Finite Group Databasebeta

← Group #276413

Character table — Group #276413

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444448888888822444888888888888888888884444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
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
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
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
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ91111111111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-1
χ101111111111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-11
χ111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ121111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-11-1
χ131111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ141111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1
χ151111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111-1
χ161111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-11
χ17222222222-2222222-2-22-2-2-2-2-222000000002222222200-200-2-2-2-200000000000000000000000000
χ18222222222-2222222-2-22-2-2-2-2-22200000000-2-2-2-2-2-2-2-200-200222200000000000000000000000000
χ19222222222-2-2-2-2-222-2-22-2-2-222-2-2000000002222-2-2-2-200200-2-22200000000000000000000000000
χ20222222222-2-2-2-2-222-2-22-2-2-222-2-200000000-2-2-2-222220020022-2-200000000000000000000000000
χ2122222222-222222-2-222-22-2-222-2-22222-2-2-2-20000000022-2-2-2000000000000000000000000000000
χ2222222222-222222-2-222-22-2-222-2-2-2-2-2-2222200000000-2-2-222000000000000000000000000000000
χ2322222222-22-2-2-2-2-2-222-22-2-2-2-2222222-2-2-2-200000000-2-2222000000000000000000000000000000
χ2422222222-22-2-2-2-2-2-222-22-2-2-2-222-2-2-2-2222200000000222-2-2000000000000000000000000000000
χ2522222222-2-22222-2-2-2-2-2-222-2-2-2-2000000000000000000200000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2622222222-2-22222-2-2-2-2-2-222-2-2-2-200000000000000000020000000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000-200000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000-20000000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ2922-222-2-2-22-20000-2-22-2222-200002i2i−2i−2i2i2i−2i−2i000000000000000002i2i−2i−2i0000000000002-200000000
χ3022-222-2-2-22-20000-2-22-2222-200002i2i−2i−2i2i2i−2i−2i00000000000000000−2i−2i2i2i000000000000-2200000000
χ3122-222-2-2-22-20000-2-22-2222-20000−2i−2i2i2i−2i−2i2i2i000000000000000002i2i−2i−2i000000000000-2200000000
χ3222-222-2-2-22-20000-2-22-2222-20000−2i−2i2i2i−2i−2i2i2i00000000000000000−2i−2i2i2i0000000000002-200000000
χ3322-222-2-2-2-2-20000222-2-22-2200002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000022-2-2002i−2i000000
χ3422-222-2-2-2-2-20000222-2-22-2200002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000-2-22200−2i2i000000
χ3522-222-2-2-2-2-20000222-2-22-220000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000022-2-200−2i2i000000
χ3622-222-2-2-2-2-20000222-2-22-220000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000-2-222002i−2i000000
χ372-22-22-22-2022i2i−2i−2i00-2-202002i−2i002i−2i2i−2i000022−2−2i2i2−i2−i22-20002−2i2−i20000i2−i2i2−i22−22−200000000000000
χ382-22-22-22-2022i2i−2i−2i00-2-202002i−2i002i−2i2i−2i0000−2−222−i2−i2i2i22-2000−22−i2i20000−i2i2−i2i2−22−2200000000000000
χ392-22-22-22-2022i2i−2i−2i00-2-202002i−2i00−2i2i−2i2i000022−2−2i2i2−i2−i2-220002−2i2−i20000−i2i2−i2i2−22−2200000000000000
χ402-22-22-22-2022i2i−2i−2i00-2-202002i−2i00−2i2i−2i2i0000−2−222−i2−i2i2i2-22000−22−i2i20000i2−i2i2−i22−22−200000000000000
χ412-22-22-22-202−2i−2i2i2i00-2-20200−2i2i002i−2i2i−2i000022−2−2−i2−i2i2i2-220002−2−i2i20000i2−i2i2−i2−22−2200000000000000
χ422-22-22-22-202−2i−2i2i2i00-2-20200−2i2i002i−2i2i−2i0000−2−222i2i2−i2−i2-22000−22i2−i20000−i2i2−i2i22−22−200000000000000
