Finite Group Databasebeta

← Group #72242612

Character table — Group #72242612

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11112244444444888888888888816161616161616161616161616161616202020202525252540404040404040404040505080808080100100100100100100100100200200200200200
order1222445510101010101045510101010101020202020202020202020202020202020202020202244222244101010102020202044202020208888888844444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1
χ311111111111111111111111111111111111111111111-11-1-1-1-1-11-111-1-111-1-1-1-111-1-1iiii−i−i−i−i-1ii−i−i
χ411111111111111111111111111111111111111111111-11-1-1-1-1-11-111-1-111-1-1-1-111-1-1−i−i−i−iiiii-1−i−iii
χ51111111111111111111111111111111111111111111-11-11-1-1-1-1-11-1-111-1-111-1-1-1-111ii−i−iii−i−i-1i−ii−i
χ61111111111111111111111111111111111111111111-11-11-1-1-1-1-11-1-111-1-111-1-1-1-111−i−iii−i−iii-1−ii−ii
χ71111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-11
χ81111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11-111-1
χ911111111111111-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111111111-1-1-1-111111111-1-1-1-1-1
χ1011111111111111-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ1111111111111111-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1111-1-111-1-1-1-1-1-111iiii−i−i−i−i1−i−iii
χ1211111111111111-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1111-1-111-1-1-1-1-1-111−i−i−i−iiiii1ii−i−i
χ1311111111111111-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-1-11-1-1-111-1-111-1-111-1-1ii−i−iii−i−i1−ii−ii
χ1411111111111111-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-1-11-1-1-111-1-111-1-111-1-1−i−iii−i−iii1i−ii−i
χ1511111111111111-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1
χ1611111111111111-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-11-1-11
χ172222-2-222222222022222222-2-2-2-20000-2-2-2-20000000022-2-22222002222-2-2-2-2-2-200000000000000000
χ182222-2-222222222022222222-2-2-2-20000-2-2-2-2000000002-2-22-2-2-2-20022-2-2-2-2222200000000000000000
χ192222-2-222222222022222222-2-2-2-20000-2-2-2-200000000-222-2-2-2-2-200-2-22222-2-22200000000000000000
χ202222-2-222222222022222222-2-2-2-20000-2-2-2-200000000-2-222222200-2-2-2-22222-2-200000000000000000
χ212-2-222-222-2-2-2-222022-2-222-2-222-2-2000022-2-20000000000002-22-200000000002-20000002i−2i2i−2i0000000
χ222-2-222-222-2-2-2-222022-2-222-2-222-2-2000022-2-20000000000002-22-200000000002-2000000−2i2i−2i2i0000000
χ232-2-222-222-2-2-2-222022-2-222-2-222-2-2000022-2-2000000000000-22-220000000000-220000002-2-220000000
χ242-2-222-222-2-2-2-222022-2-222-2-222-2-2000022-2-2000000000000-22-220000000000-22000000-222-20000000
χ252-2-22-2222-2-2-2-222022-2-222-2-2-2-2220000-2-2220000000000002-22-20000000000-2200002-200002-200000
χ262-2-22-2222-2-2-2-222022-2-222-2-2-2-2220000-2-2220000000000002-22-20000000000-220000-220000-2200000
χ272-2-22-2222-2-2-2-222022-2-222-2-2-2-2220000-2-222000000000000-22-2200000000002-200002i−2i0000−2i2i00000
χ282-2-22-2222-2-2-2-222022-2-222-2-2-2-2220000-2-222000000000000-22-2200000000002-20000−2i2i00002i−2i00000
χ294444444-14-14-14-14-1-1-1-1-1-1-1-14-14-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1040400000400-1-100-1-10000-1-10000000000000
χ304444444-14-14-14-14-1-1-1-1-1-1-1-14-14-144-1-1-1-1-1-1-1-1-1-1-1-1-1-10-40-400000-4001100110000110000000000000
χ314444444-14-14-14-1-4-1-1-1-1-1-1-1-14-14-1-4-411-1-1-1-111111111040400000-400-1-100-1-10000110000000000000
χ324444444-14-14-14-1-4-1-1-1-1-1-1-1-14-14-1-4-411-1-1-1-1111111110-40-4000004001100110000-1-10000000000000
χ33444444-14-14-14-144-1-1-1-1-1-1-1-1-14-14-1-144-1-1-1-1-1-1-1-1-1-1-1-14040000040-1-100-1-10000-1-1000000000000000
χ34444444-14-14-14-144-1-1-1-1-1-1-1-1-14-14-1-144-1-1-1-1-1-1-1-1-1-1-1-1-40-400000-40110011000011000000000000000
χ35444444-14-14-14-14-4-1-1-1-1-1-1-1-1-14-1411-4-4-1-1-1-11111111140400000-40-1-100-1-1000011000000000000000
χ36444444-14-14-14-14-4-1-1-1-1-1-1-1-1-14-1411-4-4-1-1-1-111111111-40-400000401100110000-1-1000000000000000
χ374444-4-44-14-14-14-10-1-1-1-1-1-1-1-1-41-41005−511115555−5−5−5−5040-400000000-1-1001100005−50000000000000
χ384444-4-44-14-14-14-10-1-1-1-1-1-1-1-1-41-41005−511115555−5−5−5−50-404000000001100-1-10000−550000000000000
χ394444-4-44-14-14-14-10-1-1-1-1-1-1-1-1-41-4100−551111−5−5−5−55555040-400000000-1-100110000−550000000000000
