Finite Group Databasebeta

← Group #10772488

Character table — Group #10772488

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222222444444444446666668888888888888888121212121212121616161616161616161624242424242424324848
order1222344446662248888121212122244442444466881212122424242444488884681212122424242424444881228
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-111111-1-1111111111111-1-1-11-1-111-1-11-1-1-1-111-1-1-1
χ311111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-11-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-1-1-111111-1-111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-11111-1-1-111
χ5111111111111111-1-1-1-111111111111111111-1-1111-1-1-1-1111-1-1-1-1-11-1111-1-1-1-111111-1-1-1-1-1
χ6111111111111111-1-1-1-11111111111-1-1-1-1111-1-1-1-11-1-1-1-1111-1-1-1-11-111-1-1-1-1111-1-1-1-1-1-1111
χ7111111111111111-1-1-1-11111-1-1-1-1-1-11111111-1-1111-1-1-1-1-1-1-11111-11-1111-1-1-1-1-1-1-1-1-111-111
χ8111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-111111-111-1-1-1-111-11111111-1-1
χ9111111111111-1-111111111111111111-1-1-1-1-1-1-111111111-1-11111-111-1-1-1-1-111-111-1-1-1-1-1-11
χ10111111111111-1-1111111111111111-1-111-1-1-1-1-1-1-1111111-1-111111-1-1-111-1-1-1-1-1-1-111-1-111-1
χ11111111111111-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-11111111-111-1-1-1-1-111-1-1-1-1-1111-1-11111-11-1
χ12111111111111-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111-111-1-1-1-11-1-1-111-1-1-1-1111-1-1111-11
χ13111111111111-1-11-1-1-1-1111111111111-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-1-111-1-11111-1
χ14111111111111-1-11-1-1-1-11111111111-1-111-1-1-111-1-11-1-1-1-11-1-1-1-1-1-1-1-11-1111111-1-1-11111-1-11
χ15111111111111-1-11-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-1-111111111-1-1-1-111-1-11-1-111-1-11-11
χ16111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-111-1-11-1-1-1-1-1111111-1-11-1111111111-1-1-1-1-11-1
χ17222222-2-2222200-200002-22-222-2-2222-20000000-2-2-20000-2000000020000000002-20000000
χ18222222-2-2222200-200002-22-222-2-222-22000000022-20000-20000000-2000000000-220000000
χ19222222-2-2222200-200002-22-2-2-222-2-22-20000000-2-2-20000200000002000000000-220000000
χ20222222-2-2222200-200002-22-2-2-222-2-2-22000000022-2000020000000-20000000002-20000000
χ2122222-222-222222-20000-22-2222-2-2-2-20000-2220000-200002-2-20000000-20000002000000000
χ2222222-222-222222-20000-22-22-2-222220000-2220000-20000-2220000000-2000000-2000000000
χ2322222-222-2222-2-2-20000-22-2222-2-2-2-200002-2-20000-2000022200000002000000-2000000000
χ2422222-222-2222-2-2-20000-22-22-2-2222200002-2-20000-20000-2-2-2000000020000002000000000
χ2522222-2-2-2-22220020000-2-2-2-22222-2-2002-2000000020000-200000000002-200000002-200000
χ2622222-2-2-2-22220020000-2-2-2-22222-2-200-22000000020000-20000000000-220000000-2200000
χ2722222-2-2-2-22220020000-2-2-2-2-2-2-2-222002-2000000020000200000000002-20000000-2200000
χ2822222-2-2-2-22220020000-2-2-2-2-2-2-2-22200-2200000002000020000000000-2200000002-200000
χ292222-12222-1-1-12222222-1-1-1-100000022222-1-122-1-1-1-1-1-1-100000002-12-1-1-1-1-1-1-10000000-100
χ302222-12222-1-1-12222222-1-1-1-1000000-2-2-2-22-1-12211-1-1-1-1-10000000-21-2-111-1-1110000000100
χ312222-12222-1-1-1222-2-2-2-2-1-1-1-100000022222-1-1-2-2-1-1-111110000000-2-1-2-1-1-111110000000100
χ322222-12222-1-1-1222-2-2-2-2-1-1-1-1000000-2-2-2-22-1-1-2-211-111110000000212-11111-1-10000000-100
χ332222-12222-1-1-1-2-222222-1-1-1-100000022-2-2-211-2-2-1-1-1-1-1-1-10000000-2-1211111-1-10000000100
χ342222-12222-1-1-1-2-222222-1-1-1-1000000-2-222-211-2-211-1-1-1-1-1000000021-21-1-111110000000-100
χ352222-12222-1-1-1-2-22-2-2-2-2-1-1-1-100000022-2-2-21122-1-1-1111100000002-1-2111-1-1110000000-100
