Finite Group Databasebeta

← Group #437572

Character table — Group #437572

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222222244448888888888888888888888161616161616161616161616161616161616
order12442222222444444488884444444488888888888888244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1
χ311111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111
χ51111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-111-1-111-1-1-1-111-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-111
χ9111111111111111111-1-1-1-111111111-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ10111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-11111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1-1-11111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-11111-1-1
χ17222222-22-2-2-22-22-2-2-22000000002i2i−2i−2i00000000002i2i−2i−2i002-200000000000000
χ18222222-22-2-2-22-22-2-2-22000000002i2i−2i−2i0000000000−2i−2i2i2i00-2200000000000000
χ19222222-22-2-2-22-22-2-2-2200000000−2i−2i2i2i00000000002i2i−2i−2i00-2200000000000000
χ20222222-22-2-2-22-22-2-2-2200000000−2i−2i2i2i0000000000−2i−2i2i2i002-200000000000000
χ2122222-22-2-22-22-2-222-2-2222200000000-2-2000000002i−2i2i−2i0000002i−2i0000000000
χ2222222-22-2-22-22-2-222-2-2222200000000-2-200000000−2i2i−2i2i000000−2i2i0000000000
χ2322222-22-2-22-22-2-222-2-2-2-2-2-20000000022000000002i−2i2i−2i000000−2i2i0000000000
χ2422222-22-2-22-22-2-222-2-2-2-2-2-2000000002200000000−2i2i−2i2i0000002i−2i0000000000
χ2522222-2-2-22-2222-2-2-22-20000000000000000002i2i−2i−2i2-2-220000000000002i−2i0000
χ2622222-2-2-22-2222-2-2-22-20000000000000000002i2i−2i−2i-222-2000000000000−2i2i0000
χ2722222-2-2-22-2222-2-2-22-2000000000000000000−2i−2i2i2i2-2-22000000000000−2i2i0000
χ2822222-2-2-22-2222-2-2-22-2000000000000000000−2i−2i2i2i-222-20000000000002i−2i0000
χ292222-222-2-2-22-2222-2-2-200002i2i−2i−2i00000000002i−2i2i−2i000000000000002-2000000
χ302222-222-2-2-22-2222-2-2-200002i2i−2i−2i0000000000−2i2i−2i2i00000000000000-22000000
χ312222-222-2-2-22-2222-2-2-20000−2i−2i2i2i00000000002i−2i2i−2i00000000000000-22000000
χ322222-222-2-2-22-2222-2-2-20000−2i−2i2i2i0000000000−2i2i−2i2i000000000000002-2000000
χ332222-2-2-22-222-22-2-22-220000000000000022-2-22-2-22000000000000000000002-2
χ342222-2-2-22-222-22-2-22-220000000000000022-2-2-222-200000000000000000000-22
χ352222-2-2-22-222-22-2-22-2200000000000000-2-2222-2-2200000000000000000000-22
χ362222-2-2-22-222-22-2-22-2200000000000000-2-222-222-2000000000000000000002-2
χ3722-2-22222222-2-2-2-2-2-2-22i2i−2i−2i2-22-200002i−2i000000000000000000000000002i−2i00
χ3822-2-22222222-2-2-2-2-2-2-22i2i−2i−2i-22-2200002i−2i00000000000000000000000000−2i2i00
χ3922-2-22222222-2-2-2-2-2-2-2−2i−2i2i2i2-22-20000−2i2i00000000000000000000000000−2i2i00
χ4022-2-22222222-2-2-2-2-2-2-2−2i−2i2i2i-22-220000−2i2i000000000000000000000000002i−2i00
χ4122-2-22-22-2-22-2-222-2-2222i2i−2i−2i00000000−2i2i2i−2i2i−2i0000000000002-2000000000000
χ4222-2-22-22-2-22-2-222-2-2222i2i−2i−2i00000000−2i2i−2i2i−2i2i000000000000-22000000000000
χ4322-2-22-22-2-22-2-222-2-222−2i−2i2i2i000000002i−2i2i−2i2i−2i000000000000-22000000000000
χ4422-2-22-22-2-22-2-222-2-222−2i−2i2i2i000000002i−2i−2i2i−2i2i0000000000002-2000000000000
χ4522-2-2-222-2-2-222-2-2-222200002i−2i−2i2i2i−2i2i−2i000000000000002-20000000000000000
χ4622-2-2-222-2-2-222-2-2-222200002i−2i−2i2i−2i2i−2i2i00000000000000-220000000000000000
χ4722-2-2-222-2-2-222-2-2-22220000−2i2i2i−2i2i−2i2i−2i00000000000000-220000000000000000
χ4822-2-2-222-2-2-222-2-2-22220000−2i2i2i−2i−2i2i−2i2i000000000000002-20000000000000000
χ4922-2-2-22-2-222-222-22-2-22000000002-2-22002i−2i−2i2i00000000000000002i−2i00000000
χ5022-2-2-22-2-222-222-22-2-22000000002-2-2200−2i2i2i−2i0000000000000000−2i2i00000000
χ5122-2-2-22-2-222-222-22-2-2200000000-222-2002i−2i−2i2i0000000000000000−2i2i00000000
χ5222-2-2-22-2-222-222-22-2-2200000000-222-200−2i2i2i−2i00000000000000002i−2i00000000
χ534444-44-4-444-4-4-44-444-400000000000000000000000000000000000000000000
χ544444-4-4444-4-4-4-4-44-44400000000000000000000000000000000000000000000
χ5544-4-444-44-4-4-4-44-4444-400000000000000000000000000000000000000000000
χ5644-4-44-4-4-44-44-4-4444-4400000000000000000000000000000000000000000000
χ5744-4-4-4-4444-4-4444-44-4-400000000000000000000000000000000000000000000
χ5844-4-4-4-4-44-4444-444-44-400000000000000000000000000000000000000000000
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.