2-2-2-2-2-2-20000-23-230000-233-2-233-20000000000000000000000000000
χ558888-2-2-2-2-43-2-43-200-2-2-2-21−i151+i151−i151+i151−i151+i151−i151+i1500003-23-20000−3+i15211−3−i152−3+i15211−3−i1520000000000000000000000000000
χ568888-2-2-2-2-43-2-43-200-2-2-2-21+i151−i151+i151−i151+i151−i151+i151−i1500003-23-20000−3−i15211−3+i152−3−i15211−3+i1520000000000000000000000000000
χ578888-2-2-2-2-4-23-4-2300-2-2-2-21−i151+i151+i151−i151−i151+i151+i151−i150000-23-2300001−3−i152−3+i15211−3−i152−3+i15210000000000000000000000000000
χ588888-2-2-2-2-4-23-4-2300-2-2-2-21+i151−i151−i151+i151+i151−i151−i151+i150000-23-2300001−3+i152−3−i15211−3+i152−3−i15210000000000000000000000000000
χ598-88-8-2-22283-2-8-3200-2-222-2-2-2-2222200003-2-3200003-2-23-322-30000000000000000000000000000
χ608-88-8-2-2228-23-82-300-2-222-2-2-2-222220000-232-30000-233-22-3-320000000000000000000000000000
χ618-88-8-2-222-43-24-3200-2-2221−i151+i151−i151+i15−1+i15−1−i15−1+i15−1−i1500003-2-320000−3+i15211−3−i1523−i152-1-13+i1520000000000000000000000000000
χ628-88-8-2-222-43-24-3200-2-2221+i151−i151+i151−i15−1−i15−1+i15−1−i15−1+i1500003-2-320000−3−i15211−3+i1523+i152-1-13−i1520000000000000000000000000000
χ638-88-8-2-222-4-2342-300-2-2221−i151+i151+i151−i15−1+i15−1−i15−1−i15−1+i150000-232-300001−3−i152−3+i1521-13+i1523−i152-10000000000000000000000000000
χ648-88-8-2-222-4-2342-300-2-2221+i151−i151−i151+i15−1−i15−1+i15−1+i15−1−i150000-232-300001−3+i152−3−i1521-13−i1523+i152-10000000000000000000000000000
χ651212-4-412-312-30-3-30-3-3012-41-410000000000-3-31111000-4000000000000001100000000000000000000
χ661212-4-412-312-30-3-30-3-30-12-41-410000000000331111000400000000000000-1-100000000000000000000
χ671212-4-4-312-3120-3-30-3-31201-41-400000000-3-300111100-40000000000000110000000000000000000000
χ681212-4-4-312-3120-3-30-3-3-1201-41-400000000330011110040000000000000-1-10000000000000000000000
χ6912-12-4412-3-1230-3-303300-414-10000000000−3i53i511-1-1000000000000000000i5−i500000000000000000000
χ7012-12-4412-3-1230-3-303300-414-100000000003i5−3i511-1-1000000000000000000−i5i500000000000000000000
χ7112-12-44-3123-120-3-3033001-4-1400000000−3i53i50011-1-10000000000000000i5−i50000000000000000000000
χ7212-12-44-3123-120-3-3033001-4-14000000003i5−3i50011-1-10000000000000000−i5i50000000000000000000000
χ732424-8-8-6-6-6-609-609-6002222000000000000-32-320000000000000000000000000000000000000000
χ742424-8-8-6-6-6-60-690-690022220000000000002-32-30000000000000000000000000000000000000000
χ7524-24-88-6-66609-60-960022-2-2000000000000-323-20000000000000000000000000000000000000000
χ7624-24-88-6-6660-6906-90022-2-20000000000002-3-230000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.