Finite Group Databasebeta

← Group #72242618

Character table — Group #72242618

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111122444444448888888888888101010101010101016161616161616161616161616161616252525254040404040404040404050505050505050505050505050505050505080808080200200200200200
order1222445510101010101045510101010101020202020222244442020202020202020202020202020202022224410101010202020204488888888888888882020202044444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1
χ311111111111111111111111111111-1-111-1-11111111111111111-1-1-1-11-111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1ii−i−i
χ411111111111111111111111111111-1-111-1-11111111111111111-1-1-1-11-111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1−i−iii
χ5111111111111111111111111111-1-111-1-1111111111111111111-1-1-1-1-11-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1i−ii−i
χ6111111111111111111111111111-1-111-1-1111111111111111111-1-1-1-1-11-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1−ii−ii
χ7111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11
χ8111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1
χ911111111111111-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ1011111111111111-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ1111111111111111-111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1111−i−iii
χ1211111111111111-111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1111ii−i−i
χ1311111111111111-1111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11−ii−ii
χ1411111111111111-1111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11i−ii−i
χ1511111111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-111-1
χ1611111111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-11-1-11
χ172222-2-222222222022222222-2-2-2-22222-2-2-2-20000-2-2-2-2000000002222002222-2-2-2-2-2-20000000000000000000000000
χ182222-2-222222222022222222-2-2-2-222-2-2-2-2220000-2-2-2-200000000-2-2-2-20022-2-2-2-222220000000000000000000000000
χ192222-2-222222222022222222-2-2-2-2-2-22222-2-20000-2-2-2-200000000-2-2-2-200-2-22222-2-2220000000000000000000000000
χ202222-2-222222222022222222-2-2-2-2-2-2-2-222220000-2-2-2-200000000222200-2-2-2-22222-2-20000000000000000000000000
χ2122-2-2002222-2-2-2-202222-2-2-2-200002-22-20000000000000000000022-2-2002-22-200000022−2−222−2−222−2−222−2−2000000000
χ2222-2-2002222-2-2-2-202222-2-2-2-200002-22-20000000000000000000022-2-2002-22-2000000−2−222−2−222−2−222−2−222000000000
χ2322-2-2002222-2-2-2-202222-2-2-2-200002-2-2200000000000000000000-2-222002-2-22000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000
χ2422-2-2002222-2-2-2-202222-2-2-2-200002-2-2200000000000000000000-2-222002-2-22000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000
χ2522-2-2002222-2-2-2-202222-2-2-2-20000-222-200000000000000000000-2-22200-222-2000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000
χ2622-2-2002222-2-2-2-202222-2-2-2-20000-222-200000000000000000000-2-22200-222-2000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000
χ2722-2-2002222-2-2-2-202222-2-2-2-20000-22-220000000000000000000022-2-200-22-2200000022−2−2−2−222−2−22222−2−2000000000
χ2822-2-2002222-2-2-2-202222-2-2-2-20000-22-220000000000000000000022-2-200-22-22000000−2−22222−2−222−2−2−2−222000000000
χ292-22-20022-2-222-2-2022-2-2-2-222000000002i−2i2i−2i00000000000000002-22-20000002i−2i2i−2i00i2−i2i2−i22−22−22−22−2i2−i2i2−i2000000000
χ302-22-20022-2-222-2-2022-2-2-2-222000000002i−2i2i−2i00000000000000002-22-20000002i−2i2i−2i00−i2i2−i2i2−22−22−22−22−i2i2−i2i2000000000
χ312-22-20022-2-222-2-2022-2-2-2-222000000002i−2i−2i2i0000000000000000-22-220000002i−2i−2i2i002−22−2−i2i2−i2i2i2−i2i2−i2−22−22000000000
