Finite Group Databasebeta

← Group #72221023

Character table — Group #72221023

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1122244444488888888888888888888881616161616161616161616162020202020202020252540404040404040404040404040404040505050100100100100100100200200200200200200
order1224444551010551010101010101010202020202020202020202020202020202020202020202020222244442210101010101010102020202020202020244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1ii−i−ii−iii−i−i
χ411111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1−i−iii−ii−i−iii
χ5111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1ii−i−ii−i−i−iii
χ6111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1−i−iii−iiii−i−i
χ7111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1
χ8111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111
χ911111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-11-11-11111-1-111-1-111-1-111-1-1111-1-11111-1-11-11-1
χ1011111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-11-11-11111-1-111-1-111-1-111-1-1111-1-1-1-1-1-111-11-11
χ1111111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-11-1-111-1-1-1-11111-1-1-1-111-1-1-111ii−i−i−iii−i−ii
χ1211111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-11-1-111-1-1-1-11111-1-1-1-111-1-1-111−i−iiii−i−iii−i
χ1311111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111ii−i−i−ii−iii−i
χ1411111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111−i−iiii−ii−i−ii
χ1511111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-11-1111-1-111-1-111-1-111-1-111111-1-11111-1-1-11-11
χ1611111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-11-1111-1-111-1-111-1-111-1-111111-1-1-1-1-1-1111-11-1
χ17222-2-22-222222222222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2000000002200000000000000002-2-22-20000000000
χ18222-2-22-222222222222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-200000000-2-20000000000000000-222-220000000000
χ19222-2-2-2222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222000000002200000000000000002-2-2-220000000000
χ20222-2-2-2222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222200000000-2-20000000000000000-2222-20000000000
χ2122-22-200222222-2-2-2-2-2-22222-2-20000000022-2-20000000002020-20-2220022002200-2-200-2-2-22-2000000000000
χ2222-22-200222222-2-2-2-2-2-22222-2-20000000022-2-200000000020-20-202-2-2002200-2-200-2-200222-22000000000000
χ2322-22-200222222-2-2-2-2-2-22222-2-20000000022-2-2000000000-202020-2-2-200-2-20022002200-2-22-22000000000000
χ2422-22-200222222-2-2-2-2-2-22222-2-20000000022-2-2000000000-20-202022200-2-200-2-200220022-22-2000000000000
χ2522-2-2200222222-2-2-2-2-2-222-2-22200000000-2-222000000002020-20-202222002200-2-200-2-200-2-22000000000000
χ2622-2-2200222222-2-2-2-2-2-222-2-22200000000-2-2220000000020-20-2020-2-22200-2-200-2-200220022-2000000000000
χ2722-2-2200222222-2-2-2-2-2-222-2-22200000000-2-22200000000-202020-20-2-2-2-20022002200-2-20022-2000000000000
χ2822-2-2200222222-2-2-2-2-2-222-2-22200000000-2-22200000000-20-20202022-2-200-2-20022002200-2-22000000000000
χ2944444444-14-1-1-14-1-1-1-1-1-1-14-14-144-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-100440044000000-1-1-1-10000-1-1-1-1000000000000000
