Finite Group Databasebeta

← Group #407669

Character table — Group #407669

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12224444222222444444888888882244444444448888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ51111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ61111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ911111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111
χ1011111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1
χ1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ17222222222-2-22-2-22-2-22-2-22222-2-2-2-20000000000000000000000000000002-20000002-2
χ18222222222-2-22-2-22-2-22-2-22222-2-2-2-2000000000000000000000000000000-22000000-22
χ19222222222-2-22-2-22-2-22-2-2-2-2-2-222220000000000000000000000000000002-2000000-22
χ20222222222-2-22-2-22-2-22-2-2-2-2-2-22222000000000000000000000000000000-220000002-2
χ2122222222-22-2-22-2-22-2-22-222-2-222-2-200000000000000000000000000002-20000002-200
χ2222222222-22-2-22-2-22-2-22-222-2-222-2-20000000000000000000000000000-22000000-2200
χ2322222222-22-2-22-2-22-2-22-2-2-222-2-22200000000000000000000000000002-2000000-2200
χ2422222222-22-2-22-2-22-2-22-2-2-222-2-2220000000000000000000000000000-220000002-200
χ2522222222-2-22-2-22-2-22-2-2222-2-2-2-2220000000022-2-20000000022-2-20000000000000000
χ2622222222-2-22-2-22-2-22-2-2222-2-2-2-22200000000-2-22200000000-2-2220000000000000000
χ2722222222-2-22-2-22-2-22-2-22-2-22222-2-20000000022-2-200000000-2-2220000000000000000
χ2822222222-2-22-2-22-2-22-2-22-2-22222-2-200000000-2-2220000000022-2-20000000000000000
χ292222-2-2-2-2222222-2-2-2-2-2-22i−2i2i−2i2i−2i2i−2i22-2-20000000000002i2i−2i−2i00000000000000000000
χ302222-2-2-2-2222222-2-2-2-2-2-22i−2i2i−2i2i−2i2i−2i-2-222000000000000−2i−2i2i2i00000000000000000000
χ312222-2-2-2-2222222-2-2-2-2-2-2−2i2i−2i2i−2i2i−2i2i22-2-2000000000000−2i−2i2i2i00000000000000000000
χ322222-2-2-2-2222222-2-2-2-2-2-2−2i2i−2i2i−2i2i−2i2i-2-2220000000000002i2i−2i−2i00000000000000000000
χ332222-2-2-2-22-2-22-2-2-222-2222i−2i2i−2i−2i2i−2i2i000000000000000000000000002-20000002i−2i0000
χ342222-2-2-2-22-2-22-2-2-222-2222i−2i2i−2i−2i2i−2i2i00000000000000000000000000-22000000−2i2i0000
χ352222-2-2-2-22-2-22-2-2-222-222−2i2i−2i2i2i−2i2i−2i000000000000000000000000002-2000000−2i2i0000
χ362222-2-2-2-22-2-22-2-2-222-222−2i2i−2i2i2i−2i2i−2i00000000000000000000000000-220000002i−2i0000
χ372222-2-2-2-2-22-2-22-22-222-222i−2i−2i2i2i−2i−2i2i0000000000000000000000002-20000002i−2i000000
χ382222-2-2-2-2-22-2-22-22-222-222i−2i−2i2i2i−2i−2i2i000000000000000000000000-22000000−2i2i000000
χ392222-2-2-2-2-22-2-22-22-222-22−2i2i2i−2i−2i2i2i−2i0000000000000000000000002-2000000−2i2i000000
χ402222-2-2-2-2-22-2-22-22-222-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000-220000002i−2i000000
χ412222-2-2-2-2-2-22-2-2222-222-22i−2i−2i2i−2i2i2i−2i000022-2-200002i2i−2i−2i000000000000000000000000
χ422222-2-2-2-2-2-22-2-2222-222-22i−2i−2i2i−2i2i2i−2i0000-2-2220000−2i−2i2i2i000000000000000000000000
χ432222-2-2-2-2-2-22-2-2222-222-2−2i2i2i−2i2i−2i−2i2i000022-2-20000−2i−2i2i2i000000000000000000000000
χ442222-2-2-2-2-2-22-2-2222-222-2−2i2i2i−2i2i−2i−2i2i0000-2-22200002i2i−2i−2i000000000000000000000000
χ4522-2-222-2-2222-2-2-222-2-2-22000000002-22-2000000002-22-200002-22-20000000000000000
χ4622-2-222-2-2222-2-2-222-2-2-22000000002-22-200000000-22-220000-22-220000000000000000
χ4722-2-222-2-2222-2-2-222-2-2-2200000000-22-22000000002-22-20000-22-220000000000000000
χ4822-2-222-2-2222-2-2-222-2-2-2200000000-22-2200000000-22-2200002-22-20000000000000000
χ4922-2-222-2-2-2-2222-2-2-2-22220000000000002i−2i2i−2i000000002i−2i2i−2i2-2-220000000000000000
χ5022-2-222-2-2-2-2222-2-2-2-22220000000000002i−2i2i−2i00000000−2i2i−2i2i-222-20000000000000000
χ5122-2-222-2-2-2-2222-2-2-2-2222000000000000−2i2i−2i2i000000002i−2i2i−2i-222-20000000000000000
χ5222-2-222-2-2-2-2222-2-2-2-2222000000000000−2i2i−2i2i00000000−2i2i−2i2i2-2-220000000000000000
χ5322-2-2-2-222222-2-2-2-2-2222-2000000002-2-222i−2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ5422-2-2-2-222222-2-2-2-2-2222-2000000002-2-22−2i2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ5522-2-2-2-222222-2-2-2-2-2222-200000000-222-22i−2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ5622-2-2-2-222222-2-2-2-2-2222-200000000-222-2−2i2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ5722-2-2-2-222-2-2222-2222-2-2-200000000000000002i−2i−2i2i2i−2i−2i2i-222-200000000000000000000
χ5822-2-2-2-222-2-2222-2222-2-2-200000000000000002i−2i−2i2i−2i2i2i−2i2-2-2200000000000000000000
χ5922-2-2-2-222-2-2222-2222-2-2-20000000000000000−2i2i2i−2i2i−2i−2i2i2-2-2200000000000000000000
χ6022-2-2-2-222-2-2222-2222-2-2-20000000000000000−2i2i2i−2i−2i2i2i−2i-222-200000000000000000000
χ6144-4-444-4-44-4-4-4444-44-44-4000000000000000000000000000000000000000000000000
χ6244-4-444-4-4-44-44-44-4444-4-4000000000000000000000000000000000000000000000000
χ6344-4-4-4-4444-4-4-444-44-44-44000000000000000000000000000000000000000000000000
χ6444-4-4-4-444-44-44-444-4-4-444000000000000000000000000000000000000000000000000
χ658-88-88i−8i8i−8i000000000000000000000000000000000000000000000000000000000000
χ668-88-8−8i8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ678-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ688-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000

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