Finite Group Databasebeta

← Group #10823685

Character table — Group #10823685

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444666666668888888888888888881616161616161616161616162424242424242424242424242424
order12222234444666661212121244444444444444444488881212121212121212121212122424242422444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111
χ51111111111111111111111111111-1-11-11-111-1-111-1-1-1-1-1-11-111-1-11-111-1-11-111-1-11-1-1-111-1-1
χ61111111111111111111111111111-1-11-11-1-1-111-1-11111111-1-1-1-1-11-1-1-1111-1-1-1-1-11-111-1-111
χ71111111111111111111111111111-1-1-11-1111-1-1-1-111-1-1-1-1-1111-1-1-11-1-111-1111-1-1-11-1-1-1-111
χ81111111111111111111111111111-1-1-11-11-1-11111-1-11111-11-1-1-1-1-1111-1-1-11-1-1-1-1-111111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1111111
χ1111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-111-1-11111
χ1211111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-11111-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-1-1-11-111-1-11-111-1-1-11-1-111-1111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-11111111-1-1-1-1-11-1-1-111-111111-11-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-1-1-1-1-1111-1-1-11-1-1111-1-1-1111-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-1-11111-11-1-1-1-1-1111-1-11-111111-1-1-1-1-111
χ172222222-2-2-2-222222-2-2-2-22222-2-2-2-22-2000000000000000000002-200000000002-200000000
χ182222222-2-2-2-222222-2-2-2-22222-2-2-2-2-2200000000000000000000-220000000000-2200000000
χ192222222-2-2-2-222222-2-2-2-2-2-2-2-222222-2000000000000000000002-20000000000-2200000000
χ202222222-2-2-2-222222-2-2-2-2-2-2-2-22222-2200000000000000000000-2200000000002-200000000
χ21222222-12222-1-1-1-1-1-1-1-1-10000000022222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ22222222-12222-1-1-1-1-1-1-1-1-100000000222222-2-2-2-2-2-2-2-21111-1-111-1-1-1-1111100000000000000
χ23222222-12222-1-1-1-1-1-1-1-1-10000000022-2-2-2-22222-2-2-2-2-1-1-1-111-1-1-1-111111100000000000000
χ24222222-12222-1-1-1-1-1-1-1-1-10000000022-2-2-2-2-2-2-2-2222211111111-1-111-1-1-1-100000000000000
χ25222222-12222-1-1-1-1-1-1-1-1-100000000-2-22-22-222-2-222-2-21111-11-1-111-11-1-11100000000000000
χ26222222-12222-1-1-1-1-1-1-1-1-100000000-2-22-22-2-2-222-2-222-1-1-1-1-111111-1111-1-100000000000000
χ27222222-12222-1-1-1-1-1-1-1-1-100000000-2-2-22-2222-2-2-2-22211111-1-1-1111-111-1-100000000000000
χ28222222-12222-1-1-1-1-1-1-1-1-100000000-2-2-22-22-2-22222-2-2-1-1-1-11-111111-1-1-11100000000000000
χ292222-2-222-22-2222-2-22-22-222-2-222-2-200020-20000000000000-200000200000200000-2000000
χ302222-2-222-22-2222-2-22-22-222-2-222-2-2000-2020000000000000200000-200000-2000002000000
χ312222-2-222-22-2222-2-22-22-2-2-222-2-22200020-20000000000000-200000200000-2000002000000
χ322222-2-222-22-2222-2-22-22-2-2-222-2-222000-2020000000000000200000-200000200000-2000000
χ332222-2-22-22-22222-2-2-22-2222-2-2-2-2220020-20000000000000-200000200000-20000020000000
χ342222-2-22-22-22222-2-2-22-2222-2-2-2-22200-2020000000000000200000-200000200000-20000000
χ352222-2-22-22-22222-2-2-22-22-2-22222-2-20020-20000000000000-200000200000200000-20000000
χ362222-2-22-22-22222-2-2-22-22-2-22222-2-200-2020000000000000200000-200000-20000020000000
χ372-2-222-222-2-22-22-2-22-222-22i−2i2i−2i2i−2i2i−2i00000000002i−2i000000000000002i−2i0000000000002-200