χ322-22-20022-2-222-2-2022-2-2-2-222000000002i−2i−2i2i0000000000000000-22-220000002i−2i−2i2i00−22−22i2−i2i2−i2−i2i2−i2i22−22−2000000000
χ332-22-20022-2-222-2-2022-2-2-2-22200000000−2i2i2i−2i0000000000000000-22-22000000−2i2i2i−2i002−22−2i2−i2i2−i2−i2i2−i2i2−22−22000000000
χ342-22-20022-2-222-2-2022-2-2-2-22200000000−2i2i2i−2i0000000000000000-22-22000000−2i2i2i−2i00−22−22−i2i2−i2i2i2−i2i2−i22−22−2000000000
χ352-22-20022-2-222-2-2022-2-2-2-22200000000−2i2i−2i2i00000000000000002-22-2000000−2i2i−2i2i00i2−i2i2−i2−22−22−22−22i2−i2i2−i2000000000
χ362-22-20022-2-222-2-2022-2-2-2-22200000000−2i2i−2i2i00000000000000002-22-2000000−2i2i−2i2i00−i2i2−i2i22−22−22−22−2−i2i2−i2i2000000000
χ372-2-222-222-2-2-2-222022-2-222-2-222-2-200000000000022-2-2000000002-2-2200000000002-22i−2i−2i2i000000002i−2i−2i2i000000000
χ382-2-222-222-2-2-2-222022-2-222-2-222-2-200000000000022-2-2000000002-2-2200000000002-2−2i2i2i−2i00000000−2i2i2i−2i000000000
χ392-2-222-222-2-2-2-222022-2-222-2-222-2-200000000000022-2-200000000-222-20000000000-222-2-2200000000-222-2000000000
χ402-2-222-222-2-2-2-222022-2-222-2-222-2-200000000000022-2-200000000-222-20000000000-22-222-2000000002-2-22000000000
χ412-2-22-2222-2-2-2-222022-2-222-2-2-2-222000000000000-2-222000000002-2-220000000000-2200002-2-222-2-220000000000000
χ422-2-22-2222-2-2-2-222022-2-222-2-2-2-222000000000000-2-222000000002-2-220000000000-220000-222-2-222-20000000000000
χ432-2-22-2222-2-2-2-222022-2-222-2-2-2-222000000000000-2-22200000000-222-200000000002-200002i−2i−2i2i−2i2i2i−2i0000000000000
χ442-2-22-2222-2-2-2-222022-2-222-2-2-2-222000000000000-2-22200000000-222-200000000002-20000−2i2i2i−2i2i−2i−2i2i0000000000000
χ454444444-14-14-14-14-1-1-1-1-1-1-1-14-14-10044004444-1-1-1-1-1-1-1-1-1-1-1-1-1-100000400-1-100-1-100000000000000000000-1-100000
χ464444444-14-14-14-14-1-1-1-1-1-1-1-14-14-100-4-400-4-444-1-1-1-1-1-1-1-1-1-1-1-1-1-100000-400110011000000000000000000001100000
χ474444444-14-14-14-1-4-1-1-1-1-1-1-1-14-14-100440044-4-411-1-1-1-11111111100000-400-1-100-1-1000000000000000000001100000
χ484444444-14-14-14-1-4-1-1-1-1-1-1-1-14-14-100-4-400-4-4-4-411-1-1-1-1111111110000040011001100000000000000000000-1-100000
χ49444444-14-14-14-144-1-1-1-1-1-1-1-1-14-1444004400-1-144-1-1-1-1-1-1-1-1-1-1-1-1000040-1-100-1-100000000000000000000-1-10000000
χ50444444-14-14-14-144-1-1-1-1-1-1-1-1-14-14-4-400-4-400-1-144-1-1-1-1-1-1-1-1-1-1-1-10000-4011001100000000000000000000110000000
χ51444444-14-14-14-14-4-1-1-1-1-1-1-1-1-14-144400440011-4-4-1-1-1-1111111110000-40-1-100-1-100000000000000000000110000000
χ52444444-14-14-14-14-4-1-1-1-1-1-1-1-1-14-14-4-400-4-40011-4-4-1-1-1-11111111100004011001100000000000000000000-1-10000000
χ534444-4-44-14-14-14-10-1-1-1-1-1-1-1-1-41-41004400-4-4005−511115555−5−5−5−500000000-1-10011000000000000000000005−500000
χ544444-4-44-14-14-14-10-1-1-1-1-1-1-1-1-41-41004400-4-400−551111−5−5−5−5555500000000-1-1001100000000000000000000−5500000
χ554444-4-44-14-14-14-10-1-1-1-1-1-1-1-1-41-4100-4-40044005−511115555−5−5−5−5000000001100-1-100000000000000000000−5500000
χ564444-4-44-14-14-14-10-1-1-1-1-1-1-1-1-41-4100-4-4004400−551111−5−5−5−55555000000001100-1-1000000000000000000005−500000
χ574444-4-4-14-14-14-140-1-1-1-1-1-1-1-11-41-44400-4-4005−500111155−5−555−5−5000000-1-10011000000000000000000005−50000000
χ584444-4-4-14-14-14-140-1-1-1-1-1-1-1-11-41-44400-4-400−55001111−5−555−5−555000000-1-1001100000000000000000000−550000000
χ594444-4-4-14-14-14-140-1-1-1-1-1-1-1-11-41-4-4-40044005−500111155−5−555−5−50000001100-1-100000000000000000000−550000000
χ604444-4-4-14-14-14-140-1-1-1-1-1-1-1-11-41-4-4-4004400−55001111−5−555−5−5550000001100-1-1000000000000000000005−50000000
χ61888888-2-2-2-2-2-2-2-283-23-23-23-2-2-2-2-200000000-2-2-2-23-23-233-2-2-2-23300000000000000000000000000000000000000000