χ3044444444-14-1-1-14-1-1-1-1-1-1-14-14-144-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-100-4-400-4-4000000111100001111000000000000000
χ314444444-14-14-1-1-14-1-1-1-1-1-1-14-14-1-144-1-144-1-1-1-1-1-1-1-1-1-1-1-14400440000-1-1-1-10000-1-1-1-10000000000000000000
χ324444444-14-14-1-1-14-1-1-1-1-1-1-14-14-1-144-1-144-1-1-1-1-1-1-1-1-1-1-1-1-4-400-4-400001111000011110000000000000000000
χ3344444-4-44-14-1-1-14-1-1-1-1-1-1-14-14-1-4-411-4-411-1-1-1-111111111004-4004-4000000-1-1110000-1-111000000000000000
χ3444444-4-44-14-1-1-14-1-1-1-1-1-1-14-14-1-4-411-4-411-1-1-1-11111111100-4400-4400000011-1-1000011-1-1000000000000000
χ3544444-4-4-14-14-1-1-14-1-1-1-1-1-1-14-1411-4-411-4-4-1-1-1-1111111114-4004-40000-1-1110000-1-1110000000000000000000
χ3644444-4-4-14-14-1-1-14-1-1-1-1-1-1-14-1411-4-411-4-4-1-1-1-111111111-4400-44000011-1-1000011-1-10000000000000000000
χ37444-4-44-44-14-1-1-14-1-1-1-1-1-1-1-41-4144-1-1-4-4111111-1-1-1-11111000000000000005−55−500005−55−5000000000000000
χ38444-4-44-44-14-1-1-14-1-1-1-1-1-1-1-41-4144-1-1-4-4111111-1-1-1-1111100000000000000−55−550000−55−55000000000000000
χ39444-4-44-4-14-14-1-1-14-1-1-1-1-1-11-41-4-1-14411-4-41111-1-1-1-1111100000000005−55−500005−55−50000000000000000000
χ40444-4-44-4-14-14-1-1-14-1-1-1-1-1-11-41-4-1-14411-4-41111-1-1-1-111110000000000−55−550000−55−550000000000000000000
χ41444-4-4-444-14-1-1-14-1-1-1-1-1-1-1-41-41-4-41144-1-111111111-1-1-1-1000000000000005−5−5500005−5−55000000000000000
χ42444-4-4-444-14-1-1-14-1-1-1-1-1-1-1-41-41-4-41144-1-111111111-1-1-1-100000000000000−555−50000−555−5000000000000000
χ43444-4-4-44-14-14-1-1-14-1-1-1-1-1-11-41-411-4-4-1-14411111111-1-1-1-100000000005−5−5500005−5−550000000000000000000
χ44444-4-4-44-14-14-1-1-14-1-1-1-1-1-11-41-411-4-4-1-14411111111-1-1-1-10000000000−555−50000−555−50000000000000000000
χ4544-44-4004-14-1-1-1-411111-1-14-1-41005−5005−5-1-11155−5−555−5−50004000-40000005−5-1-10000−5511000000000000000
χ4644-44-4004-14-1-1-1-411111-1-14-1-41005−5005−5-1-11155−5−555−5−5000-40004000000−551100005−5-1-1000000000000000
χ4744-44-4004-14-1-1-1-411111-1-14-1-4100−5500−55-1-111−5−555−5−5550004000-4000000−55-1-100005−511000000000000000
χ4844-44-4004-14-1-1-1-411111-1-14-1-4100−5500−55-1-111−5−555−5−555000-400040000005−5110000−55-1-1000000000000000
χ4944-44-400-14-14-1-11-41111-1-1-141-45−5005−500-1-1115−55−55−55−504000-400005−5-1-10000−55110000000000000000000
χ5044-44-400-14-14-1-11-41111-1-1-141-45−5005−500-1-1115−55−55−55−50-400040000−551100005−5-1-10000000000000000000
χ5144-44-400-14-14-1-11-41111-1-1-141-4−5500−5500-1-111−55−55−55−5504000-40000−55-1-100005−5110000000000000000000
χ5244-44-400-14-14-1-11-41111-1-1-141-4−5500−5500-1-111−55−55−55−550-4000400005−5110000−55-1-10000000000000000000
χ5344-4-44004-14-1-1-1-411111-1-1-414-1005−500−5511-1-155−5−5−5−555004000-40000000-1-15−5000011−55000000000000000
χ5444-4-44004-14-1-1-1-411111-1-1-414-1005−500−5511-1-155−5−5−5−55500-40004000000011−550000-1-15−5000000000000000
χ5544-4-44004-14-1-1-1-411111-1-1-414-100−55005−511-1-1−5−55555−5−5004000-40000000-1-1−550000115−5000000000000000
χ5644-4-44004-14-1-1-1-411111-1-1-414-100−55005−511-1-1−5−55555−5−500-400040000000115−50000-1-1−55000000000000000
χ5744-4-4400-14-14-1-11-41111-1-11-4-145−500−550011-1-15−55−5−55−554000-400000-1-15−5000011−550000000000000000000
