Finite Group Databasebeta

← Group #272089

Character table — Group #272089

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222222244444448888888888888888161616161616161616161616161616323232
order12222244444444444442244444444888888444444888888888488
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-11111-1-1-111-1-1-11-1-1-1-1-1
χ311111111111111111111111111111-1-11111-1-1-1-1-1-11-1-1111-111-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111
χ511111111111111111111-1-1-1-1-11-1-1-1111111-1-1-1-1111111-1-11-1-1-1-11
χ611111111111111111111-1-1-1-1-11-1-1-111-1-1-1-1-1-1-1-1-1-1-111-11111111-1
χ711111111111111111111-1-1-1-1-11-1-1-1-1-111111111-1-11-1-11-1-1-1-1-111-1
χ811111111111111111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1111111-1-1-1-111-111-1-11
χ91111111111111-1-11-1-11-1111-1-1-11-1-111111111-1-111-1-1-1-1-1-1111-11-1
χ101111111111111-1-11-1-11-1111-1-1-11-1-111-1-1-1-111-1-1-1-11-1-11111-1-11-11
χ111111111111111-1-11-1-11-1111-1-1-11-1-1-1-11111-1-111-1-1-111-1-1-1-1111-11
χ121111111111111-1-11-1-11-1111-1-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11-1
χ131111111111111-1-11-1-11-1-1-1-111-1-111111111-1-11111-1-1-1-1111-1-11-1-1
χ141111111111111-1-11-1-11-1-1-1-111-1-11111-1-1-1-1-1-111-1-11-1-11-1-1111-111
χ151111111111111-1-11-1-11-1-1-1-111-1-111-1-1111111-1-1-1-1-111-111-1-1-1-111
χ161111111111111-1-11-1-11-1-1-1-111-1-111-1-1-1-1-1-111-1-1111111-1-1-1111-1-1
χ172222222-222-22-222-222-2-22-2-222-22-2-2000000000000000000000000
χ182222222-222-22-222-222-2-2-222-2-2-2-222000000000000000000000000
χ192222222-222-22-2-2-2-2-2-2-222-2-2-2-22222000000000000000000000000
χ202222222-222-22-2-2-2-2-2-2-22-222222-2-2-2000000000000000000000000
χ212222-2-2222-22-2-222-2-2-22200000-20000022-2-2000000200-200000000
χ222222-2-2222-22-2-222-2-2-22200000-200000-2-222000000-200200000000
χ232222-2-2222-22-2-2-2-2-2222-20000020000022-2-2000000-200200000000
χ242222-2-2222-22-2-2-2-2-2222-200000200000-2-222000000200-200000000
χ252222-2-22-22-2-2-22222-2-2-2-200000200000000000000000002i−2i02i−2i000
χ262222-2-22-22-2-2-22222-2-2-2-20000020000000000000000000−2i2i0−2i2i000
χ272222-2-22-22-2-2-22-2-2222-2200000-200000000000000000002i−2i0−2i2i000
χ282222-2-22-22-2-2-22-2-2222-2200000-20000000000000000000−2i2i02i−2i000
χ292222-2-2-22-2222-200200-2022-2000-2002200002-20000000000-200000
χ302222-2-2-22-2222-200200-2022-2000-200-2-20000-220000000000200000
χ312222-2-2-22-2222-200200-20-2-22000200220000-220000000000-200000
χ322222-2-2-22-2222-200200-20-2-22000200-2-200002-20000000000200000
χ332222-2-2-2-2-22-22200-200202-22000-200000000002-20002-2000000000
χ342222-2-2-2-2-22-22200-200202-22000-20000000000-22000-22000000000
χ352222-2-2-2-2-22-22200-20020-22-2000200000000002-2000-22000000000
χ362222-2-2-2-2-22-22200-20020-22-200020000000000-220002-2000000000
χ37444444-44-4-44-4400-400-40000000000000000000000000000000000
χ38444444-4-4-4-4-4-4-40040040000000000000000000000000000000000
χ3944-4-4000400-400000000000000000022−2222−220000002-2000000000000
χ4044-4-4000400-400000000000000000022−22−2222000000-22000000000000
χ4144-4-4000400-4000000000000000000−222222−22000000-22000000000000
χ4244-4-4000400-4000000000000000000−2222−22220000002-2000000000000
χ434-4-444-440-4-40404i−4i04i−4i00000000000000000000000000000000000
χ444-4-444-440-4-4040−4i4i0−4i4i00000000000000000000000000000000000
χ454-4-444-4-40440-4000000000004i−4i0000000000000000000000000000
χ464-4-444-4-40440-400000000000−4i4i0000000000000000000000000000
χ474-4-44-4440-440-404i−4i0−4i4i00000000000000000000000000000000000
χ484-4-44-4440-440-40−4i4i04i−4i00000000000000000000000000000000000
χ494-4-44-44-404-4040000000000000004-4000000000000000000000000
χ504-4-44-44-404-404000000000000000-44000000000000000000000000
χ5188-8-8000-8008000000000000000000000000000000000000000000
χ528-88-8000000000000000000000000000004-4000000000000000000
χ538-88-800000000000000000000000000000-44000000000000000000

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