Finite Group Databasebeta

← Group #311321

Character table — Group #311321

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888244444888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1111-1-111-1-11-1
χ91111111111111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ101111111111111111-1-1-1-1111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-111111-111-1-1-1-1111-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11-111-1-111-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-11-1-11111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-11-1-111-1-1111-1
χ17222222222-222-2-2-220000-2-22222-2-2-2-222000022000000000000000000-2-20000000000
χ18222222222-222-2-2-220000-2-22222-2-2-2-2-2-20000-2-2000000000000000000220000000000
χ19222222222-222-2-2-220000-2-2-2-2-2-22222220000-2-2000000000000000000-220000000000
χ20222222222-222-2-2-220000-2-2-2-2-2-22222-2-20000220000000000000000002-20000000000
χ2122222222-22-2-2222-22222-2-20000000000-2-22200-2-222-2-2000000000000000000000000
χ2222222222-22-2-2222-22222-2-20000000000-2-2-2-20022-2-222000000000000000000000000
χ2322222222-22-2-2222-2-2-2-2-2-2-20000000000222200-2-2-2-222000000000000000000000000
χ2422222222-22-2-2222-2-2-2-2-2-2-2000000000022-2-2002222-2-2000000000000000000000000
χ2522-22-22-2-222-2-2-22-220000-222i2i−2i−2i2i2i−2i−2i00000000000000000000000000002-22i−2i000000
χ2622-22-22-2-222-2-2-22-220000-222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000-22−2i2i000000
χ2722-22-22-2-222-2-2-22-220000-22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002-2−2i2i000000
χ2822-22-22-2-222-2-2-22-220000-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000-222i−2i000000
χ2922-22-22-2-22-2-2-22-2222i2i−2i−2i2-22i2i−2i−2i−2i−2i2i2i002i−2i000000000022-2-200000000000000000000
χ3022-22-22-2-22-2-2-22-2222i2i−2i−2i2-2−2i−2i2i2i2i2i−2i−2i002i−2i0000000000-2-22200000000000000000000
χ3122-22-22-2-22-2-2-22-222−2i−2i2i2i2-22i2i−2i−2i−2i−2i2i2i00−2i2i0000000000-2-22200000000000000000000
χ3222-22-22-2-22-2-2-22-222−2i−2i2i2i2-2−2i−2i2i2i2i2i−2i−2i00−2i2i000000000022-2-200000000000000000000
χ3322-22-22-2-2-2-2222-22-22i2i−2i−2i-220000000000−2i2i000000000000002i2i−2i−2i22-2-2000000000000
χ3422-22-22-2-2-2-2222-22-22i2i−2i−2i-220000000000−2i2i00000000000000−2i−2i2i2i-2-222000000000000
χ3522-22-22-2-2-2-2222-22-2−2i−2i2i2i-2200000000002i−2i000000000000002i2i−2i−2i-2-222000000000000
χ3622-22-22-2-2-2-2222-22-2−2i−2i2i2i-2200000000002i−2i00000000000000−2i−2i2i2i22-2-2000000000000
χ372-222-2-22-20-20022-202-22-200i2−i2i2−i2i2−i2i2−i200002-200002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ382-222-2-22-20-20022-202-22-200i2−i2i2−i2i2−i2i2−i20000-220000-2200i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ392-222-2-22-20-20022-202-22-200−i2i2−i2i2−i2i2−i2i200002-200002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ402-222-2-22-20-20022-202-22-200−i2i2−i2i2−i2i2−i2i20000-220000-2200−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ412-222-2-22-20-20022-20-22-2200i2−i2i2−i2i2−i2i2−i200002-20000-2200−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ422-222-2-22-20-20022-20-22-2200i2−i2i2−i2i2−i2i2−i20000-2200002-200−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ432-222-2-22-20-20022-20-22-2200−i2i2−i2i2−i2i2−i2i200002-20000-2200i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ442-222-2-22-20-20022-20-22-2200−i2i2−i2i2−i2i2−i2i20000-2200002-200i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ452-2-222-2-2202002-2-202i−2i−2i2i002−2−22−222−2000000002-2002i−2i−i2i2i2−i22−2−22−i2i2i2−i2000000000000
χ462-2-222-2-2202002-2-202i−2i−2i2i002−2−22−222−200000000-2200−2i2i−i2i2i2−i2−222−2i2−i2−i2i2000000000000
χ472-2-222-2-2202002-2-202i−2i−2i2i00−222−22−2−22000000002-2002i−2ii2−i2−i2i2−222−2i2−i2−i2i2000000000000
χ482-2-222-2-2202002-2-202i−2i−2i2i00−222−22−2−2200000000-2200−2i2ii2−i2−i2i22−2−22−i2i2i2−i2000000000000
χ492-2-222-2-2202002-2-20−2i2i2i−2i002−2−22−222−2000000002-200−2i2ii2−i2−i2i22−2−22i2−i2−i2i2000000000000
χ502-2-222-2-2202002-2-20−2i2i2i−2i002−2−22−222−200000000-22002i−2ii2−i2−i2i2−222−2−i2i2i2−i2000000000000
χ512-2-222-2-2202002-2-20−2i2i2i−2i00−222−22−2−22000000002-200−2i2i−i2i2i2−i2−222−2−i2i2i2−i2000000000000
χ522-2-222-2-2202002-2-20−2i2i2i−2i00−222−22−2−2200000000-22002i−2i−i2i2i2−i22−2−22i2−i2−i2i2000000000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ54444-44-4-4-4404-4000-4000000000000000000000000000000000000000000000022−220000
χ55444-44-4-4-4404-4000-40000000000000000000000000000000000000000000000−22220000
χ56444-44-4-4-4-40-440004000000000000004i−4i000000000000000000000000000000000000
χ57444-44-4-4-4-40-44000400000000000000−4i4i000000000000000000000000000000000000
χ5844-44-44-4-4-4444-44-4-400004-40000000000000000000000000000000000000000000000
χ5944-4-4-4-44440-44000-40000000000000000000000000000000000000000000000002i2−2i200
χ6044-4-4-4-44440-44000-4000000000000000000000000000000000000000000000000−2i22i200
χ6144-4-4-4-444-404-40004000000000000000000004-4000000000000000000000000000000
χ6244-4-4-4-444-404-4000400000000000000000000-44000000000000000000000000000000
χ634-444-4-44-40400-4-4400000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ644-444-4-44-40400-4-440000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ654-4-444-4-440-400-444000000022−22−222222−22−222200000000000000000000000000000000000000
χ664-4-444-4-440-400-4440000000−222222−22−222222−2200000000000000000000000000000000000000
χ678-88-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8888-8000000000000000000000000000000000000000000000000000000000000

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