Finite Group Databasebeta

← Group #317021

Character table — Group #317021

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222244444444444444444888888888888888888888161616161616161632323232
order12222244444444488888888888888224444448888888888888444488884488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1-111-1-1
χ61111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-111-1-111
χ71111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-111-1-1-1-111
χ81111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-111-1-11111-1-1
χ9111111111111111-1-1-1-111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1111-11-1
χ10111111111111111-1-1-1-111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-11
χ11111111111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-111-1-1-1-111-11-11
χ12111111111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-11111-1-11-11-1
χ13111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-111111111-1-1-1-11-1-11
χ14111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-11111-1-1-1-11111-111-1
χ15111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-111111111-1-1-1-1-111-1
χ16111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-11111-1-1-1-111111-1-11
χ1722222222-2-222-2-2-2222200000000-2-22222-2-2-2-200000000-20000000000000000
χ1822222222-2-222-2-2-2222200000000-2-2-2-2-2-2222200000000-20000000000000000
χ1922222222-2-222-2-2-2-2-2-2-2000000002222-2-2-2-2220000000020000000000000000
χ2022222222-2-222-2-2-2-2-2-2-20000000022-2-22222-2-20000000020000000000000000
χ21222222-2-2-2-2-2-22-2200002i2i2i2i−2i−2i−2i−2i000000000000000000000002-200002i−2i0000
χ22222222-2-2-2-2-2-22-2200002i2i2i2i−2i−2i−2i−2i00000000000000000000000-220000−2i2i0000
χ23222222-2-2-2-2-2-22-220000−2i−2i−2i−2i2i2i2i2i000000000000000000000002-20000−2i2i0000
χ24222222-2-2-2-2-2-22-220000−2i−2i−2i−2i2i2i2i2i00000000000000000000000-2200002i−2i0000
χ252222-2-22-2-2-22-2-22200002i2i−2i−2i2i2i−2i−2i00000000000000000000000002-22i−2i000000
χ262222-2-22-2-2-22-2-22200002i2i−2i−2i2i2i−2i−2i0000000000000000000000000-22−2i2i000000
χ272222-2-22-2-2-22-2-2220000−2i−2i2i2i−2i−2i2i2i00000000000000000000000002-2−2i2i000000
χ282222-2-22-2-2-22-2-2220000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000-222i−2i000000
χ292222-2-2-2222-22-2-2222-2-222-2-2-2-222220000000000000000-222-2-2000000000000
χ302222-2-2-2222-22-2-2222-2-2-2-22222-2-2220000000000000000-2-2-222000000000000
χ312222-2-2-2222-22-2-22-2-22222-2-2-2-222-2-200000000000000002-2-222000000000000
χ322222-2-2-2222-22-2-22-2-222-2-22222-2-2-2-20000000000000000222-2-2000000000000
χ332222-2-2-22-2-2-2222-222-2-200000000-2-2000000002i2i−2i−2i2i2i−2i−2i20000000000000000
χ342222-2-2-22-2-2-2222-222-2-200000000-2-200000000−2i−2i2i2i−2i−2i2i2i20000000000000000
χ352222-2-2-22-2-2-2222-2-2-2220000000022000000002i2i−2i−2i−2i−2i2i2i-20000000000000000
χ362222-2-2-22-2-2-2222-2-2-222000000002200000000−2i−2i2i2i2i2i−2i−2i-20000000000000000
χ3722-2-22-22200-2-20002-22-22−22−22−22−2002-22-200002−22−22−22−202−22−2000000000000
χ3822-2-22-22200-2-20002-22-22−22−22−22−200-22-220000−22−22−22−2202−22−2000000000000
χ3922-2-22-22200-2-20002-22-2−22−22−22−22002-22-20000−22−22−22−220−22−22000000000000
χ4022-2-22-22200-2-20002-22-2−22−22−22−2200-22-2200002−22−22−22−20−22−22000000000000
χ4122-2-22-22200-2-2000-22-222−22−22−22−2002-2-2200002−22−2−22−220−22−22000000000000
χ4222-2-22-22200-2-2000-22-222−22−22−22−200-222-20000−22−222−22−20−22−22000000000000
χ4322-2-22-22200-2-2000-22-22−22−22−22−22002-2-220000−22−222−22−202−22−2000000000000
χ4422-2-22-22200-2-2000-22-22−22−22−22−2200-222-200002−22−2−22−2202−22−2000000000000
χ4522-2-2-22-22002-20002-2-222−2−22−222−20000002i−2i2i−2ii2−i2−i2i2i2−i2−i2i202−2−22000000000000
χ4622-2-2-22-22002-20002-2-222−2−22−222−2000000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i202−2−22000000000000
χ4722-2-2-22-22002-20002-2-22−222−22−2−220000002i−2i2i−2i−i2i2i2−i2−i2i2i2−i20−222−2000000000000
χ4822-2-2-22-22002-20002-2-22−222−22−2−22000000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i20−222−2000000000000
χ4922-2-2-22-22002-2000-222-22−2−22−222−20000002i−2i−2i2ii2−i2−i2i2−i2i2i2−i20−222−2000000000000
χ5022-2-2-22-22002-2000-222-22−2−22−222−2000000−2i2i2i−2i−i2i2i2−i2i2−i2−i2i20−222−2000000000000
χ5122-2-2-22-22002-2000-222-2−222−22−2−220000002i−2i−2i2i−i2i2i2−i2i2−i2−i2i202−2−22000000000000
χ5222-2-2-22-22002-2000-222-2−222−22−2−22000000−2i2i2i−2ii2−i2−i2i2−i2i2i2−i202−2−22000000000000
χ53444444-4-444-4-4-44-400000000000000000000000000000000000000000000000
χ544444-4-44-4444-44-4-400000000000000000000000000000000000000000000000
χ5544-4-44-4-4-4004400000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000
χ5644-4-44-4-4-400440000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000
χ5744-4-4-444-400-4400000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ5844-4-4-444-400-440000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ598-88-8000000000000000000000004i2−4i2000000000000000000000000000000000
χ608-88-800000000000000000000000−4i24i2000000000000000000000000000000000
χ618-8-8800008i−8i0000000000000000000000000000000000000000000000000000
χ628-8-880000−8i8i0000000000000000000000000000000000000000000000000000

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