Finite Group Databasebeta

← Group #10772497

Character table — Group #10772497

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222222444444444446666668888888888888888121212121212121616161616161616161624242424242424324848
order1222344446664448888121212122244442444466881212122424242444488882812121212242424244444488648
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-11-1-11111111111111111-1-11-1-1-111-1-11-1-1-1-111-1-1-1
χ311111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-11-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-11-1-1-111-1-1-11111-1-1-111
χ5111111111111111-1-1-1-111111111111111111-1-1111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1
χ6111111111111111-1-1-1-11111111111-1-1-1-11-1-1-1-1111-1-1-1-1111-1-1-1-1111-1-1-1-1-1111-1-1-1-1-1-1111
χ7111111111111111-1-1-1-11111-1-1-1-1-1-11111111-1-1111-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-111-111
χ8111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-11111111-1-1-1-1-111-11111111-1-1
χ9111111111111-1-111111111111111111-1-1-111-1-1-1-1111111-1-11111-11-11-1-1-1-111-11-1-11-1-1-1-11
χ10111111111111-1-1111111111111111-1-111-1-1-1-1-1-1-1111111-1-111111-1-1-111-1-1-1-1-1-111-1-1-111-1
χ11111111111111-1-1111111111-1-1-1-1-1-111-1-1-111-1-1-1-111111-111-1-1-1-1-11-11-1-1-1-1111-111-111-11-1
χ12111111111111-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111-111-1-1-1-11-1-1-111-1-1-1-111-1-11111-11
χ13111111111111-1-11-1-1-1-1111111111111-1-1-11111-1-11-1-1-1-11-1-1-1-1-1-11-1-11-1-111-1-1-11-1-111111-1
χ14111111111111-1-11-1-1-1-11111111111-1-111-1-1-111-1-11-1-1-1-11-1-1-1-1-1-1-11-1-1111111-1-111-111-1-11
χ15111111111111-1-11-1-1-1-11111-1-1-1-1-1-111-1-1-11111-1-11-1-1-1-1-11111111-1-11-1-111-1-11-111-1-1-11-11
χ16111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-111-1-11-1-1-1-1-1111111-11-1-111111111-1-11-1-1-11-1
χ17222222-2-2222200-200002-22-22222-2-22-2000220000-20000-2000000000-20000000-200200000
χ18222222-2-2222200-200002-22-22222-2-2-22000-2-20000-20000-200000000020000000200-200000
χ19222222-2-2222200-200002-22-2-2-2-2-2222-2000220000-200002000000000-20000000200-200000
χ20222222-2-2222200-200002-22-2-2-2-2-222-22000-2-20000-20000200000000020000000-200200000
χ2122222-222-222222-20000-22-2222-2-2-2-20000-2000022-200002-2-2000000-200000002000000000
χ2222222-222-222222-20000-22-22-2-222220000-2000022-20000-222000000-20000000-2000000000
χ2322222-222-2222-2-2-20000-22-2222-2-2-2-2000020000-2-2-2000022200000020000000-2000000000
χ2422222-222-2222-2-2-20000-22-22-2-22222000020000-2-2-20000-2-2-2000000200000002000000000
χ2522222-2-2-2-22220020000-2-2-2-222-2-222002-2000000020000-200000000002-20000002-2000000
χ2622222-2-2-2-22220020000-2-2-2-222-2-22200-22000000020000-20000000000-22000000-22000000
χ2722222-2-2-2-22220020000-2-2-2-2-2-222-2-2002-2000000020000200000000002-2000000-22000000
χ2822222-2-2-2-22220020000-2-2-2-2-2-222-2-200-2200000002000020000000000-220000002-2000000
χ292222-12222-1-1-12222222-1-1-1-100000022222-1-122-1-1-1-1-1-1-1000000022-1-1-1-1-1-1-1-10000000-100
χ302222-12222-1-1-12222222-1-1-1-1000000-2-2-2-221122-1-1-1-1-1-1-10000000-2-2-1111-1-1110000000100
χ312222-12222-1-1-1222-2-2-2-2-1-1-1-100000022222-1-1-2-2-1-1-111110000000-2-2-1-1-1-111110000000100
χ322222-12222-1-1-1222-2-2-2-2-1-1-1-1000000-2-2-2-2211-2-2-1-1-11111000000022-111111-1-10000000-100
χ332222-12222-1-1-1-2-222222-1-1-1-100000022-2-2-2-1-1-2-211-1-1-1-1-10000000-221-11111-1-10000000100
χ342222-12222-1-1-1-2-222222-1-1-1-1000000-2-222-211-2-211-1-1-1-1-100000002-211-1-111110000000-100
χ352222-12222-1-1-1-2-22-2-2-2-2-1-1-1-100000022-2-2-2-1-12211-1111100000002-21-111-1-1110000000-100