χ404444-4-44-14-14-14-10-1-1-1-1-1-1-1-1-41-4100−551111−5−5−5−555550-404000000001100-1-100005−50000000000000
χ414444-4-4-14-14-14-140-1-1-1-1-1-1-1-11-41-45−500111155−5−555−5−540-40000000-1-1001100005−5000000000000000
χ424444-4-4-14-14-14-140-1-1-1-1-1-1-1-11-41-45−500111155−5−555−5−5-40400000001100-1-10000−55000000000000000
χ434444-4-4-14-14-14-140-1-1-1-1-1-1-1-11-41-4−55001111−5−555−5−55540-40000000-1-100110000−55000000000000000
χ444444-4-4-14-14-14-140-1-1-1-1-1-1-1-11-41-4−55001111−5−555−5−555-40400000001100-1-100005−5000000000000000
χ4544-4-4004444-4-4-4-404444-4-4-4-40000000000000000000000004-4-4400000000000000000000000000000
χ4644-4-4004444-4-4-4-404444-4-4-4-4000000000000000000000000-444-400000000000000000000000000000
χ474-44-40044-4-444-4-4044-4-4-4-44400000000000000000000000044-4-400000000000000000000000000000
χ484-44-40044-4-444-4-4044-4-4-4-444000000000000000000000000-4-44400000000000000000000000000000
χ49888888-2-2-2-2-2-2-2-283-23-23-23-2-2-2-2-2-2-2-2-23-23-233-2-2-2-2330000000000000000000000000000000000000
χ50888888-2-2-2-2-2-2-2-28-23-23-23-23-2-2-2-2-2-2-2-2-23-23-2-23333-2-20000000000000000000000000000000000000
χ51888888-2-2-2-2-2-2-2-2-83-23-23-23-2-2-2-2-222223-23-2-3-32222-3-30000000000000000000000000000000000000
χ52888888-2-2-2-2-2-2-2-2-8-23-23-23-23-2-2-2-22222-23-2322-3-3-3-3220000000000000000000000000000000000000
χ538888-8-8-2-2-2-2-2-2-2-203-23-23-23-2222225−2525−25-32-32−5−50000550000000000000000000000000000000000000
χ548888-8-8-2-2-2-2-2-2-2-203-23-23-23-22222−2525−2525-32-32550000−5−50000000000000000000000000000000000000
χ558888-8-8-2-2-2-2-2-2-2-20-23-23-23-23222225−25−25252-32-30055−5−5000000000000000000000000000000000000000
χ568888-8-8-2-2-2-2-2-2-2-20-23-23-23-232222−252525−252-32-300−5−555000000000000000000000000000000000000000
χ5788-8-8008-28-2-82-820-2-2-2-222220000000000000000000000000000000025−2500000000000000000000000
χ5888-8-8008-28-2-82-820-2-2-2-2222200000000000000000000000000000000−252500000000000000000000000
χ5988-8-800-28-282-82-80-2-2-2-2222200000000000000000000000000000025−250000000000000000000000000
χ6088-8-800-28-282-82-80-2-2-2-22222000000000000000000000000000000−25250000000000000000000000000
χ618-88-8008-2-828-2-820-2-22222-2-20000000000000000000000000000000000002i5−2i50000000000000000000
χ628-88-8008-2-828-2-820-2-22222-2-2000000000000000000000000000000000000−2i52i50000000000000000000
χ638-88-800-282-8-282-80-2-22222-2-200000000000000000000000000000000002i5−2i5000000000000000000000
χ648-88-800-282-8-282-80-2-22222-2-20000000000000000000000000000000000−2i52i5000000000000000000000
χ658-8-888-88-2-82-828-20-2-222-2-2228-2-820000-2-222000000000000000000000000000000000000000000000
χ668-8-888-8-282-82-8-280-2-222-2-222-282-80000-2-222000000000000000000000000000000000000000000000
χ678-8-888-8-2-22222-2-203-2-323-2-32-2-22200003-2-325i−5i00005i−5i0000000000000000000000000000000000000
χ688-8-888-8-2-22222-2-203-2-323-2-32-2-22200003-2-32−5i5i0000−5i5i0000000000000000000000000000000000000
χ698-8-888-8-2-22222-2-20-232-3-232-3-2-2220000-232-3005i−5i5i−5i000000000000000000000000000000000000000
χ708-8-888-8-2-22222-2-20-232-3-232-3-2-2220000-232-300−5i5i−5i5i000000000000000000000000000000000000000
χ718-8-88-888-2-82-828-20-2-222-2-222-828-2000022-2-2000000000000000000000000000000000000000000000
χ728-8-88-88-282-82-8-280-2-222-2-2222-8-28000022-2-2000000000000000000000000000000000000000000000
χ738-8-88-88-2-22222-2-203-2-323-2-3222-2-20000-323-2i5−i52i5−2i5−2i52i5−i5i50000000000000000000000000000000000000
χ748-8-88-88-2-22222-2-203-2-323-2-3222-2-20000-323-2−i5i5−2i52i52i5−2i5i5−i50000000000000000000000000000000000000
χ758-8-88-88-2-22222-2-20-232-3-232-322-2-200002-3-232i5−2i5−i5i5i5−i5−2i52i50000000000000000000000000000000000000
χ768-8-88-88-2-22222-2-20-232-3-232-322-2-200002-3-23−2i52i5i5−i5−i5i52i5−2i50000000000000000000000000000000000000
χ771616-16-1600-4-4-4-4444406-46-4-64-64000000000000000000000000000000000000000000000000000000000
χ781616-16-1600-4-4-4-444440-46-464-64-6000000000000000000000000000000000000000000000000000000000
χ7916-1616-1600-4-444-4-44406-4-64-646-4000000000000000000000000000000000000000000000000000000000
χ8016-1616-1600-4-444-4-4440-464-64-6-46000000000000000000000000000000000000000000000000000000000

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