Finite Group Databasebeta

← Group #10827328

Character table — Group #10827328

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size1111222222222244444466888888888888888812121212121212161616161616161616161616162424242424242424242448
order12222234444666661212121244444444444488121212122244444812121212121212122424242422244444888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111-111-1-11111-1-1-1-11-1-1111-1-1-1-1-1
χ311111111111111111111111-11-1-1-111-1-111-1-1-1-11111111-11-1111-1-1-111-1-1-111-1-1-1-1-111-1
χ411111111111111111111111-11-1-1-1-1-111-1-11111111111111-1-1-11-1-1-1-1-111-1-1-1-1-1-111-1-11
χ51111111111111111111111-11-11-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1111-11-1-1-1-1111111-1-1-1-1-1-11
χ61111111111111111111111-11-11-1-1-1-11111111111-1-1-1-11-1-11-1-1-11-1-111-1-11-1-11-1-11111-1
χ71111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-11-1-1-111-1-111-1-1-1-1-111-11111-1-1-1
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1111
χ911111111111111111111-1-11111111111111111-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1
χ1011111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111-1-1-111111
χ1111111111111111111111-1-11-11-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-111-1-11-1-111111-1-11
χ1211111111111111111111-1-11-11-1-1-1-1-111-1-11111-1-1-1-1-1-1-111-1-1-11-1-1-1-1-111111111-1-111-1
χ1311111111111111111111-1-1-11-11-1-111-1-1-1-1-1-1-1-1-1-11111-11-1111-11-1-1-1-111-1-1-1-1111111-1
χ1411111111111111111111-1-1-11-11-1-1-1-111111111-1-11111-1-1-11-1-1-11-1-111-1-1-111-111-1-1-1-11
χ1511111111111111111111-1-1-1-1-1-1111111-1-11111-1-11111-1-1-1-111-1-111-1-1-1-11-1-11-1-1-1-1111
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-11-1-1-1-1-1-11111111111-1-111-1-1-1
χ172222222-2-2-2-222222-2-2-2-22200002-20000000000-2-20000200000002-2000000002-200000
χ182222222-2-2-2-222222-2-2-2-2220000-220000000000-2-2000020000000-2200000000-2200000
χ192222222-2-2-2-222222-2-2-2-2-2-200002-20000000000220000-200000002-200000000-2200000
χ202222222-2-2-2-222222-2-2-2-2-2-20000-220000000000220000-20000000-22000000002-200000
χ21222222-12222-1-1-1-1-1-1-1-1-100222222222222-1-1-1-100000002-1-1-1-1-1-1-1-1-1-1-1-100000000000
χ22222222-12222-1-1-1-1-1-1-1-1-100222222-2-2-2-2-2-211110000000-2-1-111-1-1-1-1111100000000000
χ23222222-12222-1-1-1-1-1-1-1-1-1002-22-2-2-222-2-22211110000000-2-11-1-1-1111-1-11100000000000
χ24222222-12222-1-1-1-1-1-1-1-1-1002-22-2-2-2-2-222-2-2-1-1-1-100000002-1111-111111-1-100000000000
χ25222222-12222-1-1-1-1-1-1-1-1-100-22-22-2-222-2-2-2-21111000000021-1-1-11-11111-1-100000000000
χ26222222-12222-1-1-1-1-1-1-1-1-100-22-22-2-2-2-22222-1-1-1-10000000-21-1111-111-1-11100000000000
χ27222222-12222-1-1-1-1-1-1-1-1-100-2-2-2-2222222-2-2-1-1-1-10000000-211-1-111-1-1111100000000000
χ28222222-12222-1-1-1-1-1-1-1-1-100-2-2-2-222-2-2-2-222111100000002111111-1-1-1-1-1-100000000000
χ292222-2-222-2-22222-2-22-22-22220-200000000000002-2-2-222-202000-2000000000000000000
χ302222-2-222-2-22222-2-22-22-222-20200000000000002-222-2-2-20-20002000000000000000000
χ312222-2-222-2-22222-2-22-22-2-2-220-20000000000000-2222-2-2202000-2000000000000000000
χ322222-2-222-2-22222-2-22-22-2-2-2-2020000000000000-22-2-22220-20002000000000000000000
