Finite Group Databasebeta

← Group #405608

Character table — Group #405608

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222444444444444888888888888888888888816161616161616161616161616161616
order12442222222444444488888888888822444444444488888888882244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11-11-111-1-111-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-11-11-1-111-1-111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-11-1-1-11111-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11-1111-1-1-1-11111-1-1
χ9111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-11111-1-111-1-1-1-1
χ10111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1-1-1-111-1-11111
χ11111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-11-1-1-1-1-1-1-1111111
χ12111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11-11111111-1-1-1-1-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111
χ17222222-22-2-2-22-2-222-2-200002i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000002i−2i2-2
χ18222222-22-2-2-22-2-222-2-200002i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000−2i2i-22
χ19222222-22-2-2-22-2-222-2-20000−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000002i−2i-22
χ20222222-22-2-2-22-2-222-2-20000−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000−2i2i2-2
χ2122222-22-22-2-2-22-22-22-200002i2i−2i−2i2i2i−2i−2i000000000000000000000000002-22i−2i00000000
χ2222222-22-22-2-2-22-22-22-200002i2i−2i−2i2i2i−2i−2i00000000000000000000000000-22−2i2i00000000
χ2322222-22-22-2-2-22-22-22-20000−2i−2i2i2i−2i−2i2i2i000000000000000000000000002-2−2i2i00000000
χ2422222-22-22-2-2-22-22-22-20000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000-222i−2i00000000
χ2522222-2-2-2-222-2-222-2-22222222-2-2-2-2220000000022-2-20000-2-200000000000000000000
χ2622222-2-2-2-222-2-222-2-222222-2-22222-2-200000000-2-2220000-2-200000000000000000000
χ2722222-2-2-2-222-2-222-2-22-2-2-2-222-2-2-2-22200000000-2-22200002200000000000000000000
χ2822222-2-2-2-222-2-222-2-22-2-2-2-2-2-22222-2-20000000022-2-200002200000000000000000000
χ292222-222-2-2-22222-2-2-2-200000000000000002i2i−2i−2i2-22-20000002i2i−2i−2i0000000000000000
χ302222-222-2-2-22222-2-2-2-200000000000000002i2i−2i−2i-22-22000000−2i−2i2i2i0000000000000000
χ312222-222-2-2-22222-2-2-2-20000000000000000−2i−2i2i2i2-22-2000000−2i−2i2i2i0000000000000000
χ322222-222-2-2-22222-2-2-2-20000000000000000−2i−2i2i2i-22-220000002i2i−2i−2i0000000000000000
χ332222-2-2-222-22-2-22-222-20000000000002-22-200002-2-2222-2-20000000000000000000000
χ342222-2-2-222-22-2-22-222-20000000000002-22-20000-222-2-2-2220000000000000000000000
χ352222-2-2-222-22-2-22-222-2000000000000-22-2200002-2-22-2-2220000000000000000000000
χ362222-2-2-222-22-2-22-222-2000000000000-22-220000-222-222-2-20000000000000000000000
χ3722-2-222-22-2-2-2-222-2-2222i2i−2i−2i000000000000000000002i−2i2i−2i2i−2i2-22-20000000000000000
χ3822-2-222-22-2-2-2-222-2-2222i2i−2i−2i00000000000000000000−2i2i−2i2i2i−2i-22-220000000000000000
χ3922-2-222-22-2-2-2-222-2-222−2i−2i2i2i000000000000000000002i−2i2i−2i−2i2i-22-220000000000000000
χ4022-2-222-22-2-2-2-222-2-222−2i−2i2i2i00000000000000000000−2i2i−2i2i−2i2i2-22-20000000000000000
χ4122-2-22-22-22-2-22-22-22-222i2i−2i−2i000000002-2-222i−2i2i−2i00000000−2i2i00000000000000000000
χ4222-2-22-22-22-2-22-22-22-222i2i−2i−2i00000000-222-2−2i2i−2i2i00000000−2i2i00000000000000000000
χ4322-2-22-22-22-2-22-22-22-22−2i−2i2i2i000000002-2-22−2i2i−2i2i000000002i−2i00000000000000000000
χ4422-2-22-22-22-2-22-22-22-22−2i−2i2i2i00000000-222-22i−2i2i−2i000000002i−2i00000000000000000000
χ4522-2-2-222-2-2-22-2-2-2222200002-22-22-22-20000000000000000000000020-200002-2000000
χ4622-2-2-222-2-2-22-2-2-2222200002-22-22-22-200000000000000000000000-2020000-22000000
χ4722-2-2-222-2-2-22-2-2-222220000-22-22-22-220000000000000000000000020-20000-22000000
χ4822-2-2-222-2-2-22-2-2-222220000-22-22-22-2200000000000000000000000-20200002-2000000
χ4922-2-2-22-2-222-2-22222-2-200002i−2i2i−2i−2i2i−2i2i22-2-2000000000000002i−2i−2i2i0000000000000000
χ5022-2-2-22-2-222-2-22222-2-200002i−2i2i−2i−2i2i−2i2i-2-22200000000000000−2i2i2i−2i0000000000000000
χ5122-2-2-22-2-222-2-22222-2-20000−2i2i−2i2i2i−2i2i−2i22-2-200000000000000−2i2i2i−2i0000000000000000
χ5222-2-2-22-2-222-2-22222-2-20000−2i2i−2i2i2i−2i2i−2i-2-222000000000000002i−2i−2i2i0000000000000000
χ5322-2-2-2-222-22-22-222-22-200002i−2i−2i2i2i−2i−2i2i00002-2-220000−2i2i2i−2i0000000000000000000000
χ5422-2-2-2-222-22-22-222-22-200002i−2i−2i2i2i−2i−2i2i0000-222-200002i−2i−2i2i0000000000000000000000
χ5522-2-2-2-222-22-22-222-22-20000−2i2i2i−2i−2i2i2i−2i00002-2-2200002i−2i−2i2i0000000000000000000000
χ5622-2-2-2-222-22-22-222-22-20000−2i2i2i−2i−2i2i2i−2i0000-222-20000−2i2i2i−2i0000000000000000000000
χ5722-2-2-2-2-222-2222-22-2-2200002-2-22-222-2000000000000000000000020-200000002-20000
χ5822-2-2-2-2-222-2222-22-2-2200002-2-22-222-20000000000000000000000-2020000000-220000
χ5922-2-2-2-2-222-2222-22-2-220000-222-22-2-22000000000000000000000020-20000000-220000
χ6022-2-2-2-2-222-2222-22-2-220000-222-22-2-220000000000000000000000-20200000002-20000
χ614444-44-4-444-44-4-4-4-44400000000000000000000000000000000000000000000000000
χ624444-4-444-44-4-44-4-44-4400000000000000000000000000000000000000000000000000
χ6344-4-44444444-4-4-4-4-4-4-400000000000000000000000000000000000000000000000000
χ6444-4-44-4-4-4-44444-4-444-400000000000000000000000000000000000000000000000000
χ658-88i−8i000000000000004ζ−4ζ4ζ3−4ζ30000000000000000000000000000000000000000000000
χ668-88i−8i00000000000000−4ζ4ζ−4ζ34ζ30000000000000000000000000000000000000000000000
χ678-8−8i8i000000000000004ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000000000000000
χ688-8−8i8i00000000000000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.