χ62888888-2-2-2-2-2-2-2-28-23-23-23-23-2-2-2-200000000-2-2-2-2-23-23-2-23333-2-200000000000000000000000000000000000000000
χ63888888-2-2-2-2-2-2-2-2-83-23-23-23-2-2-2-2-20000000022223-23-2-3-32222-3-300000000000000000000000000000000000000000
χ64888888-2-2-2-2-2-2-2-2-8-23-23-23-23-2-2-2-2000000002222-23-2322-3-3-3-32200000000000000000000000000000000000000000
χ658888-8-8-2-2-2-2-2-2-2-203-23-23-23-222220000000025−2525−25-32-32−5−500005500000000000000000000000000000000000000000
χ668888-8-8-2-2-2-2-2-2-2-203-23-23-23-2222200000000−2525−2525-32-32550000−5−500000000000000000000000000000000000000000
χ678888-8-8-2-2-2-2-2-2-2-20-23-23-23-2322220000000025−25−25252-32-30055−5−50000000000000000000000000000000000000000000
χ688888-8-8-2-2-2-2-2-2-2-20-23-23-23-23222200000000−252525−252-32-300−5−5550000000000000000000000000000000000000000000
χ6988-8-8008-28-2-82-820-2-2-2-222220000008-80000000000000000000000000000-220000000000000000000000000000000
χ7088-8-8008-28-2-82-820-2-2-2-22222000000-8800000000000000000000000000002-20000000000000000000000000000000
χ7188-8-800-28-282-82-80-2-2-2-2222200008-80000000000000000000000000000-22000000000000000000000000000000000
χ7288-8-800-28-282-82-80-2-2-2-222220000-8800000000000000000000000000002-2000000000000000000000000000000000
χ738-88-8008-2-828-2-820-2-22222-2-200000000008i−8i0000000000000000000000000000−2i2i000000000000000000000000000
χ748-88-8008-2-828-2-820-2-22222-2-20000000000−8i8i00000000000000000000000000002i−2i000000000000000000000000000
χ758-88-800-282-8-282-80-2-22222-2-2000000008i−8i0000000000000000000000000000−2i2i00000000000000000000000000000
χ768-88-800-282-8-282-80-2-22222-2-200000000−8i8i00000000000000000000000000002i−2i00000000000000000000000000000
χ778-8-888-88-2-82-828-20-2-222-2-2228-2-82000000000000-2-2220000000000000000000000000000000000000000000000000
χ788-8-888-8-282-82-8-280-2-222-2-222-282-8000000000000-2-2220000000000000000000000000000000000000000000000000
χ798-8-888-8-2-22222-2-203-2-323-2-32-2-2220000000000003-2-325i−5i00005i−5i00000000000000000000000000000000000000000
χ808-8-888-8-2-22222-2-203-2-323-2-32-2-2220000000000003-2-32−5i5i0000−5i5i00000000000000000000000000000000000000000
χ818-8-888-8-2-22222-2-20-232-3-232-3-2-222000000000000-232-3005i−5i5i−5i0000000000000000000000000000000000000000000
χ828-8-888-8-2-22222-2-20-232-3-232-3-2-222000000000000-232-300−5i5i−5i5i0000000000000000000000000000000000000000000
χ838-8-88-888-2-82-828-20-2-222-2-222-828-200000000000022-2-20000000000000000000000000000000000000000000000000
χ848-8-88-88-282-82-8-280-2-222-2-2222-8-2800000000000022-2-20000000000000000000000000000000000000000000000000
χ858-8-88-88-2-22222-2-203-2-323-2-3222-2-2000000000000-323-2i5−i52i5−2i5−2i52i5−i5i500000000000000000000000000000000000000000
χ868-8-88-88-2-22222-2-203-2-323-2-3222-2-2000000000000-323-2−i5i5−2i52i52i5−2i5i5−i500000000000000000000000000000000000000000
χ878-8-88-88-2-22222-2-20-232-3-232-322-2-20000000000002-3-232i5−2i5−i5i5i5−i5−2i52i500000000000000000000000000000000000000000
χ888-8-88-88-2-22222-2-20-232-3-232-322-2-20000000000002-3-23−2i52i5i5−i5−i5i52i5−2i500000000000000000000000000000000000000000
χ891616-16-1600-4-4-4-4444406-46-4-64-64000000000000000000000000000000000000000000000000000000000000000000000
χ901616-16-1600-4-4-4-444440-46-464-64-6000000000000000000000000000000000000000000000000000000000000000000000
χ9116-1616-1600-4-444-4-44406-4-64-646-4000000000000000000000000000000000000000000000000000000000000000000000
χ9216-1616-1600-4-444-4-4440-464-64-6-46000000000000000000000000000000000000000000000000000000000000000000000

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