Finite Group Databasebeta

← Group #72242596

Character table — Group #72242596

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111122444444448888888888888101010101010101016161616161616161616161616161616252525254040404040404040404050505050505050505050505050505050505080808080200200200200200
order1222445510101010101025510101010101020202020888888881010101010101010101010102020202022222240404040404040404444444444888888881010101024444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-11-11111-1-1-1-1-1iiii−i−i−i−i-1iiii−i−i−i−i11-1-1-1ii−i−i
χ41111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-11-11111-1-1-1-1-1−i−i−i−iiiii-1−i−i−i−iiiii11-1-1-1−i−iii
χ5111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-11-1-1-1-11111-1iiii−i−i−i−i-1−i−i−i−iiiii-1-111-1i−ii−i
χ6111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-11-1-1-1-11111-1−i−i−i−iiiii-1iiii−i−i−i−i-1-111-1−ii−ii
χ7111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11
χ8111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-11-111-1
χ911111111111111-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ1011111111111111-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ1111111111111111-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1iiii−i−i−i−i-1iiii−i−i−i−i-1-1111−i−iii
χ1211111111111111-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1−i−i−i−iiiii-1−i−i−i−iiiii-1-1111ii−i−i
χ1311111111111111-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-1-11111-1iiii−i−i−i−i-1−i−i−i−iiiii11-1-11−ii−ii
χ1411111111111111-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-1-11111-1−i−i−i−iiiii-1iiii−i−i−i−i11-1-11i−ii−i
χ1511111111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1
χ1611111111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111-11-1-11
χ172222-2-222222222022222222-2-2-2-200000000000000000000-2-2-2-222220000000000-222-2-222-2-2-200000000000000000
χ182222-2-222222222022222222-2-2-2-200000000000000000000-2-2-2-222220000000000-2-2-222-2-222-200000000000000000
χ192222-2-222222222022222222-2-2-2-200000000000000000000-2-2-2-2-2-2-2-2000000000022i2i−2i−2i−2i−2i2i2i200000000000000000
χ202222-2-222222222022222222-2-2-2-200000000000000000000-2-2-2-2-2-2-2-200000000002−2i−2i2i2i2i2i−2i−2i200000000000000000
χ2122-2-2002222-2-2-2-202222-2-2-2-2000022−2−222−2−2000000000000000022-2-20022−2−222−2−20002i−2i002i−2i0i2i2−i2−i2i2i2−i2−i2000000000
χ2222-2-2002222-2-2-2-202222-2-2-2-2000022−2−222−2−2000000000000000022-2-20022−2−222−2−2000−2i2i00−2i2i0−i2−i2i2i2−i2−i2i2i2000000000
χ2322-2-2002222-2-2-2-202222-2-2-2-2000022−2−2−2−2220000000000000000-2-2220022−2−2−2−2220002-200-22022−2−2−2−222000000000
χ2422-2-2002222-2-2-2-202222-2-2-2-2000022−2−2−2−2220000000000000000-2-2220022−2−2−2−222000-22002-20−2−22222−2−2000000000
χ2522-2-2002222-2-2-2-202222-2-2-2-20000−2−22222−2−20000000000000000-2-22200−2−22222−2−20002-200-220−2−22222−2−2000000000
χ2622-2-2002222-2-2-2-202222-2-2-2-20000−2−22222−2−20000000000000000-2-22200−2−22222−2−2000-22002-2022−2−2−2−222000000000
χ2722-2-2002222-2-2-2-202222-2-2-2-20000−2−222−2−222000000000000000022-2-200−2−222−2−2220002i−2i002i−2i0−i2−i2i2i2−i2−i2i2i2000000000
χ2822-2-2002222-2-2-2-202222-2-2-2-20000−2−222−2−222000000000000000022-2-200−2−222−2−222000−2i2i00−2i2i0i2i2−i2−i2i2i2−i2−i2000000000
χ292-22-20022-2-222-2-2022-2-222-2-200002−22−22−22−200000000000000002-22-2002−22−22−22−202i−2i002i−2i000i2−i2i2−i2i2−i2i2−i2000000000
χ302-22-20022-2-222-2-2022-2-222-2-200002−22−22−22−200000000000000002-22-2002−22−22−22−20−2i2i00−2i2i000−i2i2−i2i2−i2i2−i2i2000000000
χ312-22-20022-2-222-2-2022-2-222-2-200002−22−2−22−220000000000000000-22-22002−22−2−22−2202-200-220002−22−2−22−22000000000
