Finite Group Databasebeta

← Group #289054

Character table — Group #289054

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222244444444444444444888888888888888888888161616161616161632323232
order12222244444444488888888888888222244448888888888888444488884488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ6111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-111-1-111-1-1
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-111-1-111-1-111
χ9111111111111111-1-1-1-1-1-11111111111-1-111-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111-11-1
χ10111111111111111-1-1-1-1-1-11111111111-1-111-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-11-11
χ11111111111111111-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-11111-1-1-1-111-1-1-1-111-11-11
χ12111111111111111-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-11111-1-1-1-1-1-11111-1-11-11-1
χ13111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1
χ14111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-111111111-1-1-1-111111-1-11
χ15111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11111-1-1-1-111111111-1-1-1-11-1-11
χ16111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11111-1-1-1-11111-1-1-1-11111-111-1
χ17222222222-2-22-2-2-22222-2-2000000002222-2-2-2-2-2000000000000000000000000
χ18222222222-2-22-2-2-22222-2-200000000-2-2-2-22222-2000000000000000000000000
χ19222222222-2-22-2-2-2-2-2-2-2220000000022-2-2-2-2222000000000000000000000000
χ20222222222-2-22-2-2-2-2-2-2-22200000000-2-22222-2-22000000000000000000000000
χ21222222-2-2-2-2-2-22-220000002i2i2i2i−2i−2i−2i−2i000000000000000000000002-22i−2i000000
χ22222222-2-2-2-2-2-22-220000002i2i2i2i−2i−2i−2i−2i00000000000000000000000-22−2i2i000000
χ23222222-2-2-2-2-2-22-22000000−2i−2i−2i−2i2i2i2i2i000000000000000000000002-2−2i2i000000
χ24222222-2-2-2-2-2-22-22000000−2i−2i−2i−2i2i2i2i2i00000000000000000000000-222i−2i000000
χ252222-2-22-2-22222-2-200000022-2-222-2-20000000000000000000002-200002-20000
χ262222-2-22-2-22222-2-200000022-2-222-2-2000000000000000000000-220000-220000
χ272222-2-22-2-22222-2-2000000-2-222-2-2220000000000000000000002-20000-220000
χ282222-2-22-2-22222-2-2000000-2-222-2-222000000000000000000000-2200002-20000
χ292222-2-2-22222-2-2-2222-2-2220000000000000000-222-2-222-2-20000000000000000
χ302222-2-2-22222-2-2-2222-2-2220000000000000000-2-2-222-2-2220000000000000000
χ312222-2-2-22222-2-2-22-2-222-2-20000000000000000222-2-2-2-2220000000000000000
χ322222-2-2-22222-2-2-22-2-222-2-200000000000000002-2-22222-2-20000000000000000
χ332222-2-2-222-2-2-222-222-2-2-2-22i2i−2i−2i−2i−2i2i2i000000002000000002i2i−2i−2i000000000000
χ342222-2-2-222-2-2-222-222-2-2-2-2−2i−2i2i2i2i2i−2i−2i00000000200000000−2i−2i2i2i000000000000
χ352222-2-2-222-2-2-222-2-2-222222i2i−2i−2i−2i−2i2i2i00000000-200000000−2i−2i2i2i000000000000
χ362222-2-2-222-2-2-222-2-2-22222−2i−2i2i2i2i2i−2i−2i00000000-2000000002i2i−2i−2i000000000000
χ3722-2-22-222-200-20002-22-2002−22−22−22−22-22-2000002−22−22−22−22−22−2000000000000
χ3822-2-22-222-200-20002-22-2002−22−22−22−2-22-2200000−22−22−22−222−22−2000000000000
χ3922-2-22-222-200-20002-22-200−22−22−22−222-22-200000−22−22−22−22−22−22000000000000
χ4022-2-22-222-200-20002-22-200−22−22−22−22-22-22000002−22−22−22−2−22−22000000000000
χ4122-2-22-222-200-2000-22-22002−22−22−22−22-2-22000002−22−2−22−22−22−22000000000000
χ4222-2-22-222-200-2000-22-22002−22−22−22−2-222-200000−22−222−22−2−22−22000000000000
χ4322-2-22-222-200-2000-22-2200−22−22−22−222-2-2200000−22−222−22−22−22−2000000000000
χ4422-2-22-222-200-2000-22-2200−22−22−22−22-222-2000002−22−2−22−222−22−2000000000000
χ4522-2-2-22-22-20020002-2-2200i2−i2−i2i2−i2i2i2−i200002i−2i2i−2i02−2−222−2−22i2−i2−i2i2000000000000
χ4622-2-2-22-22-20020002-2-2200i2−i2−i2i2−i2i2i2−i20000−2i2i−2i2i0−222−2−222−2i2−i2−i2i2000000000000
χ4722-2-2-22-22-20020002-2-2200−i2i2i2−i2i2−i2−i2i200002i−2i2i−2i0−222−2−222−2−i2i2i2−i2000000000000
χ4822-2-2-22-22-20020002-2-2200−i2i2i2−i2i2−i2−i2i20000−2i2i−2i2i02−2−222−2−22−i2i2i2−i2000000000000
χ4922-2-2-22-22-2002000-222-200i2−i2−i2i2−i2i2i2−i200002i−2i−2i2i02−2−22−222−2−i2i2i2−i2000000000000
χ5022-2-2-22-22-2002000-222-200i2−i2−i2i2−i2i2i2−i20000−2i2i2i−2i0−222−22−2−22−i2i2i2−i2000000000000
χ5122-2-2-22-22-2002000-222-200−i2i2i2−i2i2−i2−i2i200002i−2i−2i2i0−222−22−2−22i2−i2−i2i2000000000000
χ5222-2-2-22-22-2002000-222-200−i2i2i2−i2i2−i2−i2i20000−2i2i2i−2i02−2−22−222−2i2−i2−i2i2000000000000
χ53444444-4-4-444-4-44-400000000000000000000000000000000000000000000000
χ544444-4-44-4-4-4-44-44400000000000000000000000000000000000000000000000
χ5544-4-44-4-4-440040000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000
χ5644-4-44-4-4-44004000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000
χ5744-4-4-444-4400-400000000022−22−222222−22−2222000000000000000000000000000000000
χ5844-4-4-444-4400-4000000000−222222−22−222222−22000000000000000000000000000000000
χ598-88-80000000000000004i2−4i200000000000000000000000000000000000000000
χ608-88-8000000000000000−4i24i200000000000000000000000000000000000000000
χ618-8-88000008-8000000000000000000000000000000000000000000000000000
χ628-8-8800000-88000000000000000000000000000000000000000000000000000

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