Finite Group Databasebeta

← Group #275285

Character table — Group #275285

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444224444444444448888888844444888888888888888888884444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ91111111111-1-1-1-1111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111-1-1-1-1111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111-1-1-1-1111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ121111111111-1-1-1-1111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ131111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ141111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ151111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ161111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ1722222222222222-2-22-2-2222-2-2-2-22222-2-2-2-20000000022-2-2-2000000000000000000000000000000
χ1822222222222222-2-22-2-2222-2-2-2-2-2-2-2-2222200000000-2-2-222000000000000000000000000000000
χ192222222222-2-2-2-2-2-22-2-22-2-2-2-2222222-2-2-2-200000000-2-2222000000000000000000000000000000
χ202222222222-2-2-2-2-2-22-2-22-2-2-2-222-2-2-2-2222200000000222-2-2000000000000000000000000000000
χ2122222222-2-2222222-222-2-2-2-2-222000000002222222200-200-2-2-2-200000000000000000000000000
χ2222222222-2-2222222-222-2-2-2-2-22200000000-2-2-2-2-2-2-2-200-200222200000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-222-2-200000000000000000020000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-222-2-20000000000000000002000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ2522222222-2-2-2-2-2-222-222-222-2-2-2-2000000002222-2-2-2-200200-2-22200000000000000000000000000
χ2622222222-2-2-2-2-2-222-222-222-2-2-2-200000000-2-2-2-222220020022-2-200000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000-20000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000-2000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ292222-2-2-2-22222-2-200-200-22-2000022-2-2000022−2−222−2−22-20002−22−22−22−22−22−2000000000000000000
χ302222-2-2-2-22222-2-200-200-22-2000022-2-20000−2−222−2−2222-2000−22−22−22−22−22−22000000000000000000
χ312222-2-2-2-22222-2-200-200-22-20000-2-222000022−2−222−2−2-220002−22−2−22−22−22−22000000000000000000
χ322222-2-2-2-22222-2-200-200-22-20000-2-2220000−2−222−2−222-22000−22−222−22−22−22−2000000000000000000
χ332222-2-2-2-222-2-22200-200-2-22000022-2-2000022−2−2−2−222-220002−2−222−22−2−22−22000000000000000000
χ342222-2-2-2-222-2-22200-200-2-22000022-2-20000−2−22222−2−2-22000−222−2−22−222−22−2000000000000000000
χ352222-2-2-2-222-2-22200-200-2-220000-2-222000022−2−2−2−2222-20002−2−22−22−222−22−2000000000000000000
χ362222-2-2-2-222-2-22200-200-2-220000-2-2220000−2−22222−2−22-2000−222−22−22−2−22−22000000000000000000
χ372222-2-2-2-2-2-222-2-2002002-22000000002i2i−2i−2i22−2−222−2−20002i−2i−22−22i2−i2−i2i2i2−i2−i2i2000000000000000000
χ382222-2-2-2-2-2-222-2-2002002-22000000002i2i−2i−2i−2−222−2−2220002i−2i2−22−2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ392222-2-2-2-2-2-222-2-2002002-2200000000−2i−2i2i2i22−2−222−2−2000−2i2i−22−22−i2i2i2−i2−i2i2i2−i2000000000000000000
χ402222-2-2-2-2-2-222-2-2002002-2200000000−2i−2i2i2i−2−222−2−222000−2i2i2−22−2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ412222-2-2-2-2-2-2-2-2220020022-2000000002i2i−2i−2i22−2−2−2−222000−2i2i−222−2i2−i2−i2i2−i2i2i2−i2000000000000000000
χ422222-2-2-2-2-2-2-2-2220020022-2000000002i2i−2i−2i−2−22222−2−2000−2i2i2−2−22−i2i2i2−i2i2−i2−i2i2000000000000000000
χ432222-2-2-2-2-2-2-2-2220020022-200000000−2i−2i2i2i22−2−2−2−2220002i−2i−222−2−i2i2i2−i2i2−i2−i2i2000000000000000000
