Finite Group Databasebeta

← Group #72223300

Character table — Group #72223300

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11112244444444448888888888881616161616161616161616161616161620202020252525254040404040404040404050505050505080808080100100100100100100100100100100100100200200
order1222442255101010101010551010101010102020202010101010101010101010101020202020888822222240404040404040404444441010101022444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-11-11111-1-1-1-1-1ii−i−i-111-1-1-1-1i−iii−i−iii−i−ii−i
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-11-11111-1-1-1-1-1−i−iii-111-1-1-1-1−ii−i−iii−i−iii−ii
χ511111111111111111111111111111111111111111111-1-111-1-1-1-1-11-1-1-1-11111-1ii−i−i-1-1-111-1-1i−iii−i−i−i−iii−ii
χ611111111111111111111111111111111111111111111-1-111-1-1-1-1-11-1-1-1-11111-1−i−iii-1-1-111-1-1−ii−i−iiiii−i−ii−i
χ711111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1
χ811111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111-1-1-1-1-1-1111111
χ9111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1
χ10111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111
χ11111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1ii−i−i-1-1-11111i−i−i−iiiii−i−i−ii
χ12111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1−i−iii-1-1-11111−iiii−i−i−i−iiii−i
χ13111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-1-1-1-1-11111-1ii−i−i-111-1-111i−i−i−iii−i−iiii−i
χ14111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-1-1-1-1-11111-1−i−iii-111-1-111−iiii−i−iii−i−i−ii
χ15111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-111
χ16111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-111111111-1-1
χ172222-2-2002222222222222222-2-2-2-2000000000000-2-2-2-2000022220000000000-22222-2000000-2-20000000000
χ182222-2-2002222222222222222-2-2-2-2000000000000-2-2-2-2000022220000000000-2-2-2-2-2-2000000220000000000
χ192222-2-2002222222222222222-2-2-2-2000000000000-2-2-2-20000-2-2-2-2000000000022i2i−2i−2i2000000−2i2i0000000000
χ202222-2-2002222222222222222-2-2-2-2000000000000-2-2-2-20000-2-2-2-200000000002−2i−2i2i2i20000002i−2i0000000000
χ2122-2-200002222-2-2-2-22222-2-2-2-2000000000000000000002−22−222-2-20022−2−222−2−202i−2i2i−2i0000000000000i2−i2i2−i200
χ2222-2-200002222-2-2-2-22222-2-2-2-2000000000000000000002−22−222-2-20022−2−222−2−20−2i2i−2i2i0000000000000−i2i2−i2i200
χ2322-2-200002222-2-2-2-22222-2-2-2-2000000000000000000002−2−22-2-2220022−2−2−2−22202-2-2200000000000002−2−2200
χ2422-2-200002222-2-2-2-22222-2-2-2-2000000000000000000002−2−22-2-2220022−2−2−2−2220-222-20000000000000−222−200
χ2522-2-200002222-2-2-2-22222-2-2-2-200000000000000000000−222−2-2-22200−2−22222−2−202-2-220000000000000−222−200
χ2622-2-200002222-2-2-2-22222-2-2-2-200000000000000000000−222−2-2-22200−2−22222−2−20-222-200000000000002−2−2200
χ2722-2-200002222-2-2-2-22222-2-2-2-200000000000000000000−22−2222-2-200−2−222−2−22202i−2i2i−2i0000000000000−i2i2−i2i200
χ2822-2-200002222-2-2-2-22222-2-2-2-200000000000000000000−22−2222-2-200−2−222−2−2220−2i2i−2i2i0000000000000i2−i2i2−i200
χ292-2-222-20022-2-2-2-22222-2-2-2-22222-2-200000000000022-2-200002-22-2000000000020000-2000000002i−2i2i−2i000000
