Finite Group Databasebeta

← Group #10778317

Character table — Group #10778317

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size1111222222224444444446666666666888888888888812121216161616161616161616242424242424242432324848
order122234444666488881212121222444488882488888812242424244884461224242424242424888888121244
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-11111111111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-1-1-1-1-1-1-11111111111-1-1
χ91111111111111-1-1-1-11111111111-1-1-1-111-1-111-1-11-1-1-1-11-1-11-111-1-111-1-111-1-111-1-11-11-1
χ101111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1111-1-1-1-11-1-1-1111-1-1-1-11111-1-1-1-111-11-11
χ111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-11-1-1-1-11-1-1-11-1-11111-1-1-1-11111-1-1-11-11
χ121111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1111-1-1-1-11-1-11-1-1-111-1-111-1-111-1-1111-11-1
χ131111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-11-1-1-1-1-1111-111-1-111-1-1-1-111-1-1111-1-11
χ141111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-1-111-1111-1-1-1-111-1-11111-1-1-111-1
χ151111111111111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-11-1-1-1-1-111-11-1-11111-1-111-1-1-1-111-111-1
χ161111111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1111-1-1-1-1-1111-1-1-111-1-11111-1-111-1-11-1-11
χ17222222-2-22222-200002-2-2222-2-22200002-2000000-20000-200002-2000000-220000000000
χ18222222-2-22222-200002-2-2222-2-2220000-22000000-20000-20000-220000002-20000000000
χ19222222-2-22222-200002-2-22-2-222-2-200002-2000000-20000200002-20000002-20000000000
χ20222222-2-22222-200002-2-22-2-222-2-20000-22000000-2000020000-22000000-220000000000
χ2122222-222-2222-222-2-2-222-22222-2-2-2-2-2-200000000-222-2-2-2220000000000000000000000
χ2222222-222-2222-222-2-2-222-2-2-2-2-222222200000000-222-2-22-2-20000000000000000000000
χ2322222-222-2222-2-2-222-222-22222-2-2222200000000-2-2-222-2-2-20000000000000000000000
χ2422222-222-2222-2-2-222-222-2-2-2-2-222-2-2-2-200000000-2-2-2222220000000000000000000000
χ2522222-2-2-2-222220000-2-2-2-222-2-2-2-20000002i−2i00002000020000002i−2i0000002i−2i00000000
χ2622222-2-2-2-222220000-2-2-2-222-2-2-2-2000000−2i2i0000200002000000−2i2i000000−2i2i00000000
χ2722222-2-2-2-222220000-2-2-2-2-2-222220000002i−2i000020000-20000002i−2i000000−2i2i00000000
χ2822222-2-2-2-222220000-2-2-2-2-2-22222000000−2i2i000020000-2000000−2i2i0000002i−2i00000000
χ292222-12222-1-1-122222-1-1-1-1000000000022222222-1-1-1-1-100022-1-1-1-1-1-1-1-100000000-1-100
χ302222-12222-1-1-122222-1-1-1-100000000002222-2-2-2-2-1-1-1-1-1000-2-2-1-1-1-11111000000001100
χ312222-12222-1-1-122222-1-1-1-10000000000-2-2-2-22222-1-1-1-1-1000-2-21111-1-1-1-1000000001100
χ322222-12222-1-1-122222-1-1-1-10000000000-2-2-2-2-2-2-2-2-1-1-1-1-1000221111111100000000-1-100
χ332222-12222-1-1-12-2-2-2-2-1-1-1-1000000000022-2-222-2-2-111110002-2-1-111-1-11100000000-1100
χ342222-12222-1-1-12-2-2-2-2-1-1-1-1000000000022-2-2-2-222-11111000-22-1-11111-1-1000000001-100
χ352222-12222-1-1-12-2-2-2-2-1-1-1-10000000000-2-22222-2-2-11111000-2211-1-1-1-111000000001-100
χ362222-12222-1-1-12-2-2-2-2-1-1-1-10000000000-2-222-2-222-111110002-211-1-111-1-100000000-1100