χ362222-12222-1-1-1-2-22-2-2-2-2-1-1-1-1000000-2-222-2112211-111110000000-2211-1-1-1-1-1-10000000100
χ3722-2-2202-20-2-222-2022−2−20-202002i−2i2i−2i00000002−22-2022−2−202i−2i−i2−i2i2i20000002−20000000−i2i2000
χ3822-2-2202-20-2-222-2022−2−20-20200−2i2i−2i2i00000002−22-2022−2−20−2i2ii2i2−i2−i20000002−20000000i2−i2000
χ3922-2-2202-20-2-222-20−2−2220-202002i−2i2i−2i0000000−222-20−2−22202i−2ii2i2−i2−i2000000−220000000i2−i2000
χ4022-2-2202-20-2-222-20−2−2220-20200−2i2i−2i2i0000000−222-20−2−2220−2i2i−i2−i2i2i2000000−220000000−i2i2000
χ4122-2-2202-20-2-22-22022−2−20-202002i−2i2i−2i0000000−22-22022−2−20−2i2i−i2−i2i2i2000000−220000000i2−i2000
χ4222-2-2202-20-2-22-22022−2−20-20200−2i2i−2i2i0000000−22-22022−2−202i−2ii2i2−i2−i2000000−220000000−i2i2000
χ4322-2-2202-20-2-22-220−2−2220-202002i−2i2i−2i00000002−2-220−2−2220−2i2ii2i2−i2−i20000002−20000000−i2i2000
χ4422-2-2202-20-2-22-220−2−2220-20200−2i2i−2i2i00000002−2-220−2−22202i−2i−i2−i2i2i20000002−20000000i2−i2000
χ454444-24-4-44-2-2-200-40000-22-220000004-4000-2-2000020000000000000020000000000000000
χ464444-24-4-44-2-2-200-40000-22-22000000-44000220000200000000000000-20000000000000000
χ474444-2-444-4-2-2-244-400002-22-20000000000-40000-2-220000000000000200000000000000000
χ484444-2-444-4-2-2-2-4-4-400002-22-20000000000400002220000000000000-200000000000000000
χ494444-2-4-4-4-4-2-2-200400002222000000004-40000000-2000000000000000-2200000000000000
χ504444-2-4-4-4-4-2-2-20040000222200000000-440000000-20000000000000002-200000000000000
χ5144-4-440-440-4-440000000040-4004i−4i−4i4i0000000000000000000000000000000000000000000
χ5244-4-440-440-4-440000000040-400−4i4i4i−4i0000000000000000000000000000000000000000000
χ5344-4-4-204-4022-24-402222−22−22020-2000000000000022−22-220−2−2220000000000000−22000000000000
χ5444-4-4-204-4022-24-40−22−222222020-20000000000000−2222-22022−2−200000000000002−2000000000000
χ5544-4-4-204-4022-2-4402222−22−22020-20000000000000−22222-20−2−22200000000000002−2000000000000
χ5644-4-4-204-4022-2-440−22−222222020-2000000000000022−222-2022−2−20000000000000−22000000000000
χ574-44-44400-44-4-4000000040-40000000000000000000000000022−2222−2200000000000000000000
χ584-44-44400-44-4-4000000040-400000000000000000000000000−2222−222200000000000000000000
χ594-44-44-40044-4-4000−2i22i2−2i22i2-4040000000000000000000−2i22i2−2i22i2000000000000000000000000000
χ604-44-44-40044-4-40002i2−2i22i2−2i2-40400000000000000000002i2−2i22i2−2i2000000000000000000000000000
χ614-44-4-2-4004-222000−2i22i2−2i22i220-2000000000000−2i32i300000i2−i2i2−i20000000000000006−60000000000
χ624-44-4-2-4004-222000−2i22i2−2i22i220-20000000000002i3−2i300000i2−i2i2−i2000000000000000−660000000000
χ634-44-4-2-4004-2220002i2−2i22i2−2i220-2000000000000−2i32i300000−i2i2−i2i2000000000000000−660000000000
χ644-44-4-2-4004-2220002i2−2i22i2−2i220-20000000000002i3−2i300000−i2i2−i2i20000000000000006−60000000000
χ654-4-4440000-44-40002i−2i−2i2i00004-400000000000000002i−2i−2i2i0002i−2i−2i2i00000000000000000000
χ664-4-4440000-44-40002i−2i−2i2i0000-4400000000000000002i−2i−2i2i000−2i2i2i−2i00000000000000000000
χ674-4-4440000-44-4000−2i2i2i−2i00004-40000000000000000−2i2i2i−2i000−2i2i2i−2i00000000000000000000
χ684-4-4440000-44-4000−2i2i2i−2i0000-440000000000000000−2i2i2i−2i0002i−2i−2i2i00000000000000000000
χ6988-8-8-40-88044-400000000-4040000000000000000000000000000000000000000000000000
χ708-88-8-4800-8-4440000000-40400000000000000000000000000000000000000000000000000
χ718-8-88-400004-440004i−4i−4i4i0000000000000000000000−2i2i2i−2i000000000000000000000000000
χ728-8-88-400004-44000−4i4i4i−4i00000000000000000000002i−2i−2i2i000000000000000000000000000

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