Finite Group Databasebeta

← Group #317367

Character table — Group #317367

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444444444448888224444888888888824444444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111
χ311111111111111111111111111-1-111-1-1111111-1-1-1-1-1111111-111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-11111-1-1-1-1-11111-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111-111-1-1-1-1111111
χ9111111111111111111-1-1-1-1111111-1-11111-1-1-1-11111-111-1-111-1-1-111-1-111-1-1-1-1
χ10111111111111111111-1-1-1-1111111-1-11111-1-1-1-11111-1-1-111-1-1-111-1-111-1-111-1-1
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1111-1-1-1-111-1-11111
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-111-1-111111-1-111-1-111
χ13111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-111-1-1-1-1-111-1-11111-1-111
χ14111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-11111-1-1-111-1-1-1-11111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-111111-1-1-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111111-1-1-1-11111-1-1-1-1
χ17222222222-2-2-2222-2-2-222-2-20000222-2-2-20000000000-20000002000000000000
χ18222222222-2-2-2222-2-2-222-2-20000-2-22-22200000000002000000-2000000000000
χ19222222222-2-2-2222-2-2-2-2-222000022-22-2-200000000002000000-2000000000000
χ20222222222-2-2-2222-2-2-2-2-2220000-2-2-22220000000000-20000002000000000000
χ2122222222-2222-2-2-22-2-22222222200-2-200-2-222-2-2000000000000000000000000
χ2222222222-2222-2-2-22-2-22222-2-2-2-200-2-20022-2-222000000000000000000000000
χ2322222222-2222-2-2-22-2-2-2-2-2-22222002200-2-2-2-222000000000000000000000000
χ2422222222-2222-2-2-22-2-2-2-2-2-2-2-2-2-20022002222-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2000000-22000000002i2i−2i−2i0000000000000000002i−2i
χ2622222222-2-2-2-2-2-2-2-22222-2-2000000-2200000000−2i−2i2i2i000000000000000000−2i2i
χ2722222222-2-2-2-2-2-2-2-222-2-2220000002-2000000002i2i−2i−2i000000000000000000−2i2i
χ2822222222-2-2-2-2-2-2-2-222-2-2220000002-200000000−2i−2i2i2i0000000000000000002i−2i
χ2922-2-22-2-22022-2000-2002-22-22i2i−2i−2i000000002i−2i00000000000000002−22−2i2−i2i2−i200
χ3022-2-22-2-22022-2000-2002-22-22i2i−2i−2i000000002i−2i0000000000000000−22−22−i2i2−i2i200
χ3122-2-22-2-22022-2000-2002-22-2−2i−2i2i2i00000000−2i2i00000000000000002−22−2−i2i2−i2i200
χ3222-2-22-2-22022-2000-2002-22-2−2i−2i2i2i00000000−2i2i0000000000000000−22−22i2−i2i2−i200
χ3322-2-22-2-22022-2000-200-22-222i2i−2i−2i00000000−2i2i00000000000000002−2−22i2−i2−i2i200
χ3422-2-22-2-22022-2000-200-22-222i2i−2i−2i00000000−2i2i0000000000000000−222−2−i2i2i2−i200
χ3522-2-22-2-22022-2000-200-22-22−2i−2i2i2i000000002i−2i00000000000000002−2−22−i2i2i2−i200
χ3622-2-22-2-22022-2000-200-22-22−2i−2i2i2i000000002i−2i0000000000000000−222−2i2−i2−i2i200
χ372-22-2-22-2222-22-2-22-22-200002i−2i2i−2i0000002i−2i0000000002-2002i−2i0000000000000
χ382-22-2-22-2222-22-2-22-22-200002i−2i2i−2i0000002i−2i000000000-2200−2i2i0000000000000
χ392-22-2-22-2222-22-2-22-22-20000−2i2i−2i2i000000−2i2i0000000002-200−2i2i0000000000000
χ402-22-2-22-2222-22-2-22-22-20000−2i2i−2i2i000000−2i2i000000000-22002i−2i0000000000000
χ412-22-2-22-22-22-2222-2-2-2200002i−2i2i−2i000000−2i2i000000000002i−2i0002-20000000000
χ422-22-2-22-22-22-2222-2-2-2200002i−2i2i−2i000000−2i2i00000000000−2i2i000-220000000000
χ432-22-2-22-22-22-2222-2-2-220000−2i2i−2i2i0000002i−2i000000000002i−2i000-220000000000
χ442-22-2-22-22-22-2222-2-2-220000−2i2i−2i2i0000002i−2i00000000000−2i2i0002-20000000000
χ4544-44-44-4-440004-4-40000000000000000000000022−2222−2200000000000000000000
χ4644-44-44-4-440004-4-400000000000000000000000−2222−222200000000000000000000
χ4744-44-44-4-4-4000-444000000000000000000000002i2−2i2−2i22i200000000000000000000
χ4844-44-44-4-4-4000-44400000000000000000000000−2i22i22i2−2i200000000000000000000
χ4944-4-44-4-440-4-440004004-4-440000000000000000000000000000000000000000
χ5044-4-44-4-440-4-44000400-444-40000000000000000000000000000000000000000
χ514-44-4-44-444-44-4-4-444-4400000000000000000000000000000000000000000000
χ524-44-4-44-44-4-44-444-444-400000000000000000000000000000000000000000000
χ534-4-44-4-44404-4-400040000004-4-44000000000000000000000000000000000000
χ544-4-44-4-44404-4-40004000000-444-4000000000000000000000000000000000000
χ554-4-44-4-4440-444000-4000000000000000000004i−4i000000000000000000000000
χ564-4-44-4-4440-444000-400000000000000000000−4i4i000000000000000000000000
χ574-4-4-4444-44000-44-40000000000000004i−4i000000000000000000000000000000
χ584-4-4-4444-44000-44-4000000000000000−4i4i000000000000000000000000000000
χ594-4-4-4444-4-40004-44000000000004-40000000000000000000000000000000000
χ604-4-4-4444-4-40004-4400000000000-440000000000000000000000000000000000
χ61888-8-8-88-8000000000000000000000000000000000000000000000000000000
χ628-8888-8-8-8000000000000000000000000000000000000000000000000000000

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