Finite Group Databasebeta

← Group #449675

Character table — Group #449675

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222222888888888888888888888888888816161616161616161616161616161616
order12222222224444444422222222444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1
χ61111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1
χ9111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111-1-1
χ10111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111
χ11111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-111-1-111-1-1-1-111-1-111
χ12111111111111111111-1-1-1-111-1-111-1-111-1-111-1-1-1-111-1-111-1-11111-1-111-1-111-1-1
χ13111111111111111111-1-1-1-1-1-111-1-1111111-1-111111111-1-1-1-111-1-1-1-111-1-1-1-111
χ14111111111111111111-1-1-1-1-1-111-1-11111-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1111111-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-111
χ172222222222-2-2-2-2-2-2-2-222-2-22200-2-20000000022-2-20000000000000000000000
χ182222222222-2-2-2-2-2-2-2-222-2-2-2-2002200000000-2-2220000000000000000000000
χ192222222222-2-2-2-2-2-2-2-2-2-2222200-2-200000000-2-2220000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-222-2-200220000000022-2-20000000000000000000000
χ2122222-2-2-2-2222-2-222-2-22-22-2000000002200000000-2-200000000002-200000000
χ2222222-2-2-2-2222-2-222-2-22-22-200000000-2-200000000220000000000-2200000000
χ2322222-2-2-2-2222-2-222-2-2-22-22000000002200000000-2-20000000000-2200000000
χ2422222-2-2-2-2222-2-222-2-2-22-2200000000-2-2000000002200000000002-200000000
χ2522222-2-2-2-22-2-222-2-2222-2-22002200-2-2000000000000000000002-20000000000
χ2622222-2-2-2-22-2-222-2-2222-2-2200-2-2002200000000000000000000-220000000000
χ2722222-2-2-2-22-2-222-2-222-222-2002200-2-200000000000000000000-220000000000
χ2822222-2-2-2-22-2-222-2-222-222-200-2-20022000000000000000000002-20000000000
χ292222-2-2-222-22-22-22-22-20000000000000000222-22-20000-2-22-200000000000000
χ302222-2-2-222-22-22-22-22-2000000000000000022-22-220000-2-2-2200000000000000
χ312222-2-2-222-22-22-22-22-20000000000000000-2-22-22-2000022-2200000000000000
χ322222-2-2-222-22-22-22-22-20000000000000000-2-2-22-220000222-200000000000000
χ332222-2-2-222-2-22-22-22-220000000000000022002-2-2200-2-200002-2000000000000
χ342222-2-2-222-2-22-22-22-22000000000000002200-222-200-2-20000-22000000000000
χ352222-2-2-222-2-22-22-22-2200000000000000-2-2002-2-2200220000-22000000000000
χ362222-2-2-222-2-22-22-22-2200000000000000-2-200-222-2002200002-2000000000000
χ3722-2-222-22-2-2-2-22-222-220000000000002i−2i002i−2i00002i−2i002i−2i0000000000002-200
χ3822-2-222-22-2-2-2-22-222-220000000000002i−2i00−2i2i00002i−2i00−2i2i000000000000-2200
χ3922-2-222-22-2-2-2-22-222-22000000000000−2i2i002i−2i0000−2i2i002i−2i000000000000-2200
χ4022-2-222-22-2-2-2-22-222-22000000000000−2i2i00−2i2i0000−2i2i00−2i2i0000000000002-200
χ4122-2-22-22-22-2-2-2-22222-20000000000002i−2i2i−2i000000−2i2i2i−2i00000000000000002-2
χ4222-2-22-22-22-2-2-2-22222-20000000000002i−2i−2i2i000000−2i2i−2i2i0000000000000000-22
χ4322-2-22-22-22-2-2-2-22222-2000000000000−2i2i2i−2i0000002i−2i2i−2i0000000000000000-22
χ4422-2-22-22-22-2-2-2-22222-2000000000000−2i2i−2i2i0000002i−2i−2i2i00000000000000002-2
χ4522-2-2-22-2-2222-222-22-2-20000002-2002-2002i−2i00000000−2i2i00000000002i−2i000000
χ4622-2-2-22-2-2222-222-22-2-20000002-2002-200−2i2i000000002i−2i0000000000−2i2i000000
χ4722-2-2-22-2-2222-222-22-2-2000000-2200-22002i−2i00000000−2i2i0000000000−2i2i000000
χ4822-2-2-22-2-2222-222-22-2-2000000-2200-2200−2i2i000000002i−2i00000000002i−2i000000
χ4922-2-2-2-222-22-22222-2-2-20000002-200-2200002i−2i00000000−2i2i00000000002i−2i0000
χ5022-2-2-2-222-22-22222-2-2-20000002-200-220000−2i2i000000002i−2i0000000000−2i2i0000
χ5122-2-2-2-222-22-22222-2-2-2000000-22002-200002i−2i00000000−2i2i0000000000−2i2i0000
χ5222-2-2-2-222-22-22222-2-2-2000000-22002-20000−2i2i000000002i−2i00000000002i−2i0000
χ534444-444-4-4-44-4-444-4-4400000000000000000000000000000000000000000000
χ544444-444-4-4-4-444-4-444-400000000000000000000000000000000000000000000
χ5544-4-444-44-4-444-44-4-44-400000000000000000000000000000000000000000000
χ5644-4-44-44-44-4444-4-4-4-4400000000000000000000000000000000000000000000
χ5744-4-4-44-4-444-44-4-44-44400000000000000000000000000000000000000000000
χ5844-4-4-4-444-444-4-4-4-444400000000000000000000000000000000000000000000
χ598-88-800000000000000000000004i−4i0000000000000000000000000000000000
χ608-88-80000000000000000000000−4i4i0000000000000000000000000000000000
χ618-8-880000000000000000004-400000000000000000000000000000000000000
χ628-8-88000000000000000000-4400000000000000000000000000000000000000

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