χ332222-2-22-222-2222-2-2-22-2222020-2000000000000-220000-2002000-2000000200-20000000
χ342222-2-22-222-2222-2-2-22-22220-202000000000000-220000-200-20002000000-20020000000
χ352222-2-22-222-2222-2-2-22-22-2-2020-20000000000002-200002002000-2000000-20020000000
χ362222-2-22-222-2222-2-2-22-22-2-20-2020000000000002-20000200-20002000000200-20000000
χ372-2-222-2222-2-2-22-2-222-2-220000000000002i−2i0000002i−2i2i−2i00000000002i−2i0002-200000000
χ382-2-222-2222-2-2-22-2-222-2-220000000000002i−2i000000−2i2i−2i2i00000000002i−2i000-2200000000
χ392-2-222-2222-2-2-22-2-222-2-22000000000000−2i2i0000002i−2i2i−2i0000000000−2i2i000-2200000000
χ402-2-222-2222-2-2-22-2-222-2-22000000000000−2i2i000000−2i2i−2i2i0000000000−2i2i0002-200000000
χ412-2-22-2222-22-2-22-22-222-2-2000000002-200000000002i−2i−2i2i00002-200000000000000002i−2i0
χ422-2-22-2222-22-2-22-22-222-2-2000000002-20000000000−2i2i2i−2i00002-20000000000000000−2i2i0
χ432-2-22-2222-22-2-22-22-222-2-200000000-2200000000002i−2i−2i2i0000-220000000000000000−2i2i0
χ442-2-22-2222-22-2-22-22-222-2-200000000-220000000000−2i2i2i−2i0000-2200000000000000002i−2i0
χ45444444-2-4-4-4-4-2-2-2-2-222220000004-4000000000000000000000000-22000000000000000
χ46444444-2-4-4-4-4-2-2-2-2-22222000000-440000000000000000000000002-2000000000000000
χ474444-4-4-24-4-44-2-2-222-22-220040-4000000000000000000000-20002000000000000000000
χ484444-4-4-24-4-44-2-2-222-22-2200-4040000000000000000000002000-2000000000000000000
χ494444-4-4-2-444-4-2-2-2222-22-200040-4000000000000000000000-2000200000000000000000
χ504444-4-4-2-444-4-2-2-2222-22-2000-4040000000000000000000002000-200000000000000000
χ514-44-40040000-4-440000004i−4i000000002i−2i002i2i−2i−2i000000000000000000000000002-2000
χ524-44-40040000-4-440000004i−4i00000000−2i2i00−2i−2i2i2i00000000000000000000000000-22000
χ534-44-40040000-4-44000000−4i4i000000002i−2i002i2i−2i−2i00000000000000000000000000-22000
χ544-44-40040000-4-44000000−4i4i00000000−2i2i00−2i−2i2i2i000000000000000000000000002-2000
χ554-4-444-44-4-444-44-4-44-444-40000000000000000000000000000000000000000000000000
χ564-4-444-4-244-4-42-222-2-222-20000000000004i−4i00000000000000000000−2i2i0000000000000
χ574-4-444-4-244-4-42-222-2-222-2000000000000−4i4i000000000000000000002i−2i0000000000000
χ584-4-444-4-2-4-4442-222-22-2-2200000000000000000000000000000000000023−2300000000000
χ594-4-444-4-2-4-4442-222-22-2-22000000000000000000000000000000000000−232300000000000
χ604-4-44-444-44-44-44-44-4-4-4440000000000000000000000000000000000000000000000000
χ614-4-44-44-24-44-42-22-22-2-222000000004-4000000000000000000-220000000000000000000
χ624-4-44-44-24-44-42-22-22-2-22200000000-440000000000000000002-20000000000000000000
χ634-4-44-44-2-44-442-22-2222-2-20000000000000023−2323−230000000000000000000000000000000
χ644-4-44-44-2-44-442-22-2222-2-200000000000000−2323−23230000000000000000000000000000000
χ6588-8-800800008-8-80000000000000000000000000000000000000000000000000000000
χ6688-8-800-40000-44400000000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ6788-8-800-40000-444000000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ688-88-800-4000044-400000000000000004i−4i00−2i−2i2i2i0000000000000000000000000000000
χ698-88-800-4000044-40000000000000000−4i4i002i2i−2i−2i0000000000000000000000000000000

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