χ442222-2-2-2-2-2-2-2-2220020022-200000000−2i−2i2i2i−2−22222−2−20002i−2i2−2−22i2−i2−i2i2−i2i2i2−i2000000000000000000
χ4522-2-222-2-22-200002-2-22-22002-2002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000022-2-2002i−2i000000
χ4622-2-222-2-22-200002-2-22-22002-2002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000-2-22200−2i2i000000
χ4722-2-222-2-22-200002-2-22-22002-200−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000022-2-200−2i2i000000
χ4822-2-222-2-22-200002-2-22-22002-200−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000-2-222002i−2i000000
χ4922-2-222-2-22-20000-22-2-22200-22002i−2i2i−2i−2i2i−2i2i000000000000000000000000022-2-200002i−2i00000000
χ5022-2-222-2-22-20000-22-2-22200-22002i−2i2i−2i−2i2i−2i2i0000000000000000000000000-2-2220000−2i2i00000000
χ5122-2-222-2-22-20000-22-2-22200-2200−2i2i−2i2i2i−2i2i−2i000000000000000000000000022-2-20000−2i2i00000000
χ5222-2-222-2-22-20000-22-2-22200-2200−2i2i−2i2i2i−2i2i−2i0000000000000000000000000-2-22200002i−2i00000000
χ532-22-2-222-2002i−2i2i−2i-2202-2000002i−2i000000002-22-22i−2i2i−2i00000000000000000i2−i2i2−i22−22−20000i2−i22−200
χ542-22-2-222-2002i−2i2i−2i-2202-2000002i−2i000000002-22-22i−2i2i−2i00000000000000000−i2i2−i2i2−22−220000−i2i2−2200
χ552-22-2-222-2002i−2i2i−2i-2202-2000002i−2i00000000-22-22−2i2i−2i2i00000000000000000i2−i2i2−i22−22−20000−i2i2−2200
χ562-22-2-222-2002i−2i2i−2i-2202-2000002i−2i00000000-22-22−2i2i−2i2i00000000000000000−i2i2−i2i2−22−220000i2−i22−200
χ572-22-2-222-200−2i2i−2i2i-2202-200000−2i2i000000002-22-2−2i2i−2i2i00000000000000000i2−i2i2−i2−22−220000i2−i2−2200
χ582-22-2-222-200−2i2i−2i2i-2202-200000−2i2i000000002-22-2−2i2i−2i2i00000000000000000−i2i2−i2i22−22−20000−i2i22−200
χ592-22-2-222-200−2i2i−2i2i-2202-200000−2i2i00000000-22-222i−2i2i−2i00000000000000000i2−i2i2−i2−22−220000−i2i22−200
χ602-22-2-222-200−2i2i−2i2i-2202-200000−2i2i00000000-22-222i−2i2i−2i00000000000000000−i2i2−i2i22−22−20000i2−i2−2200
χ6144-4-444-4-4-4400004-444-4-400-4400000000000000000000000000000000000000000000000000000
χ6244-4-444-4-4-440000-444-44-4004-400000000000000000000000000000000000000000000000000000
χ6344-4-4-4-4444-4000000400-40000004i−4i−4i4i00000000000000000000000000000000000000000000000
χ6444-4-4-4-4444-4000000400-4000000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ6544-4-4-4-444-44000000-400400000000004-4-440000000000000000000000000000000000000000000
χ6644-4-4-4-444-44000000-40040000000000-444-40000000000000000000000000000000000000000000
χ674-44-44-4-44004i−4i−4i4i0000000000000000000022−22−22222i2−2i2−2i22i200000000000000000000000000000000000
χ684-44-44-4-44004i−4i−4i4i00000000000000000000−222222−22−2i22i22i2−2i200000000000000000000000000000000000
χ694-44-44-4-4400−4i4i4i−4i0000000000000000000022−22−2222−2i22i22i2−2i200000000000000000000000000000000000
χ704-44-44-4-4400−4i4i4i−4i00000000000000000000−222222−222i2−2i2−2i22i200000000000000000000000000000000000
χ714-44-4-444-4004i−4i4i−4i4-40-4400000−4i4i000000000000000000000000000000000000000000000000000
χ724-44-4-444-400−4i4i−4i4i4-40-44000004i−4i000000000000000000000000000000000000000000000000000
χ734-4-44-44-44000000440-4-400000000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ744-4-44-44-44000000440-4-40000000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ754-4-44-44-44000000-4-40440000000000000000000000000000000000000000000022−22−22220000000000
χ764-4-44-44-44000000-4-404400000000000000000000000000000000000000000000−222222−220000000000
χ778-8-888-88-8000000000000000000000000000000000000000000000000000000000000000000000

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