Finite Group Databasebeta

← Group #311104

Character table — Group #311104

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888444444444488888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11-1-1-11111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1111-1-1-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1111-1-111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111-111-1-111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-11-1-111-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1111111-1-1-1-11-111-1-1-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-11-1-11111-1-1-11
χ17222222222-2-22-2-22200000000-22222-200002222-2-2-2-200000000-2-2002200-2-200000000000000000000
χ18222222222-2-22-2-22200000000-22222-20000-2-2-2-2222200000000-2-200-2-2002200000000000000000000
χ19222222222-2-22-2-22200000000-2-2-2-2-2-200002222-2-2-2-2000000002200-2-2002200000000000000000000
χ20222222222-2-22-2-22200000000-2-2-2-2-2-20000-2-2-2-222220000000022002200-2-200000000000000000000
χ2122222222-222-222-2-222222222-20000-2-2-2-2-20000000000000000002200220000000000-2-20000000000
χ2222222222-222-222-2-222222222-20000-2-2-2-2-2000000000000000000-2-200-2-20000000000220000000000
χ2322222222-222-222-2-2-2-2-2-2-2-2-2-2-20000-222220000000000000000002200-2-20000000000-220000000000
χ2422222222-222-222-2-2-2-2-2-2-2-2-2-2-20000-22222000000000000000000-2-2002200000000002-20000000000
χ2522-2-2-2-222200200-2-22222−2−2−2−202i2i−2i−2i022−2−222-2-200002222−2−2−2−200002i−2i0000i2i2−i2−i2i2i2−i2−i2000000000000
χ2622-2-2-2-222200200-2-22222−2−2−2−202i2i−2i−2i022−2−2-2-2220000−2−2−2−222220000−2i2i0000i2i2−i2−i2−i2−i2i2i2000000000000
χ2722-2-2-2-222200200-2-22222−2−2−2−20−2i−2i2i2i022−2−222-2-200002222−2−2−2−20000−2i2i0000−i2−i2i2i2−i2−i2i2i2000000000000
χ2822-2-2-2-222200200-2-22222−2−2−2−20−2i−2i2i2i022−2−2-2-2220000−2−2−2−2222200002i−2i0000−i2−i2i2i2i2i2−i2−i2000000000000
χ2922-2-2-2-222200200-2-2−2−2−2−2222202i2i−2i−2i0−2−22222-2-20000−2−2−2−2222200002i−2i0000−i2−i2i2i2−i2−i2i2i2000000000000
χ3022-2-2-2-222200200-2-2−2−2−2−2222202i2i−2i−2i0−2−222-2-22200002222−2−2−2−20000−2i2i0000−i2−i2i2i2i2i2−i2−i2000000000000
χ3122-2-2-2-222200200-2-2−2−2−2−222220−2i−2i2i2i0−2−22222-2-20000−2−2−2−222220000−2i2i0000i2i2−i2−i2i2i2−i2−i2000000000000
χ3222-2-2-2-222200200-2-2−2−2−2−222220−2i−2i2i2i0−2−222-2-22200002222−2−2−2−200002i−2i0000i2i2−i2−i2−i2−i2i2i2000000000000
χ332-222-2-22-22-2-2-2222-22i2i−2i−2i2i2i−2i−2i-2000022i−2i2i−2i0000000000000000000000000000000000002-22i−2i000000
χ342-222-2-22-22-2-2-2222-22i2i−2i−2i2i2i−2i−2i-2000022i−2i2i−2i000000000000000000000000000000000000-22−2i2i000000
χ352-222-2-22-22-2-2-2222-2−2i−2i2i2i−2i−2i2i2i-200002−2i2i−2i2i0000000000000000000000000000000000002-2−2i2i000000
χ362-222-2-22-22-2-2-2222-2−2i−2i2i2i−2i−2i2i2i-200002−2i2i−2i2i000000000000000000000000000000000000-222i−2i000000
χ372-222-2-22-2-2222-2-2-2200000000-22i−2i2i−2i200000000000022-2-222-2-22i−2i0000000000002i−2i2i−2i000000000000
χ382-222-2-22-2-2222-2-2-2200000000-22i−2i2i−2i2000000000000-2-222-2-2222i−2i000000000000−2i2i−2i2i000000000000
χ392-222-2-22-2-2222-2-2-2200000000-2−2i2i−2i2i200000000000022-2-222-2-2−2i2i000000000000−2i2i−2i2i000000000000
χ402-222-2-22-2-2222-2-2-2200000000-2−2i2i−2i2i2000000000000-2-222-2-222−2i2i0000000000002i−2i2i−2i000000000000
χ412-222-2-22-2-2-2-2222-222i2i−2i−2i2i2i−2i−2i22i−2i2i−2i-2−2i2i−2i2i0000000000000000−2i2i000000002-22-20000000000000000
χ422-222-2-22-2-2-2-2222-222i2i−2i−2i2i2i−2i−2i2−2i2i−2i2i-2−2i2i−2i2i00000000000000002i−2i00000000-22-220000000000000000
χ432-222-2-22-2-2-2-2222-22−2i−2i2i2i−2i−2i2i2i22i−2i2i−2i-22i−2i2i−2i0000000000000000−2i2i00000000-22-220000000000000000