χ362222-12222-1-1-1-2-22-2-2-2-2-1-1-1-1000000-2-222-2112211-111110000000-2121-1-1-1-1-1-10000000100
χ3722-2-220-220-2-222-20−i2−i2i2i2020-2002i−2i2i−2i000002-2−i2i2000−i2−i2i2i202i−2i22−2−2000000−i2i200000002−2000
χ3822-2-220-220-2-222-20−i2−i2i2i2020-200−2i2i−2i2i000002-2−i2i2000−i2−i2i2i20−2i2i−2−222000000−i2i20000000−22000
χ3922-2-220-220-2-222-20i2i2−i2−i2020-2002i−2i2i−2i000002-2i2−i2000i2i2−i2−i202i−2i−2−222000000i2−i20000000−22000
χ4022-2-220-220-2-222-20i2i2−i2−i2020-200−2i2i−2i2i000002-2i2−i2000i2i2−i2−i20−2i2i22−2−2000000i2−i200000002−2000
χ4122-2-220-220-2-22-220−i2−i2i2i2020-2002i−2i2i−2i00000-22i2−i2000−i2−i2i2i20−2i2i22−2−2000000i2−i20000000−22000
χ4222-2-220-220-2-22-220−i2−i2i2i2020-200−2i2i−2i2i00000-22i2−i2000−i2−i2i2i202i−2i−2−222000000i2−i200000002−2000
χ4322-2-220-220-2-22-220i2i2−i2−i2020-2002i−2i2i−2i00000-22−i2i2000i2i2−i2−i20−2i2i−2−222000000−i2i200000002−2000
χ4422-2-220-220-2-22-220i2i2−i2−i2020-200−2i2i−2i2i00000-22−i2i2000i2i2−i2−i202i−2i22−2−2000000−i2i20000000−22000
χ454444-24-4-44-2-2-200-40000-22-220000004-40000000222000000000000-2000000000000000000
χ464444-24-4-44-2-2-200-40000-22-22000000-440000000-2-220000000000002000000000000000000
χ474444-2-444-4-2-2-244-400002-22-20000000000-4-2-2000020000000000000020000000000000000
χ484444-2-444-4-2-2-2-4-4-400002-22-200000000004220000200000000000000-20000000000000000
χ494444-2-4-4-4-4-2-2-200400002222000000004-40000000-2000000000000000-2200000000000000
χ504444-2-4-4-4-4-2-2-20040000222200000000-440000000-20000000000000002-200000000000000
χ5144-4-4404-40-4-4400000000-404004i−4i−4i4i0000000000000000000000000000000000000000000
χ5244-4-4404-40-4-4400000000-40400−4i4i4i−4i0000000000000000000000000000000000000000000
χ5344-4-4-20-44022-24-40−2i2−2i22i22i20-20200000000000-22−2i22i2000i2i2−i2−i20000000000000i2−i2000000000000
χ5444-4-4-20-44022-24-402i22i2−2i2−2i20-20200000000000-222i2−2i2000−i2−i2i2i20000000000000−i2i2000000000000
χ5544-4-4-20-44022-2-440−2i2−2i22i22i20-202000000000002-22i2−2i2000i2i2−i2−i20000000000000−i2i2000000000000
χ5644-4-4-20-44022-2-4402i22i2−2i2−2i20-202000000000002-2−2i22i2000−i2−i2i2i20000000000000i2−i2000000000000
χ574-44-440000-44-40002i−2i2i−2i00004-400000000000000002i−2i2i−2i0002i−2i2i−2i00000000000000000000
χ584-44-440000-44-40002i−2i2i−2i0000-4400000000000000002i−2i2i−2i000−2i2i−2i2i00000000000000000000
χ594-44-440000-44-4000−2i2i−2i2i00004-40000000000000000−2i2i−2i2i000−2i2i−2i2i00000000000000000000
χ604-44-440000-44-4000−2i2i−2i2i0000-440000000000000000−2i2i−2i2i0002i−2i2i−2i00000000000000000000
χ614-4-444400-44-4-4000000040-400000000000000000000000000−2i22i22i2−2i200000000000000000000
χ624-4-444400-44-4-4000000040-4000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ634-4-444-40044-4-400022−22−2222-404000000000000000000022−22−2222000000000000000000000000000
χ644-4-444-40044-4-4000−222222−22-4040000000000000000000−222222−22000000000000000000000000000
χ654-4-44-2-4004-22200022−22−222220-2000000000000000023−230−222−20000000000000006−60000000000
χ664-4-44-2-4004-22200022−22−222220-20000000000000000−23230−222−2000000000000000−660000000000
χ674-4-44-2-4004-222000−222222−2220-2000000000000000023−2302−2−22000000000000000−660000000000
χ684-4-44-2-4004-222000−222222−2220-20000000000000000−232302−2−220000000000000006−60000000000
χ6988-8-8-408-8044-40000000040-40000000000000000000000000000000000000000000000000
χ708-88-8-400004-440004i−4i4i−4i0000000000000000000000−2i2i−2i2i000000000000000000000000000
χ718-88-8-400004-44000−4i4i−4i4i00000000000000000000002i−2i2i−2i000000000000000000000000000
χ728-8-88-4800-8-4440000000-40400000000000000000000000000000000000000000000000000

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