χ302-2-222-20022-2-2-2-22222-2-2-2-22222-2-200000000000022-2-200002-22-2000000000020000-200000000−2i2i−2i2i000000
χ312-2-222-20022-2-2-2-22222-2-2-2-22222-2-200000000000022-2-20000-22-220000000000-200002000000002-2-22000000
χ322-2-222-20022-2-2-2-22222-2-2-2-22222-2-200000000000022-2-20000-22-220000000000-20000200000000-222-2000000
χ332-2-22-222-222-2-2-2-22222-2-2-2-222-2-22222-2-22222-2-2-2-2-2-22200002-22-20000000000-20000200002-2000000000000
χ342-2-22-222-222-2-2-2-22222-2-2-2-222-2-22222-2-22222-2-2-2-2-2-2220000-22-22000000000020000-20000-22000000000000
χ352-2-22-22-2222-2-2-2-22222-2-2-2-222-2-222-2-222-2-2-2-22222-2-22200002-22-20000000000-2000020000-22000000000000
χ362-2-22-22-2222-2-2-2-22222-2-2-2-222-2-222-2-222-2-2-2-22222-2-2220000-22-22000000000020000-200002-2000000000000
χ37444444444-14-14-14-1-1-1-1-1-1-1-1-14-14-14-14-1-1-1-1-1-1-1-1-1-1-1-1-100440000040000-1-1-1-100000000-1-100000000000000
χ38444444444-14-14-14-1-1-1-1-1-1-1-1-14-14-14-14-1-1-1-1-1-1-1-1-1-1-1-1-100-4-400000-400001111000000001100000000000000
χ3944444444-14-14-14-14-1-1-1-1-1-1-1-1-14-14-14-14-1-1-1-1-1-1-1-1-1-1-1-14400000040-1-1-1-10000000000-1-10000000000000000
χ4044444444-14-14-14-14-1-1-1-1-1-1-1-1-14-14-14-14-1-1-1-1-1-1-1-1-1-1-1-1-4-4000000-4011110000000000110000000000000000
χ41444444-4-44-14-14-14-1-1-1-1-1-1-1-1-14-14-1-41-4111111111-1-1-1-1004400000-40000-1-1-1-1000000001100000000000000
χ42444444-4-44-14-14-14-1-1-1-1-1-1-1-1-14-14-1-41-4111111111-1-1-1-100-4-40000040000111100000000-1-100000000000000
χ43444444-4-4-14-14-14-14-1-1-1-1-1-1-1-1-14-141-41-411111111-1-1-1-144000000-40-1-1-1-10000000000110000000000000000
χ44444444-4-4-14-14-14-14-1-1-1-1-1-1-1-1-14-141-41-411111111-1-1-1-1-4-40000004011110000000000-1-10000000000000000
χ454-44-4000044-4-444-4-444-4-444-4-40000000000000000000000004-4-440000000000000000000000000000000000
χ464-44-4000044-4-444-4-444-4-444-4-4000000000000000000000000-444-40000000000000000000000000000000000
χ474-4-44-444-44-1-41-414-1-1-11111-1-1-414-14-1-41-1-1-1-1111111-1-1000000000000005−55−5000000005−500000000000000
χ484-4-44-444-44-1-41-414-1-1-11111-1-1-414-14-1-41-1-1-1-1111111-1-100000000000000−55−5500000000−5500000000000000
χ494-4-44-444-4-141-41-4-14-1-11111-1-11-4-14-141-4-1-1-1-1111111-1-100000000005−55−500000000005−50000000000000000
χ504-4-44-444-4-141-41-4-14-1-11111-1-11-4-14-141-4-1-1-1-1111111-1-10000000000−55−550000000000−550000000000000000
χ514-4-44-44-444-1-41-414-1-1-11111-1-1-414-1-414-11111-1-1-1-111-1-1000000000000005−55−500000000−5500000000000000
χ524-4-44-44-444-1-41-414-1-1-11111-1-1-414-1-414-11111-1-1-1-111-1-100000000000000−55−55000000005−500000000000000
χ534-4-44-44-44-141-41-4-14-1-11111-1-11-4-141-4-141111-1-1-1-111-1-100000000005−55−50000000000−550000000000000000
χ544-4-44-44-44-141-41-4-14-1-11111-1-11-4-141-4-141111-1-1-1-111-1-10000000000−55−5500000000005−50000000000000000
χ5588888888-2-2-2-2-2-2-2-23-23-23-23-2-2-2-2-2-2-2-2-233-2-233-2-23-23-2000000000000000000000000000000000000000000
χ5688888888-2-2-2-2-2-2-2-2-23-23-23-23-2-2-2-2-2-2-2-2-2-233-2-233-23-23000000000000000000000000000000000000000000
χ57888888-8-8-2-2-2-2-2-2-2-23-23-23-23-2-2-2-2-22222-3-322-3-3223-23-2000000000000000000000000000000000000000000
