Finite Group Databasebeta

← Group #418257

Character table — Group #418257

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222222888888888888888888888888888816161616161616161616161616161616
order12222222224444444422444444444444448888888888882444444444888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ3111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-11111
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111
χ14111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1
χ16111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ17222222-2-2-2-2-2-22222-2-22-22-20000000022-2-20000000000002-200000000000000
χ18222222-2-2-2-2-2-22222-2-22-22-200000000-2-222000000000000-2200000000000000
χ19222222-2-2-2-2-2-22222-2-2-22-220000000022-2-2000000000000-2200000000000000
χ20222222-2-2-2-2-2-22222-2-2-22-2200000000-2-2220000000000002-200000000000000
χ212222-2-22-22-22-222-2-22-20000000022-2-22-22-20000000000000000000000002-200
χ222222-2-22-22-22-222-2-22-20000000022-2-2-22-22000000000000000000000000-2200
χ232222-2-22-22-22-222-2-22-200000000-2-2222-22-2000000000000000000000000-2200
χ242222-2-22-22-22-222-2-22-200000000-2-222-22-220000000000000000000000002-200
χ252222-2-22-22-2-22-2-222-222-2-220000000000000000000022-2-200002-20000000000
χ262222-2-22-22-2-22-2-222-222-2-2200000000000000000000-2-2220000-220000000000
χ272222-2-22-22-2-22-2-222-22-222-20000000000000000000022-2-20000-220000000000
χ282222-2-22-22-2-22-2-222-22-222-200000000000000000000-2-22200002-20000000000
χ292222-2-2-22-222-2-2-2222-222-2-200000000000022-2-200000000002-2000000000000
χ302222-2-2-22-222-2-2-2222-222-2-2000000000000-2-2220000000000-22000000000000
χ312222-2-2-22-222-2-2-2222-2-2-22200000000000022-2-20000000000-22000000000000
χ322222-2-2-22-222-2-2-2222-2-2-222000000000000-2-22200000000002-2000000000000
χ332222-2-2-22-22-2222-2-2-22000022-2-200002-2-2200000000000000000000002-20000
χ342222-2-2-22-22-2222-2-2-22000022-2-20000-222-20000000000000000000000-220000
χ352222-2-2-22-22-2222-2-2-220000-2-22200002-2-220000000000000000000000-220000
χ362222-2-2-22-22-2222-2-2-220000-2-2220000-222-200000000000000000000002-20000
χ3722-2-22-22-2-22-2-22-22-22200002i−2i2i−2i000000002i−2i2i−2i22-2-200000000000000000000
χ3822-2-22-22-2-22-2-22-22-22200002i−2i2i−2i00000000−2i2i−2i2i-2-22200000000000000000000
χ3922-2-22-22-2-22-2-22-22-2220000−2i2i−2i2i000000002i−2i2i−2i-2-22200000000000000000000
χ4022-2-22-22-2-22-2-22-22-2220000−2i2i−2i2i00000000−2i2i−2i2i22-2-200000000000000000000
χ4122-2-22-2-222-2-2-2-22-2222000000002i−2i2i−2i0000000000002i−2i2i−2i000000000000002-2
χ4222-2-22-2-222-2-2-2-22-2222000000002i−2i2i−2i000000000000−2i2i−2i2i00000000000000-22
χ4322-2-22-2-222-2-2-2-22-222200000000−2i2i−2i2i0000000000002i−2i2i−2i00000000000000-22
χ4422-2-22-2-222-2-2-2-22-222200000000−2i2i−2i2i000000000000−2i2i−2i2i000000000000002-2
χ4522-2-2-22-2-2222-22-2-22-2200002i−2i−2i2i00000000000000002i−2i−2i2i000000002-2000000
χ4622-2-2-22-2-2222-22-2-22-2200002i−2i−2i2i0000000000000000−2i2i2i−2i00000000-22000000
χ4722-2-2-22-2-2222-22-2-22-220000−2i2i2i−2i00000000000000002i−2i−2i2i00000000-22000000
χ4822-2-2-22-2-2222-22-2-22-220000−2i2i2i−2i0000000000000000−2i2i2i−2i000000002-2000000
χ4922-2-2-22-2-222-22-222-22-2000000002i−2i−2i2i00002i−2i−2i2i000000000000002-200000000
χ5022-2-2-22-2-222-22-222-22-2000000002i−2i−2i2i0000−2i2i2i−2i00000000000000-2200000000
χ5122-2-2-22-2-222-22-222-22-200000000−2i2i2i−2i00002i−2i−2i2i00000000000000-2200000000
χ5222-2-2-22-2-222-22-222-22-200000000−2i2i2i−2i0000−2i2i2i−2i000000000000002-200000000
χ534444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000
χ54444444-4-4-4-444-4-4-4-44400000000000000000000000000000000000000000000
χ5544-4-44-44-4-4444-44-44-4-400000000000000000000000000000000000000000000
χ5644-4-44-4-444-4444-44-4-4-400000000000000000000000000000000000000000000
χ5744-4-4-4444-4-44-4-444-4-4400000000000000000000000000000000000000000000
χ5844-4-4-4444-4-4-444-4-444-400000000000000000000000000000000000000000000
χ598-88-800000000000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ608-88-80000000000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ618-8-8800000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ628-8-880000000000000000000000000000000000−2i22i22i2−2i200000000000000000000

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