Finite Group Databasebeta

← Group #424587

Character table — Group #424587

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222222244448888888888888888888888161616161616161616161616161616161616
order12222222224444444488882222224444444444888888444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1111111-111-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-111111111-1-1
χ51111111111111111111111-1-1-1-1111111-1-111-1-11111111-1-11-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11-1-1111111111-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ9111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ10111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-11111
χ11111111111111111111-1-1-1-11111-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-111-1-11111-1-111
χ13111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-111
χ14111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-111-1-111-1-111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-111-111-1-1-1-111-1-11111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111111111-1-111-1-111-1-1-1-1
χ17222222-2-2-2-2222-2-22-2-2000000000000002200-2-2002i2i−2i−2i000000002i−2i00000000
χ18222222-2-2-2-2222-2-22-2-2000000000000002200-2-200−2i−2i2i2i00000000−2i2i00000000
χ19222222-2-2-2-2222-2-22-2-200000000000000-2-20022002i2i−2i−2i00000000−2i2i00000000
χ20222222-2-2-2-2222-2-22-2-200000000000000-2-2002200−2i−2i2i2i000000002i−2i00000000
χ21222222-2-2-2-2-2-2-222-22222-2-2000000002200-2-2002-20000200-200000000000000
χ22222222-2-2-2-2-2-2-222-22222-2-200000000-2-20022002-20000-200200000000000000
χ23222222-2-2-2-2-2-2-222-222-2-222000000002200-2-200-220000-200200000000000000
χ24222222-2-2-2-2-2-2-222-222-2-22200000000-2-2002200-220000200-200000000000000
χ252222-2-222-2-22-2-22-22-2222-2-200000000002-2002-2-22000000000000000000002-2
χ262222-2-222-2-22-2-22-22-2222-2-20000000000-2200-22-2200000000000000000000-22
χ272222-2-222-2-22-2-22-22-22-2-22200000000002-2002-22-200000000000000000000-22
χ282222-2-222-2-22-2-22-22-22-2-2220000000000-2200-222-2000000000000000000002-2
χ292222-2-2-2-2222-2-2-2222-20000000022-2-2002-200-2200000000000000002-2000000
χ302222-2-2-2-2222-2-2-2222-20000000022-2-200-22002-20000000000000000-22000000
χ312222-2-2-2-2222-2-2-2222-200000000-2-222002-200-220000000000000000-22000000
χ322222-2-2-2-2222-2-2-2222-200000000-2-22200-22002-200000000000000002-2000000
χ332222-2-2-2-222-2222-2-2-22222222-2-2000000000000-2-2000002-2000000000000000
χ342222-2-2-2-222-2222-2-2-222222-2-222000000000000-2-200000-22000000000000000
χ352222-2-2-2-222-2222-2-2-22-2-2-2-222-2-20000000000002200000-22000000000000000
χ362222-2-2-2-222-2222-2-2-22-2-2-2-2-2-22200000000000022000002-2000000000000000
χ3722-2-22-22-22-222-222-2-2-200002-22-22-22-20000000000000000002-2000000000000
χ3822-2-22-22-22-222-222-2-2-200002-22-2-22-22000000000000000000-22000000000000
χ3922-2-22-22-22-222-222-2-2-20000-22-222-22-2000000000000000000-22000000000000
χ4022-2-22-22-22-222-222-2-2-20000-22-22-22-220000000000000000002-2000000000000
χ4122-2-2-222-2-22-22-2-222-220000000000002i−2i002i−2i00002-22-2000000000000002i−2i00
χ4222-2-2-222-2-22-22-2-222-220000000000002i−2i002i−2i0000-22-2200000000000000−2i2i00
χ4322-2-2-222-2-22-22-2-222-22000000000000−2i2i00−2i2i00002-22-200000000000000−2i2i00
χ4422-2-2-222-2-22-22-2-222-22000000000000−2i2i00−2i2i0000-22-22000000000000002i−2i00
χ4522-2-2-22-222-22-22-22-2-22000000002-2-222i−2i00−2i2i000000000000000000002i−2i0000
χ4622-2-2-22-222-22-22-22-2-22000000002-2-22−2i2i002i−2i00000000000000000000−2i2i0000
χ4722-2-2-22-222-22-22-22-2-2200000000-222-22i−2i00−2i2i00000000000000000000−2i2i0000
χ4822-2-2-22-222-22-22-22-2-2200000000-222-2−2i2i002i−2i000000000000000000002i−2i0000
χ4922-2-2-22-222-2-22-22-222-200002-2-22000000000000002i−2i−2i2i0000002i−2i0000000000
χ5022-2-2-22-222-2-22-22-222-200002-2-2200000000000000−2i2i2i−2i000000−2i2i0000000000
χ5122-2-2-22-222-2-22-22-222-20000-222-2000000000000002i−2i−2i2i000000−2i2i0000000000
χ5222-2-2-22-222-2-22-22-222-20000-222-200000000000000−2i2i2i−2i0000002i−2i0000000000
χ534444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000
χ544444-4-444-4-4-444-44-44-400000000000000000000000000000000000000000000
χ5544-4-44-44-44-4-4-44-4-444400000000000000000000000000000000000000000000
χ5644-4-44-4-44-4444-4-4-4-44400000000000000000000000000000000000000000000
χ5744-4-44-4-44-44-4-44444-4-400000000000000000000000000000000000000000000
χ5844-4-4-444-4-444-444-4-44-400000000000000000000000000000000000000000000
χ598-88-800000000000000004i2−4i20000000000000000000000000000000000000000
χ608-88-80000000000000000−4i24i20000000000000000000000000000000000000000
χ618-8-880000000000000042−42000000000000000000000000000000000000000000
χ628-8-8800000000000000−4242000000000000000000000000000000000000000000

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