χ5844-4-4400-14-14-1-11-41111-1-11-4-145−500−550011-1-15−55−5−55−55-400040000011−550000-1-15−50000000000000000000
χ5944-4-4400-14-14-1-11-41111-1-11-4-14−55005−50011-1-1−55−555−55−54000-400000-1-1−550000115−50000000000000000000
χ6044-4-4400-14-14-1-11-41111-1-11-4-14−55005−50011-1-1−55−555−55−5-4000400000115−50000-1-1−550000000000000000000
χ614-40000044-4-444000000-4-4000000000000000000000000000000004-40000000000000000000002-22-2000000
χ624-40000044-4-444000000-4-4000000000000000000000000000000004-4000000000000000000000-22-22000000
χ634-40000044-4-444000000-4-400000000000000000000000000000000-440000000000000000000002i−2i−2i2i000000
χ644-40000044-4-444000000-4-400000000000000000000000000000000-44000000000000000000000−2i2i2i−2i000000
χ658888888-2-2-2-23-2-2-233-2-23-2-2-2-2-2-2-2-2-2-2-2-2-23-23-23-2-233-2-2300000000000000000000000000000000000000000
χ668888888-2-2-2-2-23-2-2-2-233-23-2-2-2-2-2-2-2-2-2-2-2-2-23-23-233-2-233-200000000000000000000000000000000000000000
χ6788888-8-8-2-2-2-23-2-2-233-2-23-2-2-2-2-2222222223-23-2-322-3-322-300000000000000000000000000000000000000000
χ6888888-8-8-2-2-2-2-23-2-2-2-233-23-2-2-2-222222222-23-232-3-322-3-3200000000000000000000000000000000000000000
χ69888-8-88-8-2-2-2-23-2-2-233-2-23-22222-2-2-2-22222-32-323-2-23-322-300000000000000000000000000000000000000000
χ70888-8-88-8-2-2-2-2-23-2-2-2-233-232222-2-2-2-222222-32-3-233-22-3-3200000000000000000000000000000000000000000
χ71888-8-8-88-2-2-2-23-2-2-233-2-23-222222222-2-2-2-2-32-32-322-33-2-2300000000000000000000000000000000000000000
χ72888-8-8-88-2-2-2-2-23-2-2-2-233-2322222222-2-2-2-22-32-32-3-32-233-200000000000000000000000000000000000000000
χ7388-88-800-2-2-2-23-222-3-3223-2-2-22225−2525−2525−2525−253-2-32−5005−500500000000000000000000000000000000000000000
χ7488-88-800-2-2-2-23-222-3-3223-2-2-222−2525−2525−2525−25253-2-32500−5500−500000000000000000000000000000000000000000
χ7588-88-800-2-2-2-2-232222-3-3-23-2-22225−25−252525−25−2525-232-305−5005−5000000000000000000000000000000000000000000
χ7688-88-800-2-2-2-2-232222-3-3-23-2-222−252525−25−252525−25-232-30−5500−55000000000000000000000000000000000000000000
χ7788-8-8800-2-2-2-23-222-3-3223-222-2-225−2525−25−2525−2525-323-2−5005500−500000000000000000000000000000000000000000
χ7888-8-8800-2-2-2-23-222-3-3223-222-2-2−2525−252525−2525−25-323-2500−5−500500000000000000000000000000000000000000000
χ7988-8-8800-2-2-2-2-232222-3-3-2322-2-225−25−2525−252525−252-3-2305−500−55000000000000000000000000000000000000000000
χ8088-8-8800-2-2-2-2-232222-3-3-2322-2-2−252525−2525−25−25252-3-230−55005−5000000000000000000000000000000000000000000
χ8116-160000016-4-164-4-40000004400000000000000000000000000000000000000000000000000000000000000000
χ8216-1600000-4164-16-4-40000004400000000000000000000000000000000000000000000000000000000000000000
χ8316-1600000-4-4446-40010-1000-6400000000000000000000000000000000000000000000000000000000000000000
χ8416-1600000-4-4446-400-101000-6400000000000000000000000000000000000000000000000000000000000000000
χ8516-1600000-4-444-46000010-104-600000000000000000000000000000000000000000000000000000000000000000
χ8616-1600000-4-444-460000-10104-600000000000000000000000000000000000000000000000000000000000000000

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