χ3722-2-220-2202-2-20002-20-2202-22-20022-2-20000i2−i2i2−i20002-2000000000i2−i2i2−i20000i2−i2i2−i20000
χ3822-2-220-2202-2-20002-20-2202-22-20022-2-20000−i2i2−i2i20002-2000000000−i2i2−i2i20000−i2i2−i2i20000
χ3922-2-220-2202-2-20002-20-220-22-2200-2-2220000i2−i2i2−i20002-2000000000i2−i2i2−i20000−i2i2−i2i20000
χ4022-2-220-2202-2-20002-20-220-22-2200-2-2220000−i2i2−i2i20002-2000000000−i2i2−i2i20000i2−i2i2−i20000
χ4122-2-220-2202-2-2000-220-2202-22-200-2-2220000i2−i2−i2i2000-22000000000i2−i2−i2i20000i2−i2−i2i20000
χ4222-2-220-2202-2-2000-220-2202-22-200-2-2220000−i2i2i2−i2000-22000000000−i2i2i2−i20000−i2i2i2−i20000
χ4322-2-220-2202-2-2000-220-220-22-220022-2-20000i2−i2−i2i2000-22000000000i2−i2−i2i20000−i2i2i2−i20000
χ4422-2-220-2202-2-2000-220-220-22-220022-2-20000−i2i2i2−i2000-22000000000−i2i2i2−i20000i2−i2−i2i20000
χ454444-24-4-44-2-2-2-40000-222-200000000004-40000002000000000-22000000000000000000
χ464444-24-4-44-2-2-2-40000-222-20000000000-4400000020000000002-2000000000000000000
χ474444-2-444-4-2-2-2-444-4-42-2-220000000000000000002-2-2220000000000000000000000000
χ484444-2-444-4-2-2-2-4-4-4442-2-22000000000000000000222-2-20000000000000000000000000
χ494444-2-4-4-4-4-2-2-24000022220000000000004i−4i0000-200000000000−2i2i0000000000000000
χ504444-2-4-4-4-4-2-2-2400002222000000000000−4i4i0000-2000000000002i−2i0000000000000000
χ5144-4-4404-404-4-40000004-404-4-4400000000000000000000000000000000000000000000
χ5244-4-4404-404-4-40000004-40-444-400000000000000000000000000000000000000000000
χ5344-4-4-20-440-2220004-402-20000000000000002i2−2i22i2−2i2000-22000000000−i2i2−i2i2000000000000
χ5444-4-4-20-440-2220004-402-2000000000000000−2i22i2−2i22i2000-22000000000i2−i2i2−i2000000000000
χ5544-4-4-20-440-222000-4402-20000000000000002i2−2i2−2i22i20002-2000000000−i2i2i2−i2000000000000
χ5644-4-4-20-440-222000-4402-2000000000000000−2i22i22i2−2i20002-2000000000i2−i2−i2i2000000000000
χ574-44-440000-44-402i2−2i200000000004i−4i22−2222−220000000002i2−2i2000000000000000000000000000
χ584-44-440000-44-402i2−2i20000000000−4i4i−2222−22220000000002i2−2i2000000000000000000000000000
χ594-44-440000-44-40−2i22i200000000004i−4i−2222−2222000000000−2i22i2000000000000000000000000000
χ604-44-440000-44-40−2i22i20000000000−4i4i22−2222−22000000000−2i22i2000000000000000000000000000
χ614-4-444400-4-4-4400000400-400000022−22−22220000000000000022−220000000000000000000000
χ624-4-444400-4-4-4400000400-4000000−222222−2200000000000000−22220000000000000000000000
χ634-4-444-4004-4-4400000-400400000022−22−222200000000000000−22220000000000000000000000
χ644-4-444-4004-4-4400000-4004000000−222222−220000000000000022−220000000000000000000000
χ6588-8-8-408-80-444000000-440000000000000000000000000000000000000000000000000
χ668-88-8-400004-4404i2−4i20000000000000000000000000−2i22i2000000000000000000000000000
χ678-88-8-400004-440−4i24i200000000000000000000000002i2−2i2000000000000000000000000000
χ688-8-88-4800-844-400000-4004000000000000000000000000000000000000000000000000
χ698-8-88-4-800844-400000400-4000000000000000000000000000000000000000000000000

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