Finite Group Databasebeta

← Group #349125

Character table — Group #349125

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222244444444444444444888888888888888888888161616161616161632323232
order12222244444444444448888888888222444444488888888888888888884488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-11-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ61111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ71111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ81111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ911111111111111-1-1-1-11111111-1-1-1-1-111-111-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1-1-111
χ1011111111111111-1-1-1-11111111-1-1-1-1-111-111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ1111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-111-1-1
χ1211111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-111
χ1311111111111111-1-1-1-11-1-1-1-1-1-11111-111-111-1-1-1-1-111-1-1-1-1111111-1-1-1-111-111-1
χ1411111111111111-1-1-1-11-1-1-1-1-1-11111-111-111-1-1-1-1-111-1-1-1-11111-1-11111-1-11-1-11
χ1511111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-11111-1111111-1-1-1-111-1-1-1-1111-1-11
χ1611111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-11111-1111111-1-1-1-1-1-11111-1-1-111-1
χ172222222-2222-2-2-22222-22222-2-22222-200-2000000-2-2-200000000000000000000
χ182222222-2222-2-2-22222-2-2-2-2-222-2-2-2-2-200-200000022200000000000000000000
χ192222222-2222-2-2-2-2-2-2-2-22222-2-2-2-2-2-22002000000-22200000000000000000000
χ202222222-2222-2-2-2-2-2-2-2-2-2-2-2-222222220020000002-2-200000000000000000000
χ21222222-22-2-2-222-20000-20000002i2i−2i−2i00000022-2-202i−2i2i2i−2i−2i0000000000000000
χ22222222-22-2-2-222-20000-20000002i2i−2i−2i000000-2-22202i−2i−2i−2i2i2i0000000000000000
χ23222222-22-2-2-222-20000-2000000−2i−2i2i2i00000022-2-20−2i2i−2i−2i2i2i0000000000000000
χ24222222-22-2-2-222-20000-2000000−2i−2i2i2i000000-2-2220−2i2i2i2i−2i−2i0000000000000000
χ25222222-2-2-2-2-2-2-22000020000002i2i−2i−2i02-202-200000−2i2i00002i2i−2i−2i000000000000
χ26222222-2-2-2-2-2-2-22000020000002i2i−2i−2i0-220-2200000−2i2i0000−2i−2i2i2i000000000000
χ27222222-2-2-2-2-2-2-2200002000000−2i−2i2i2i02-202-2000002i−2i0000−2i−2i2i2i000000000000
χ28222222-2-2-2-2-2-2-2200002000000−2i−2i2i2i0-220-22000002i−2i00002i2i−2i−2i000000000000
χ292222-2-2222-2-22-2-222-2-220000000000222-2-2-22-22-200000000000000000000000
χ302222-2-2222-2-22-2-222-2-2200000000002-2-2-222-22-2200000000000000000000000
χ312222-2-2222-2-22-2-2-2-22220000000000-2222-2-2-22-2200000000000000000000000
χ322222-2-2222-2-22-2-2-2-22220000000000-2-2-22222-22-200000000000000000000000
χ332222-2-22-22-2-2-22222-2-2-20000000000-20020000000002i−2i2i−2i2i−2i2i−2i000000000000
χ342222-2-22-22-2-2-22222-2-2-20000000000-2002000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ352222-2-22-22-2-2-222-2-222-20000000000200-20000000002i−2i2i−2i−2i2i−2i2i000000000000
χ362222-2-22-22-2-2-222-2-222-20000000000200-2000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ372222-2-2-22-2222-220000-222-2-22200000000002-2-22-20000002-2-22000000000000
χ382222-2-2-22-2222-220000-222-2-2220000000000-222-2-2000000-222-2000000000000
χ392222-2-2-22-2222-220000-2-2-222-2-200000000002-2-222000000-222-2000000000000
χ402222-2-2-22-2222-220000-2-2-222-2-20000000000-222-220000002-2-22000000000000
χ412222-2-2-2-2-222-22-20000222-2-2-2-2000002-20-2200002002-2-220000000000000000
χ422222-2-2-2-2-222-22-20000222-2-2-2-200000-2202-20000200-222-20000000000000000
χ432222-2-2-2-2-222-22-200002-2-22222000002-20-220000-200-222-20000000000000000
χ442222-2-2-2-2-222-22-200002-2-2222200000-2202-20000-2002-2-220000000000000000
χ4522-2-22-2-2022-20002i−2i2i−2i02-22-2002i−2i2i−2i0000000000000000000002−22−2i2−i2i2−i20000
χ4622-2-22-2-2022-20002i−2i2i−2i02-22-2002i−2i2i−2i000000000000000000000−22−22−i2i2−i2i20000
χ4722-2-22-2-2022-20002i−2i2i−2i0-22-2200−2i2i−2i2i0000000000000000000002−2−22i2−i2−i2i20000
χ4822-2-22-2-2022-20002i−2i2i−2i0-22-2200−2i2i−2i2i000000000000000000000−222−2−i2i2i2−i20000
χ4922-2-22-2-2022-2000−2i2i−2i2i02-22-200−2i2i−2i2i0000000000000000000002−22−2−i2i2−i2i20000
χ5022-2-22-2-2022-2000−2i2i−2i2i02-22-200−2i2i−2i2i000000000000000000000−22−22i2−i2i2−i20000
χ5122-2-22-2-2022-2000−2i2i−2i2i0-22-22002i−2i2i−2i0000000000000000000002−2−22−i2i2i2−i20000
χ5222-2-22-2-2022-2000−2i2i−2i2i0-22-22002i−2i2i−2i000000000000000000000−222−2i2−i2−i2i20000
χ5344-4-44-440-4-44000000000000004-4-44000000000000000000000000000000000
χ5444-4-44-440-4-4400000000000000-444-4000000000000000000000000000000000
χ5544-4-4-4440-44-4000000004-4-44000000000000000000000000000000000000000
χ5644-4-4-4440-44-400000000-444-4000000000000000000000000000000000000000
χ5744-4-4-44-404-440004i−4i−4i4i00000000000000000000000000000000000000000000
χ5844-4-4-44-404-44000−4i4i4i−4i00000000000000000000000000000000000000000000
χ598-88-800000000000000000004i2−4i20000000000000000000000000000000000000
χ608-88-80000000000000000000−4i24i20000000000000000000000000000000000000
χ618-8-880008000-800000000000000000000000000000000000000000000000000
χ628-8-88000-8000800000000000000000000000000000000000000000000000000

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