Finite Group Databasebeta

← Group #10705707

Character table — Group #10705707

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1111222222444444668888888888812121212121616161616161616161616161616161624242424242424484848
order12222236664444662244488881212121224444488121212121224242424242424244448888288
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1
χ31111111111111111111-1-11111111111111-1-1-11-1-1-1-1-1-1-1-111111-1-11111-1-1-1
χ41111111111111111111-1-1-1-1-1-1111111111-1111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-111
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
χ71111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-111-1-1-1-1111
χ81111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-11111111-1-1
χ91111111111-1-1-1-11111111ii−i−i-1-1-1-11-1-111-1i−i1-1-111ii−i−iii−i−i-111ii−i−i-1i−i
χ101111111111-1-1-1-11111111−i−iii-1-1-1-11-1-111-1−ii1-1-111−i−iii−i−iii-111−i−iii-1−ii
χ111111111111-1-1-1-111111-1-1ii−i−i-1-1-1-11-1-1111−ii111-1-1−i−iiiii−i−i-1-1-1ii−i−i1−ii
χ121111111111-1-1-1-111111-1-1−i−iii-1-1-1-11-1-1111i−i111-1-1ii−i−i−i−iii-1-1-1−i−iii1i−i
χ131111111111-1-1-1-111-1-1111ii−i−i-1-1-1-1-111-1-1-1i−i1-1-111ii−i−iii−i−i1-1-1−i−iii1−ii
χ141111111111-1-1-1-111-1-1111−i−iii-1-1-1-1-111-1-1-1−ii1-1-111−i−iii−i−iii1-1-1ii−i−i1i−i
χ151111111111-1-1-1-111-1-11-1-1ii−i−i-1-1-1-1-111-1-11−ii111-1-1−i−iiiii−i−i111−i−iii-1i−i
χ161111111111-1-1-1-111-1-11-1-1−i−iii-1-1-1-1-111-1-11i−i111-1-1ii−i−i−i−iii111ii−i−i-1−ii
χ1722222222222-2-222222-20000002-2-22222-2-2000-2000000000000-2000000000
χ1822222222222-2-2222-2-2-20000002-2-22-2-2-222000-20000000000002000000000
χ192222222222-222-22222-2000000-222-22-2-2-2-2000-20000000000002000000000
χ202222222222-222-222-2-2-2000000-222-2-22222000-2000000000000-2000000000
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
χ23222222-1-1-1-12222-1-1002-2-22222-1-1-1-100000-2-2-2-111111111-1-1-1-10000000000
χ24222222-1-1-1-12222-1-1002-2-2-2-2-2-2-1-1-1-100000-222-11111-1-1-1-111110000000000
χ25222222-1-1-1-1-2-2-2-2-1-1002222i2i−2i−2i111100000-22i−2i-111-1-1−i−iii−i−iii0000000000
χ26222222-1-1-1-1-2-2-2-2-1-100222−2i−2i2i2i111100000-2−2i2i-111-1-1ii−i−iii−i−i0000000000
χ27222222-1-1-1-1-2-2-2-2-1-1002-2-22i2i−2i−2i1111000002−2i2i-1-1-111ii−i−i−i−iii0000000000
χ28222222-1-1-1-1-2-2-2-2-1-1002-2-2−2i−2i2i2i11110000022i−2i-1-1-111−i−iiiii−i−i0000000000
χ292-22-22-222-2-202i−2i0-22000001+i−1−i1−i−1+i02i−2i002-22i−2i0000000000001+i−1−i1−i−1+i0001−i−1+i1+i−1−i000
χ302-22-22-222-2-202i−2i0-22000001+i−1−i1−i−1+i02i−2i00-22−2i2i0000000000001+i−1−i1−i−1+i000−1+i1−i−1−i1+i000
χ312-22-22-222-2-202i−2i0-2200000−1−i1+i−1+i1−i02i−2i002-22i−2i000000000000−1−i1+i−1+i1−i000−1+i1−i−1−i1+i000
χ322-22-22-222-2-202i−2i0-2200000−1−i1+i−1+i1−i02i−2i00-22−2i2i000000000000−1−i1+i−1+i1−i0001−i−1+i1+i−1−i000
χ332-22-22-222-2-20−2i2i0-22000001−i−1+i1+i−1−i0−2i2i002-2−2i2i0000000000001−i−1+i1+i−1−i0001+i−1−i1−i−1+i000
χ342-22-22-222-2-20−2i2i0-22000001−i−1+i1+i−1−i0−2i2i00-222i−2i0000000000001−i−1+i1+i−1−i000−1−i1+i−1+i1−i000
χ352-22-22-222-2-20−2i2i0-2200000−1+i1−i−1−i1+i0−2i2i002-2−2i2i000000000000−1+i1−i−1−i1+i000−1−i1+i−1+i1−i000
χ362-22-22-222-2-20−2i2i0-2200000−1+i1−i−1−i1+i0−2i2i00-222i−2i000000000000−1+i1−i−1−i1+i0001+i−1−i1−i−1+i000
χ37444444-2-2-2-24-4-44-2-200-4000000-222-20000000020000000000000000000000
χ38444444-2-2-2-2-444-4-2-200-40000002-2-220000000020000000000000000000000
χ394444-4-444440000-4-44400000000000-4000000000000000000000000000000
χ404444-4-444440000-4-4-4-4000000000004000000000000000000000000000000
χ4144-4-4004-44-40000004-402i−2i00000000000000000002i−2i0000000002i−2i0000000
χ4244-4-4004-44-40000004-40−2i2i0000000000000000000−2i2i000000000−2i2i0000000
χ4344-4-4004-44-4000000-4402i−2i00000000000000000002i−2i000000000−2i2i0000000
χ4444-4-4004-44-4000000-440−2i2i0000000000000000000−2i2i0000000002i−2i0000000
χ454-44-44-4-2-22204i−4i02-2000002+2i−2−2i2−2i−2+2i0−2i2i000000000000000000−1−i1+i−1+i1−i0000000000
χ464-44-44-4-2-22204i−4i02-200000−2−2i2+2i−2+2i2−2i0−2i2i0000000000000000001+i−1−i1−i−1+i0000000000
χ474-44-44-4-2-2220−4i4i02-2000002−2i−2+2i2+2i−2−2i02i−2i000000000000000000−1+i1−i−1−i1+i0000000000
χ484-44-44-4-2-2220−4i4i02-200000−2+2i2−2i−2−2i2+2i02i−2i0000000000000000001−i−1+i1+i−1−i0000000000
χ494-44-4-4444-4-4400-44-4000000000400-40000000000000000000000000000000
χ504-44-4-4444-4-4-40044-4000000000-40040000000000000000000000000000000
χ514-44-4-44-2-222400-4-22000000000-20020000000000000i6−i6i6−i600000000000000
χ524-44-4-44-2-222400-4-22000000000-20020000000000000−i6i6−i6i600000000000000
χ534-44-4-44-2-222-4004-22000000000200-200000000000006−6−6600000000000000
χ544-44-4-44-2-222-4004-22000000000200-20000000000000−666−600000000000000
χ558888-8-8-4-4-4-400004400000000000000000000000000000000000000000000
χ5688-8-800-44-440000000004i−4i0000000000000000000−2i2i000000000000000000
χ5788-8-800-44-44000000000−4i4i00000000000000000002i−2i000000000000000000
χ588-8-88008-8-8800000000000000000000000000000000000000000000000000
χ598-8-8800-444-4000000000000000000000000000023−2300000000000000000000
χ608-8-8800-444-40000000000000000000000000000−232300000000000000000000

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