χ432-22-22-22-202−2i−2i2i2i00-2-20200−2i2i00−2i2i−2i2i000022−2−2−i2−i2i2i22-20002−2−i2i20000−i2i2−i2i22−22−200000000000000
χ442-22-22-22-202−2i−2i2i2i00-2-20200−2i2i00−2i2i−2i2i0000−2−222i2i2−i2−i22-2000−22i2−i20000i2−i2i2−i2−22−2200000000000000
χ452-22-22-22-20-22i2i−2i−2i00220-200−2i2i0000002-22-222−2−2i2i2−i2−i20002i−2i−22−i2i200002−2−22−i2i2i2−i200000000000000
χ462-22-22-22-20-22i2i−2i−2i00220-200−2i2i0000002-22-2−2−222−i2−i2i2i20002i−2i2−2i2−i20000−222−2i2−i2−i2i200000000000000
χ472-22-22-22-20-22i2i−2i−2i00220-200−2i2i000000-22-2222−2−2i2i2−i2−i2000−2i2i−22−i2i20000−222−2i2−i2−i2i200000000000000
χ482-22-22-22-20-22i2i−2i−2i00220-200−2i2i000000-22-22−2−222−i2−i2i2i2000−2i2i2−2i2−i200002−2−22−i2i2i2−i200000000000000
χ492-22-22-22-20-2−2i−2i2i2i00220-2002i−2i0000002-22-222−2−2−i2−i2i2i2000−2i2i−22i2−i200002−2−22i2−i2−i2i200000000000000
χ502-22-22-22-20-2−2i−2i2i2i00220-2002i−2i0000002-22-2−2−222i2i2−i2−i2000−2i2i2−2−i2i20000−222−2−i2i2i2−i200000000000000
χ512-22-22-22-20-2−2i−2i2i2i00220-2002i−2i000000-22-2222−2−2−i2−i2i2i20002i−2i−22i2−i20000−222−2−i2i2i2−i200000000000000
χ522-22-22-22-20-2−2i−2i2i2i00220-2002i−2i000000-22-22−2−222i2i2−i2−i20002i−2i2−2−i2i200002−2−22i2−i2−i2i200000000000000
χ532-2-22-2-222202-22-22-200-2000002-2000000002i−2i2i−2i2i−2i2i−2i000000000i2−i2i2−i200000000i2−i2i2−i200002−22−200
χ542-2-22-2-222202-22-22-200-2000002-2000000002i−2i2i−2i2i−2i2i−2i000000000−i2i2−i2i200000000−i2i2−i2i20000−22−2200
χ552-2-22-2-222202-22-22-200-2000002-200000000−2i2i−2i2i−2i2i−2i2i000000000i2−i2i2−i200000000i2−i2i2−i20000−22−2200
χ562-2-22-2-222202-22-22-200-2000002-200000000−2i2i−2i2i−2i2i−2i2i000000000−i2i2−i2i200000000−i2i2−i2i200002−22−200
χ572-2-22-2-22220-22-222-200-200000-22000000002i−2i2i−2i−2i2i−2i2i000000000i2−i2i2−i200000000−i2i2−i2i200002−2−2200
χ582-2-22-2-22220-22-222-200-200000-22000000002i−2i2i−2i−2i2i−2i2i000000000−i2i2−i2i200000000i2−i2i2−i20000−222−200
χ592-2-22-2-22220-22-222-200-200000-2200000000−2i2i−2i2i2i−2i2i−2i000000000i2−i2i2−i200000000−i2i2−i2i20000−222−200
χ602-2-22-2-22220-22-222-200-200000-2200000000−2i2i−2i2i2i−2i2i−2i000000000−i2i2−i2i200000000i2−i2i2−i200002−2−2200
χ6144-444-4-4-4440000-4-4-444-4-440000000000000000000000000000000000000000000000000000000
χ6244-444-4-4-4-44000044-44-4-44-40000000000000000000000000000000000000000000000000000000
χ6344-4-4-444-4004i−4i−4i4i000000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000000000000000000
χ6444-4-4-444-4004i−4i−4i4i00000000000000000000−2i22i22i2−2i222−22−222200000000000000000000000000000000000
χ6544-4-4-444-400−4i4i4i−4i000000000000000000002i2−2i2−2i22i222−22−222200000000000000000000000000000000000
χ6644-4-4-444-400−4i4i4i−4i00000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000000000000000000
χ674-444-44-4-4400000-4400-40000000000000000000000000000000022−22−22220000000000000000000000
χ684-444-44-4-4400000-4400-400000000000000000000000000000000−222222−220000000000000000000000
χ694-444-44-4-4-4000004-4004000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ704-444-44-4-4-4000004-400400000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ714-4-44-4-444-404-44-4-4400400000-44000000000000000000000000000000000000000000000000000
χ724-4-44-4-444-40-44-44-44004000004-4000000000000000000000000000000000000000000000000000
χ734-4-4-444-44040000004-40-400000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ744-4-4-444-44040000004-40-40000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ754-4-4-444-440-4000000-44040000004-4-4400000000000000000000000000000000000000000000000
χ764-4-4-444-440-4000000-4404000000-444-400000000000000000000000000000000000000000000000
χ77888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000000000

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