χ322-22-20022-2-222-2-2022-2-222-2-200002−22−2−22−220000000000000000-22-22002−22−2−22−220-22002-2000−22−222−22−2000000000
χ332-22-20022-2-222-2-2022-2-222-2-20000−22−222−22−20000000000000000-22-2200−22−222−22−202-200-22000−22−222−22−2000000000
χ342-22-20022-2-222-2-2022-2-222-2-20000−22−222−22−20000000000000000-22-2200−22−222−22−20-22002-20002−22−2−22−22000000000
χ352-22-20022-2-222-2-2022-2-222-2-20000−22−22−22−2200000000000000002-22-200−22−22−22−2202i−2i002i−2i000−i2i2−i2i2−i2i2−i2i2000000000
χ362-22-20022-2-222-2-2022-2-222-2-20000−22−22−22−2200000000000000002-22-200−22−22−22−220−2i2i00−2i2i000i2−i2i2−i2i2−i2i2−i2000000000
χ372-2-222-222-2-2-2-222022-2-2-2-22222-2-20000000000000000000022-2-22-2-220000000000-20000000022-2-222-2-22000000000
χ382-2-222-222-2-2-2-222022-2-2-2-22222-2-20000000000000000000022-2-22-2-220000000000-2000000002-222-2-222-2000000000
χ392-2-222-222-2-2-2-222022-2-2-2-22222-2-20000000000000000000022-2-2-222-20000000000200000000-22i−2i−2i2i−2i2i2i−2i000000000
χ402-2-222-222-2-2-2-222022-2-2-2-22222-2-20000000000000000000022-2-2-222-20000000000200000000-2−2i2i2i−2i2i−2i−2i2i000000000
χ412-2-22-2222-2-2-2-222022-2-2-2-222-2-2222-2-222-2-22000000000000-2-2222-2-22002-2-222-2-22200000000-200000000000000000
χ422-2-22-2222-2-2-2-222022-2-2-2-222-2-2222-2-22-222-2000000000000-2-222-222-2002-2-22-222-2-200000000200000000000000000
χ432-2-22-2222-2-2-2-222022-2-2-2-222-2-222-222-22-2-22000000000000-2-222-222-200-222-22-2-22-200000000200000000000000000
χ442-2-22-2222-2-2-2-222022-2-2-2-222-2-222-222-2-222-2000000000000-2-2222-2-2200-222-2-222-2200000000-200000000000000000
χ454444444-14-14-14-14-1-1-1-1-1-1-1-14-14-10000444444-1-1-1-1-1-1-1-1-1-1-1-1-1-10000040000-1-1-1-100000000000000000000-1-100000
χ464444444-14-14-14-14-1-1-1-1-1-1-1-14-14-10000-4-4-4-444-1-1-1-1-1-1-1-1-1-1-1-1-1-100000-400001111000000000000000000001100000
χ474444444-14-14-14-1-4-1-1-1-1-1-1-1-14-14-100004444-4-41111111111-1-1-1-100000-40000-1-1-1-1000000000000000000001100000
χ484444444-14-14-14-1-4-1-1-1-1-1-1-1-14-14-10000-4-4-4-4-4-41111111111-1-1-1-10000040000111100000000000000000000-1-100000
χ49444444-14-14-14-144-1-1-1-1-1-1-1-1-14-1444440000-1-144-1-1-1-1-1-1-1-1-1-1-1-1000040-1-1-1-10000000000000000000000-1-10000000
χ50444444-14-14-14-144-1-1-1-1-1-1-1-1-14-14-4-4-4-40000-1-144-1-1-1-1-1-1-1-1-1-1-1-10000-4011110000000000000000000000110000000
χ51444444-14-14-14-14-4-1-1-1-1-1-1-1-1-14-144444000011-4-411111111-1-1-1-10000-40-1-1-1-10000000000000000000000110000000
χ52444444-14-14-14-14-4-1-1-1-1-1-1-1-1-14-14-4-4-4-4000011-4-411111111-1-1-1-100004011110000000000000000000000-1-10000000
χ534-4-44-444-1-41-414-10-1-11111-1-1-414-100004-4-44005−55555−5−5−5−511-1-10000000000-111-1000000000000000000005−500000
χ544-4-44-444-1-41-414-10-1-11111-1-1-414-100004-4-4400−55−5−5−5−5555511-1-10000000000-111-100000000000000000000−5500000
χ554-4-44-444-1-41-414-10-1-11111-1-1-414-10000-444-4005−55555−5−5−5−511-1-100000000001-1-1100000000000000000000−5500000
χ564-4-44-444-1-41-414-10-1-11111-1-1-414-10000-444-400−55−5−5−5−5555511-1-100000000001-1-11000000000000000000005−500000
χ574-4-44-44-141-41-4-140-1-11111-1-11-4-144-4-4400005−50055−5−555−5−511-1-1000000-111-100000000000000000000005−50000000
χ584-4-44-44-141-41-4-140-1-11111-1-11-4-144-4-440000−5500−5−555−5−55511-1-1000000-111-10000000000000000000000−550000000
χ594-4-44-44-141-41-4-140-1-11111-1-11-4-14-444-400005−50055−5−555−5−511-1-10000001-1-110000000000000000000000−550000000
χ604-4-44-44-141-41-4-140-1-11111-1-11-4-14-444-40000−5500−5−555−5−55511-1-10000001-1-1100000000000000000000005−50000000
χ61888888-2-2-2-2-2-2-2-283-23-23-23-2-2-2-2-200000000-2-2-2-233-2-2-2-2333-23-200000000000000000000000000000000000000000