χ58888888-8-8-2-2-2-2-2-2-2-2-23-23-23-23-2-2-2-2222222-3-322-3-3-23-23000000000000000000000000000000000000000000
χ598888-8-8008-28-28-28-2-2-2-2-2-2-2-2-2-82-820000000000002222000000000000000000000000000000000000000000
χ608888-8-800-28-28-28-28-2-2-2-2-2-2-2-22-82-80000000000002222000000000000000000000000000000000000000000
χ618888-8-800-2-2-2-2-2-2-2-23-23-23-23-2222200005-5005-500-32-32000000000000000000000000000000000000000000
χ628888-8-800-2-2-2-2-2-2-2-23-23-23-23-222220000-5500-5500-32-32000000000000000000000000000000000000000000
χ638888-8-800-2-2-2-2-2-2-2-2-23-23-23-2322220000005-5005-52-32-3000000000000000000000000000000000000000000
χ648888-8-800-2-2-2-2-2-2-2-2-23-23-23-232222000000-5500-552-32-3000000000000000000000000000000000000000000
χ6588-8-800008-28-2-82-82-2-2-2-22222000000000000000000000042−420000000000−2−222000000000000000000000000
χ6688-8-800008-28-2-82-82-2-2-2-222220000000000000000000000−4242000000000022−2−2000000000000000000000000
χ6788-8-80000-28-282-82-8-2-2-2-222220000000000000000000042−4200000000−2−2220000000000000000000000000000
χ6888-8-80000-28-282-82-8-2-2-2-2222200000000000000000000−42420000000022−2−20000000000000000000000000000
χ698-88-800008-2-828-2-82-2-222-2-222000000000000000000000000000000000010−10−1010000000000000000000000000
χ708-88-800008-2-828-2-82-2-222-2-2220000000000000000000000000000000000−101010−10000000000000000000000000
χ718-88-80000-282-8-282-8-2-222-2-22200000000000000000000000000000010−10−10100000000000000000000000000000
χ728-88-80000-282-8-282-8-2-222-2-222000000000000000000000000000000−101010−100000000000000000000000000000
χ738-8-888-8008-2-82-828-2-2-22222-2-28-2-82000000000000-2-222000000000000000000000000000000000000000000
χ748-8-888-800-282-82-8-28-2-22222-2-2-282-8000000000000-2-222000000000000000000000000000000000000000000
χ758-8-888-800-2-22222-2-23-2-32-323-2-2-22200005-500-55003-2-32000000000000000000000000000000000000000000
χ768-8-888-800-2-22222-2-23-2-32-323-2-2-2220000-55005-5003-2-32000000000000000000000000000000000000000000
χ778-8-888-800-2-22222-2-2-232-32-3-23-2-2220000005-500-55-232-3000000000000000000000000000000000000000000
χ788-8-888-800-2-22222-2-2-232-32-3-23-2-222000000-55005-5-232-3000000000000000000000000000000000000000000
χ798-8-88-888-8-2-22222-2-23-2-32-323-222-2-2-2-22233-2-2-3-322-323-2000000000000000000000000000000000000000000
χ808-8-88-888-8-2-22222-2-2-232-32-3-2322-2-2-2-222-2-23322-3-32-3-23000000000000000000000000000000000000000000
χ818-8-88-88-88-2-22222-2-23-2-32-323-222-2-222-2-2-3-32233-2-2-323-2000000000000000000000000000000000000000000
χ828-8-88-88-88-2-22222-2-2-232-32-3-2322-2-222-2-222-3-3-2-2332-3-23000000000000000000000000000000000000000000
χ831616-16-160000-4-4-4-444446-46-4-64-6400000000000000000000000000000000000000000000000000000000000000
χ841616-16-160000-4-4-4-44444-46-464-64-600000000000000000000000000000000000000000000000000000000000000
χ8516-1616-160000-4-444-4-4446-4-646-4-6400000000000000000000000000000000000000000000000000000000000000
χ8616-1616-160000-4-444-4-444-464-6-464-600000000000000000000000000000000000000000000000000000000000000

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