Finite Group Databasebeta

← Group #10705794

Character table — Group #10705794

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1111222222444444668888888888812121212121616161616161616161616161616161624242424242424484848
order122222366622446644444444466121222444488121212121212121212242424244444444488
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1
χ31111111111111111111-1-11111111111111-1-1-11-1-1-1-11111-1-1-1-11-1-11111-1-1-1
χ41111111111111111111-1-1-1-1-1-1111111111-1111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-111
χ51111111111111111-1-111111111111-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111-1-1111-1-1-1-11111-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-1-1-1-11111-111
χ71111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-111-1-1-1-1111
χ81111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111-11111111-1-1
χ91111111111-1-1-1-11111111ii−i−i-1-1-1-1111-1-1-1i−i111-1-1ii−i−iii−i−i-111ii−i−i-1i−i
χ101111111111-1-1-1-11111111−i−iii-1-1-1-1111-1-1-1−ii111-1-1−i−iii−i−iii-111−i−iii-1−ii
χ111111111111-1-1-1-111111-1-1ii−i−i-1-1-1-1111-1-11−ii1-1-111ii−i−i−i−iii-1-1-1ii−i−i1−ii
χ121111111111-1-1-1-111111-1-1−i−iii-1-1-1-1111-1-11i−i1-1-111−i−iiiii−i−i-1-1-1−i−iii1i−i
χ131111111111-1-1-1-111-1-1111ii−i−i-1-1-1-1-1-1-111-1i−i111-1-1ii−i−iii−i−i1-1-1−i−iii1−ii
χ141111111111-1-1-1-111-1-1111−i−iii-1-1-1-1-1-1-111-1−ii111-1-1−i−iii−i−iii1-1-1ii−i−i1i−i
χ151111111111-1-1-1-111-1-11-1-1ii−i−i-1-1-1-1-1-1-1111−ii1-1-111ii−i−i−i−iii111−i−iii-1i−i
χ161111111111-1-1-1-111-1-11-1-1−i−iii-1-1-1-1-1-1-1111i−i1-1-111−i−iiiii−i−i111ii−i−i-1−ii
χ17222222222222-2-22222-200000022-2-2-2-2222000-2000000000000-2000000000
χ18222222222222-2-222-2-2-200000022-2-222-2-2-2000-20000000000002000000000
χ192222222222-2-2222222-2000000-2-222-2-22-2-2000-20000000000002000000000
χ202222222222-2-22222-2-2-2000000-2-22222-222000-2000000000000-2000000000
χ21222222-1-1-1-12222-1-1002222222-1-1-1-100000222-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ22222222-1-1-1-12222-1-100222-2-2-2-2-1-1-1-1000002-2-2-1-1-1-1-1111111110000000000
χ23222222-1-1-1-12222-1-1002-2-22222-1-1-1-100000-2-2-2-11111-1-1-1-111110000000000
χ24222222-1-1-1-12222-1-1002-2-2-2-2-2-2-1-1-1-100000-222-111111111-1-1-1-10000000000
χ25222222-1-1-1-1-2-2-2-2-1-1002222i2i−2i−2i111100000-22i−2i-1-1-111−i−iii−i−iii0000000000
χ26222222-1-1-1-1-2-2-2-2-1-100222−2i−2i2i2i111100000-2−2i2i-1-1-111ii−i−iii−i−i0000000000
χ27222222-1-1-1-1-2-2-2-2-1-1002-2-22i2i−2i−2i1111000002−2i2i-111-1-1−i−iiiii−i−i0000000000
χ28222222-1-1-1-1-2-2-2-2-1-1002-2-2−2i−2i2i2i11110000022i−2i-111-1-1ii−i−i−i−iii0000000000
χ292-22-2-2222-2-2002i−2i-22000001+i−1−i1−i−1+i002i−2i2-202i−2i000000001+i−1−i1−i−1+i00000001+i−1−i1−i−1+i000