χ62888888-2-2-2-2-2-2-2-28-23-23-23-23-2-2-2-200000000-2-2-2-2-2-23333-2-2-23-2300000000000000000000000000000000000000000
χ63888888-2-2-2-2-2-2-2-2-83-23-23-23-2-2-2-2-2000000002222-3-32222-3-33-23-200000000000000000000000000000000000000000
χ64888888-2-2-2-2-2-2-2-2-8-23-23-23-23-2-2-2-200000000222222-3-3-3-322-23-2300000000000000000000000000000000000000000
χ658888-8-88-28-28-28-20-2-2-2-2-2-2-2-2-82-8200000000000000000000222200000000000000000000000000000000000000000
χ668888-8-8-28-28-28-280-2-2-2-2-2-2-2-22-82-800000000000000000000222200000000000000000000000000000000000000000
χ678888-8-8-2-2-2-2-2-2-2-203-23-23-23-222220000000000005−525−2525−255−5-32-3200000000000000000000000000000000000000000
χ688888-8-8-2-2-2-2-2-2-2-203-23-23-23-22222000000000000−55−2525−2525−55-32-3200000000000000000000000000000000000000000
χ698888-8-8-2-2-2-2-2-2-2-20-23-23-23-23222200000000000025−25−55−5525−252-32-300000000000000000000000000000000000000000
χ708888-8-8-2-2-2-2-2-2-2-20-23-23-23-232222000000000000−25255−55−5−25252-32-300000000000000000000000000000000000000000
χ7188-8-8008-28-2-82-820-2-2-2-22222000000004242−42−4200000000000000000000000000−2−222000000000000000000000000000
χ7288-8-8008-28-2-82-820-2-2-2-2222200000000−42−4242420000000000000000000000000022−2−2000000000000000000000000000
χ7388-8-800-28-282-82-80-2-2-2-2222200004242−42−4200000000000000000000000000−2−2220000000000000000000000000000000
χ7488-8-800-28-282-82-80-2-2-2-222220000−42−4242420000000000000000000000000022−2−20000000000000000000000000000000
χ758-88-8008-2-828-2-820-2-222-2-2220000000042−4242−4200000000000000000000000000−22−22000000000000000000000000000
χ768-88-8008-2-828-2-820-2-222-2-22200000000−4242−4242000000000000000000000000002−22−2000000000000000000000000000
χ778-88-800-282-8-282-80-2-222-2-222000042−4242−4200000000000000000000000000−22−220000000000000000000000000000000
χ788-88-800-282-8-282-80-2-222-2-2220000−4242−4242000000000000000000000000002−22−20000000000000000000000000000000
χ798-8-888-88-2-82-828-20-2-22222-2-28-2-8200000000000000000000-2-22200000000000000000000000000000000000000000
χ808-8-888-8-282-82-8-280-2-22222-2-2-282-800000000000000000000-2-22200000000000000000000000000000000000000000
χ818-8-888-8-2-22222-2-203-2-32-323-2-2-2220000000000005-50000-553-2-3200000000000000000000000000000000000000000
χ828-8-888-8-2-22222-2-203-2-32-323-2-2-222000000000000-5500005-53-2-3200000000000000000000000000000000000000000
χ838-8-888-8-2-22222-2-20-232-32-3-23-2-222000000000000005-5-5500-232-300000000000000000000000000000000000000000
χ848-8-888-8-2-22222-2-20-232-32-3-23-2-22200000000000000-555-500-232-300000000000000000000000000000000000000000
χ858-8-88-88-2-22222-2-203-2-32-323-222-2-20000000025−2525−25−5−5000055-323-200000000000000000000000000000000000000000
χ868-8-88-88-2-22222-2-203-2-32-323-222-2-200000000−2525−2525550000−5−5-323-200000000000000000000000000000000000000000
χ878-8-88-88-2-22222-2-20-232-32-3-2322-2-20000000025−25−25250055−5−5002-3-2300000000000000000000000000000000000000000
χ888-8-88-88-2-22222-2-20-232-32-3-2322-2-200000000−252525−2500−5−555002-3-2300000000000000000000000000000000000000000
χ891616-16-1600-4-4-4-4444406-46-4-64-64000000000000000000000000000000000000000000000000000000000000000000000
χ901616-16-1600-4-4-4-444440-46-464-64-6000000000000000000000000000000000000000000000000000000000000000000000
χ9116-1616-1600-4-444-4-44406-4-646-4-64000000000000000000000000000000000000000000000000000000000000000000000
χ9216-1616-1600-4-444-4-4440-464-6-464-6000000000000000000000000000000000000000000000000000000000000000000000

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