χ382-2-222-222-2-22-22-2-22-222-22i−2i2i−2i2i−2i2i−2i0000000000−2i2i00000000000000−2i2i000000000000-2200
χ392-2-222-222-2-22-22-2-22-222-2−2i2i−2i2i−2i2i−2i2i00000000002i−2i000000000000002i−2i000000000000-2200
χ402-2-222-222-2-22-22-2-22-222-2−2i2i−2i2i−2i2i−2i2i0000000000−2i2i00000000000000−2i2i0000000000002-200
χ412-2-222-22-222-2-22-2-222-2-222i−2i2i−2i−2i2i−2i2i0000000000002i−2i000000000000002i−2i0000000000002-2
χ422-2-222-22-222-2-22-2-222-2-222i−2i2i−2i−2i2i−2i2i000000000000−2i2i00000000000000−2i2i000000000000-22
χ432-2-222-22-222-2-22-2-222-2-22−2i2i−2i2i2i−2i2i−2i0000000000002i−2i000000000000002i−2i000000000000-22
χ442-2-222-22-222-2-22-2-222-2-22−2i2i−2i2i2i−2i2i−2i000000000000−2i2i00000000000000−2i2i0000000000002-2
χ452-2-22-22222-2-2-22-22-2-2-2222i−2i−2i2i2i−2i−2i2i000000002i−2i00002i2i−2i−2i000000000000000000002-20000
χ462-2-22-22222-2-2-22-22-2-2-2222i−2i−2i2i2i−2i−2i2i00000000−2i2i0000−2i−2i2i2i00000000000000000000-220000
χ472-2-22-22222-2-2-22-22-2-2-222−2i2i2i−2i−2i2i2i−2i000000002i−2i00002i2i−2i−2i00000000000000000000-220000
χ482-2-22-22222-2-2-22-22-2-2-222−2i2i2i−2i−2i2i2i−2i00000000−2i2i0000−2i−2i2i2i000000000000000000002-20000
χ492-2-22-222-2-222-22-22-222-2-22i−2i−2i2i−2i2i2i−2i0000002-20000000000002-200000000002i−2i0000000000
χ502-2-22-222-2-222-22-22-222-2-22i−2i−2i2i−2i2i2i−2i000000-22000000000000-220000000000−2i2i0000000000
χ512-2-22-222-2-222-22-22-222-2-2−2i2i2i−2i2i−2i−2i2i0000002-20000000000002-20000000000−2i2i0000000000
χ522-2-22-222-2-222-22-22-222-2-2−2i2i2i−2i2i−2i−2i2i000000-22000000000000-2200000000002i−2i0000000000
χ53444444-2-4-4-4-4-2-2-2-2-22222000000004-400000000000000000000-2200000000000000000000
χ54444444-2-4-4-4-4-2-2-2-2-2222200000000-44000000000000000000002-200000000000000000000
χ554444-4-4-24-44-4-2-2-222-22-220000000000040-40000000000000200000-2000000000000000000
χ564444-4-4-24-44-4-2-2-222-22-2200000000000-4040000000000000-2000002000000000000000000
χ574444-4-4-2-44-44-2-2-2222-22-2000000000040-40000000000000200000-20000000000000000000
χ584444-4-4-2-44-44-2-2-2222-22-20000000000-4040000000000000-20000020000000000000000000
χ594-4-444-4-24-4-442-222-22-2-220000000000000000004i−4i00000000000000−2i2i0000000000000000
χ604-4-444-4-24-4-442-222-22-2-22000000000000000000−4i4i000000000000002i−2i0000000000000000
χ614-4-444-4-2-444-42-222-2-222-2000000000000000000004i−4i00000000000000−2i2i00000000000000
χ624-4-444-4-2-444-42-222-2-222-200000000000000000000−4i4i000000000000002i−2i00000000000000
χ634-4-44-44-244-4-42-22-2222-2-200000000000000004i−4i0000−2i−2i2i2i00000000000000000000000000
χ644-4-44-44-244-4-42-22-2222-2-20000000000000000−4i4i00002i2i−2i−2i00000000000000000000000000
χ654-4-44-44-2-4-4442-22-22-2-222000000000000004-4000000000000-220000000000000000000000
χ664-4-44-44-2-4-4442-22-22-2-22200000000000000-440000000000002-20000000000000000000000
χ6788-8-80080000-8-880000000000000000000000000000000000000000000000000000000000
χ6888-8-800-4000044-4000000000000000000000000000023−2323−2300000000000000000000000000
χ6988-8-800-4000044-40000000000000000000000000000−2323−232300000000000000000000000000
χ708-88-800800008-8-80000000000000000000000000000000000000000000000000000000000
χ718-88-800-40000-4440000000000000000000000000000−2i32i32i3−2i300000000000000000000000000
χ728-88-800-40000-44400000000000000000000000000002i3−2i3−2i32i300000000000000000000000000

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