χ302-22-2-2222-2-2002i−2i-22000001+i−1−i1−i−1+i002i−2i-220−2i2i000000001+i−1−i1−i−1+i0000000−1−i1+i−1+i1−i000
χ312-22-2-2222-2-2002i−2i-2200000−1−i1+i−1+i1−i002i−2i2-202i−2i00000000−1−i1+i−1+i1−i0000000−1−i1+i−1+i1−i000
χ322-22-2-2222-2-2002i−2i-2200000−1−i1+i−1+i1−i002i−2i-220−2i2i00000000−1−i1+i−1+i1−i00000001+i−1−i1−i−1+i000
χ332-22-2-2222-2-200−2i2i-22000001−i−1+i1+i−1−i00−2i2i2-20−2i2i000000001−i−1+i1+i−1−i00000001−i−1+i1+i−1−i000
χ342-22-2-2222-2-200−2i2i-22000001−i−1+i1+i−1−i00−2i2i-2202i−2i000000001−i−1+i1+i−1−i0000000−1+i1−i−1−i1+i000
χ352-22-2-2222-2-200−2i2i-2200000−1+i1−i−1−i1+i00−2i2i2-20−2i2i00000000−1+i1−i−1−i1+i0000000−1+i1−i−1−i1+i000
χ362-22-2-2222-2-200−2i2i-2200000−1+i1−i−1−i1+i00−2i2i-2202i−2i00000000−1+i1−i−1−i1+i00000001−i−1+i1+i−1−i000
χ37444444-2-2-2-244-4-4-2-200-4000000-2-2220000000020000000000000000000000
χ38444444-2-2-2-2-4-444-2-200-400000022-2-20000000020000000000000000000000
χ394444-4-444440000-4-4440000000000000-40000000000000000000000000000
χ404444-4-444440000-4-4-4-4000000000000040000000000000000000000000000
χ414-44-44-444-4-44-4004-4000000000-44000000000000000000000000000000000
χ424-44-44-444-4-4-44004-40000000004-4000000000000000000000000000000000
χ434-44-44-4-2-2224-400-220000000002-200000000000000000006−66−60000000000
χ444-44-44-4-2-2224-400-220000000002-20000000000000000000−66−660000000000
χ454-44-44-4-2-222-4400-22000000000-220000000000000000000i6−i6−i6i60000000000
χ464-44-44-4-2-222-4400-22000000000-220000000000000000000−i6i6i6−i60000000000
χ474-44-4-44-2-222004i−4i2-2000002+2i−2−2i2−2i−2+2i00−2i2i0000000000000−1−i1+i−1+i1−i00000000000000
χ484-44-4-44-2-222004i−4i2-200000−2−2i2+2i−2+2i2−2i00−2i2i00000000000001+i−1−i1−i−1+i00000000000000
χ494-44-4-44-2-22200−4i4i2-2000002−2i−2+2i2+2i−2−2i002i−2i0000000000000−1+i1−i−1−i1+i00000000000000
χ504-44-4-44-2-22200−4i4i2-200000−2+2i2−2i−2−2i2+2i002i−2i00000000000001−i−1+i1+i−1−i00000000000000
χ514-4-44004-4-440000004-402-2000000000000000002-2000000000002-20000000
χ524-4-44004-4-440000004-40-2200000000000000000-2200000000000-220000000
χ534-4-44004-4-44000000-4402-2000000000000000002-200000000000-220000000
χ544-4-44004-4-44000000-440-2200000000000000000-22000000000002-20000000
χ558888-8-8-4-4-4-400004400000000000000000000000000000000000000000000
χ5688-8-8008-88-800000000000000000000000000000000000000000000000000
χ5788-8-800-44-4400000000000000000000000000000023−23000000000000000000
χ5888-8-800-44-44000000000000000000000000000000−2323000000000000000000
χ598-8-8800-444-40000000004-400000000000000000-2200000000000000000000
χ608-8-8800-444-4000000000-44000000000000000002-200000000000000000000

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