Finite Group Databasebeta

← Group #317795

Character table — Group #317795

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444444444448888444444888888888822444444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111111-1-11-1-1111111-1-1-1-111-11111-111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
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
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1
χ71111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-1111111-111-1-1-1-1-11111-1-1-1-111
χ81111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-111-111-1-1-1-1111111
χ9111111111111111111-1-1-1-11111-111-11111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-1
χ10111111111111111111-1-1-1-11111-111-11111-1-1-1-11111-1-1-11111-1-1-1-1-111-1-111-1-1
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-111-1-11111
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111
χ13111111111111111111-1-1-1-1-1-1-1-1-111-111-1-11111-1-1-1-111-1-1-111-1-1-1-1-11111-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-111-111-1-11111-1-1-1-1-1-1-111-1-1-11111-1-1-1-11111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111-1-111-1-1-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-1111-1-11111-1-1-1-1
χ17222222222-2-2-2222-2-2-222-2-20000-2222-2-2000000000000-200002000000000000
χ18222222222-2-2-2222-2-2-222-2-20000-2-2-222200000000000020000-2000000000000
χ19222222222-2-2-2222-2-2-2-2-2220000222-2-2-200000000000020000-2000000000000
χ20222222222-2-2-2222-2-2-2-2-22200002-2-2-222000000000000-200002000000000000
χ2122222222-2222-2-2-22-2-222222222-200-200-2-222-2-2000000000000000000000000
χ2222222222-2222-2-2-22-2-22222-2-2-2-2-200-20022-2-222000000000000000000000000
χ2322222222-2222-2-2-22-2-2-2-2-2-22222200200-2-2-2-222000000000000000000000000
χ2422222222-2222-2-2-22-2-2-2-2-2-2-2-2-2-22002002222-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-20000200-2000000002i2i−2i−2i0000000000000000002i−2i
χ2622222222-2-2-2-2-2-2-2-22222-2-20000200-200000000−2i−2i2i2i000000000000000000−2i2i
χ2722222222-2-2-2-2-2-2-2-222-2-2220000-2002000000002i2i−2i−2i000000000000000000−2i2i
χ2822222222-2-2-2-2-2-2-2-222-2-2220000-200200000000−2i−2i2i2i0000000000000000002i−2i
χ29222-22-2-2-202-2-20002002-22-22i2i−2i−2i000000002i−2i00000000000000002−22−2i2−i2i2−i200
χ30222-22-2-2-202-2-20002002-22-22i2i−2i−2i000000002i−2i0000000000000000−22−22−i2i2−i2i200
χ31222-22-2-2-202-2-20002002-22-2−2i−2i2i2i00000000−2i2i00000000000000002−22−2−i2i2−i2i200
χ32222-22-2-2-202-2-20002002-22-2−2i−2i2i2i00000000−2i2i0000000000000000−22−22i2−i2i2−i200
χ33222-22-2-2-202-2-2000200-22-222i2i−2i−2i00000000−2i2i00000000000000002−2−22i2−i2−i2i200
χ34222-22-2-2-202-2-2000200-22-222i2i−2i−2i00000000−2i2i0000000000000000−222−2−i2i2i2−i200
χ35222-22-2-2-202-2-2000200-22-22−2i−2i2i2i000000002i−2i00000000000000002−2−22−i2i2i2−i200
χ36222-22-2-2-202-2-2000200-22-22−2i−2i2i2i000000002i−2i0000000000000000−222−2i2−i2−i2i200
χ3722-22-22-2-22-22-2-2-2222-200002i−2i2i−2i0000002i−2i000000000002i−2i2-20000000000000
χ3822-22-22-2-22-22-2-2-2222-200002i−2i2i−2i0000002i−2i00000000000−2i2i-220000000000000
χ3922-22-22-2-22-22-2-2-2222-20000−2i2i−2i2i000000−2i2i000000000002i−2i-220000000000000
χ4022-22-22-2-22-22-2-2-2222-20000−2i2i−2i2i000000−2i2i00000000000−2i2i2-20000000000000
χ4122-22-22-2-2-2-22-222-22-2200002i−2i2i−2i000000−2i2i000000002-20000002i−2i0000000000
χ4222-22-22-2-2-2-22-222-22-2200002i−2i2i−2i000000−2i2i00000000-22000000−2i2i0000000000
χ4322-22-22-2-2-2-22-222-22-220000−2i2i−2i2i0000002i−2i000000002-2000000−2i2i0000000000
χ4422-22-22-2-2-2-22-222-22-220000−2i2i−2i2i0000002i−2i00000000-220000002i−2i0000000000
χ45444-44-4-4-40-444000-4004-4-440000000000000000000000000000000000000000
χ46444-44-4-4-40-444000-400-444-40000000000000000000000000000000000000000
χ4744-44-44-4-444-44-4-44-4-4400000000000000000000000000000000000000000000
χ4844-44-44-4-4-44-4444-4-44-400000000000000000000000000000000000000000000
χ4944-4-4-4-444044-4000-4000000000000000000004i−4i000000000000000000000000
χ5044-4-4-4-444044-4000-400000000000000000000−4i4i000000000000000000000000
χ5144-4-4-4-4440-4-4400040000004-4-44000000000000000000000000000000000000
χ5244-4-4-4-4440-4-440004000000-444-4000000000000000000000000000000000000
χ534-44-4-44-4440004-4-4000000000000000000000002i2−2i22i2−2i200000000000000000000
χ544-44-4-44-4440004-4-400000000000000000000000−2i22i2−2i22i200000000000000000000
χ554-44-4-44-44-4000-4440000000000000000000000022−22−222200000000000000000000
χ564-44-4-44-44-4000-44400000000000000000000000−222222−2200000000000000000000
χ574-4-4-4444-44000-44-40000000000000004i−4i000000000000000000000000000000
χ584-4-4-4444-44000-44-4000000000000000−4i4i000000000000000000000000000000
χ594-4-4-4444-4-40004-440000000000004-4000000000000000000000000000000000
χ604-4-4-4444-4-40004-44000000000000-44000000000000000000000000000000000
χ618-888-8-88-8000000000000000000000000000000000000000000000000000000
χ628-8-888-8-88000000000000000000000000000000000000000000000000000000

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