Finite Group Databasebeta

← Group #420901

Character table — Group #420901

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222222244448888888888888888888888161616161616161616161616161616161616
order12442222222444444488882222224444444444888888444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-111
χ4111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1
χ51111111111111111111111-1-111-1-1-1-111-1-11111111111-1-111-1-111-1-111-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111111
χ71111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11111-1-1
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111
χ9111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111
χ10111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1
χ11111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111
χ12111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-111-1-1-1-1
χ13111111111111111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1
χ14111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ16111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111
χ172222222-2-2-2-22-222-2-2-20000002-200002-2002i2i−2i−2i000000002i−2i00000000000000
χ182222222-2-2-2-22-222-2-2-20000002-200002-200−2i−2i2i2i00000000−2i2i00000000000000
χ192222222-2-2-2-22-222-2-2-2000000-220000-22002i2i−2i−2i00000000−2i2i00000000000000
χ202222222-2-2-2-22-222-2-2-2000000-220000-2200−2i−2i2i2i000000002i−2i00000000000000
χ2122222-2-2-222-2-2-22-22-22000000002-200002-200000022-2-2000000000000002-200
χ2222222-2-2-222-2-2-22-22-22000000002-200002-2000000-2-22200000000000000-2200
χ2322222-2-2-222-2-2-22-22-2200000000-220000-2200000022-2-200000000000000-2200
χ2422222-2-2-222-2-2-22-22-2200000000-220000-22000000-2-222000000000000002-200
χ252222-22-2-22-22-22-22-2-2222222-200002-200000000-2-200002-20000000000000000
χ262222-22-2-22-22-22-22-2-222222-220000-2200000000-2-20000-220000000000000000
χ272222-22-2-22-22-22-22-2-22-2-2-2-22-200002-200000000220000-220000000000000000
χ282222-22-2-22-22-22-22-2-22-2-2-2-2-220000-22000000002200002-20000000000000000
χ2922-2-22222222-2-2-2-2-2-2-20000002-20000-22000000002i−2i2i−2i00000000002i−2i000000
χ3022-2-22222222-2-2-2-2-2-2-20000002-20000-2200000000−2i2i−2i2i0000000000−2i2i000000
χ3122-2-22222222-2-2-2-2-2-2-2000000-2200002-2000000002i−2i2i−2i0000000000−2i2i000000
χ3222-2-22222222-2-2-2-2-2-2-2000000-2200002-200000000−2i2i−2i2i00000000002i−2i000000
χ3322-2-2222-2-2-2-2-22-2-22222i2i−2i−2i00220000-2-20000002i−2i00000000002i−2i0000000000
χ3422-2-2222-2-2-2-2-22-2-22222i2i−2i−2i00-2-20000220000002i−2i0000000000−2i2i0000000000
χ3522-2-2222-2-2-2-2-22-2-2222−2i−2i2i2i00220000-2-2000000−2i2i0000000000−2i2i0000000000
χ3622-2-2222-2-2-2-2-22-2-2222−2i−2i2i2i00-2-2000022000000−2i2i00000000002i−2i0000000000
χ3722-2-22-2-2-222-222-22-22-200002-20000-2200000000002i−2i−2i2i000000002i−2i00000000
χ3822-2-22-2-2-222-222-22-22-200002-20000-220000000000−2i2i2i−2i00000000−2i2i00000000
χ3922-2-22-2-2-222-222-22-22-20000-2200002-200000000002i−2i−2i2i00000000−2i2i00000000
χ4022-2-22-2-2-222-222-22-22-20000-2200002-20000000000−2i2i2i−2i000000002i−2i00000000
χ4122-2-2-22-22-22-2222-2-2-222i2i−2i−2i00002-20000-220000−2i2i000000002i−2i000000000000
χ4222-2-2-22-22-22-2222-2-2-222i2i−2i−2i0000-2200002-20000−2i2i00000000−2i2i000000000000
χ4322-2-2-22-22-22-2222-2-2-22−2i−2i2i2i00002-20000-2200002i−2i00000000−2i2i000000000000
χ4422-2-2-22-22-22-2222-2-2-22−2i−2i2i2i0000-2200002-200002i−2i000000002i−2i000000000000
χ4522-2-2-2-2222-2-2-22222-2-20000220000-2-200002i−2i2i−2i00000000000000000000002i−2i
χ4622-2-2-2-2222-2-2-22222-2-20000220000-2-20000−2i2i−2i2i0000000000000000000000−2i2i
χ4722-2-2-2-2222-2-2-22222-2-20000-2-200002200002i−2i2i−2i0000000000000000000000−2i2i
χ4822-2-2-2-2222-2-2-22222-2-20000-2-20000220000−2i2i−2i2i00000000000000000000002i−2i
χ4922-2-2-2-22-2-222-2-222-22200000000220000-2-22-2-220000000000000000002-20000
χ5022-2-2-2-22-2-222-2-222-22200000000220000-2-2-222-2000000000000000000-220000
χ5122-2-2-2-22-2-222-2-222-22200000000-2-20000222-2-22000000000000000000-220000
χ5222-2-2-2-22-2-222-2-222-22200000000-2-2000022-222-20000000000000000002-20000
χ5344444-4-44-4-44-444-4-44-400000000000000000000000000000000000000000000
χ544444-44-44-44-4-4-4-4444-400000000000000000000000000000000000000000000
χ554444-4-4444-4-44-4-4-4-44400000000000000000000000000000000000000000000
χ564444-4-44-4-44444-4-44-4-400000000000000000000000000000000000000000000
χ5744-4-44-4-44-4-444-4-444-4400000000000000000000000000000000000000000000
χ5844-4-4-44-4-44-444-44-444-400000000000000000000000000000000000000000000
χ598-88i−8i000000000000004ζ−4ζ4ζ3−4ζ30000000000000000000000000000000000000000
χ608-88i−8i00000000000000−4ζ4ζ−4ζ34ζ30000000000000000000000000000000000000000
χ618-8−8i8i000000000000004ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000000000
χ628-8−8i8i00000000000000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000000000

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