χ442-222-2-22-2-2-2-2222-22−2i−2i2i2i−2i−2i2i2i2−2i2i−2i2i-22i−2i2i−2i00000000000000002i−2i000000002-22-20000000000000000
χ452-22-22-2-2202-202-2002i−2i2i−2i2i−2i2i−2i0000000000i2−i2i2−i2i2i2−i2−i22−22−22−22−2002i−2i002-200000000000000002−2i2−i200
χ462-22-22-2-2202-202-2002i−2i2i−2i2i−2i2i−2i0000000000i2−i2i2−i2i2i2−i2−i22−22−22−22−200−2i2i00-220000000000000000−22−i2i200
χ472-22-22-2-2202-202-2002i−2i2i−2i2i−2i2i−2i0000000000−i2i2−i2i2−i2−i2i2i2−22−22−22−22002i−2i002-20000000000000000−22−i2i200
χ482-22-22-2-2202-202-2002i−2i2i−2i2i−2i2i−2i0000000000−i2i2−i2i2−i2−i2i2i2−22−22−22−2200−2i2i00-2200000000000000002−2i2−i200
χ492-22-22-2-2202-202-200−2i2i−2i2i−2i2i−2i2i0000000000i2−i2i2−i2i2i2−i2−i2−22−22−22−22002i−2i00-2200000000000000002−2−i2i200
χ502-22-22-2-2202-202-200−2i2i−2i2i−2i2i−2i2i0000000000i2−i2i2−i2i2i2−i2−i2−22−22−22−2200−2i2i002-20000000000000000−22i2−i200
χ512-22-22-2-2202-202-200−2i2i−2i2i−2i2i−2i2i0000000000−i2i2−i2i2−i2−i2i2i22−22−22−22−2002i−2i00-220000000000000000−22i2−i200
χ522-22-22-2-2202-202-200−2i2i−2i2i−2i2i−2i2i0000000000−i2i2−i2i2−i2−i2i2i22−22−22−22−200−2i2i002-200000000000000002−2−i2i200
χ532-2-2-2222-2-2002002-2i2i2−i2−i2−i2−i2i2i202-2-220−i2i2i2−i200002i−2i2i−2i22−2−2−2−222000000002i−2i−i2i2i2−i22−2−22000000000000
χ542-2-2-2222-2-2002002-2i2i2−i2−i2−i2−i2i2i202-2-220−i2i2i2−i20000−2i2i−2i2i−2−22222−2−200000000−2i2i−i2i2i2−i2−222−2000000000000
χ552-2-2-2222-2-2002002-2i2i2−i2−i2−i2−i2i2i20-222-20−i2i2i2−i200002i−2i2i−2i22−2−2−2−22200000000−2i2ii2−i2−i2i2−222−2000000000000
χ562-2-2-2222-2-2002002-2i2i2−i2−i2−i2−i2i2i20-222-20−i2i2i2−i20000−2i2i−2i2i−2−22222−2−2000000002i−2ii2−i2−i2i22−2−22000000000000
χ572-2-2-2222-2-2002002-2−i2−i2i2i2i2i2−i2−i202-2-220i2−i2−i2i200002i−2i2i−2i−2−22222−2−2000000002i−2ii2−i2−i2i2−222−2000000000000
χ582-2-2-2222-2-2002002-2−i2−i2i2i2i2i2−i2−i202-2-220i2−i2−i2i20000−2i2i−2i2i22−2−2−2−22200000000−2i2ii2−i2−i2i22−2−22000000000000
χ592-2-2-2222-2-2002002-2−i2−i2i2i2i2i2−i2−i20-222-20i2−i2−i2i200002i−2i2i−2i−2−22222−2−200000000−2i2i−i2i2i2−i22−2−22000000000000
χ602-2-2-2222-2-2002002-2−i2−i2i2i2i2i2−i2−i20-222-20i2−i2−i2i20000−2i2i−2i2i22−2−2−2−222000000002i−2i−i2i2i2−i2−222−2000000000000
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ62444-4-44-4-404-40-44000000000000000000000000000022−22−222222−22−2222000000000000000000000000000000
χ63444-4-44-4-404-40-440000000000000000000000000000−222222−22−222222−22000000000000000000000000000000
χ64444-4-44-4-40-4404-4004-4-444-4-4400000000000000000000000000000000000000000000000000000000
χ65444-4-44-4-40-4404-400-444-4-444-400000000000000000000000000000000000000000000000000000000
χ6644-444-4-4-40000000022−22−2222−222222−220000000000000022−22−22222-2-22-222-2000000000000000000000000000000
χ6744-444-4-4-40000000022−22−2222−222222−2200000000000000−222222−22-222-22-2-22000000000000000000000000000000
χ6844-444-4-4-400000000−222222−2222−22−22220000000000000022−22−2222-222-22-2-22000000000000000000000000000000
χ6944-444-4-4-400000000−222222−2222−22−222200000000000000−222222−222-2-22-222-2000000000000000000000000000000
χ7044-4-4-4-444-400-4004422222222−22−22−22−22000000−22−2222220000000000000000000000000000000000000000000000
χ7144-4-4-4-444-400-40044−22−22−22−22222222220000002222−22−220000000000000000000000000000000000000000000000
χ724-444-4-44-4444-4-4-44-40000000040000-400000000000000000000000000000000000000000000000000
χ734-44-44-4-440-440-44000000000000000000002i2−2i22i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ744-44-44-4-440-440-4400000000000000000000−2i22i2−2i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ754-4-44-44-44000000002i2−2i22i2−2i2−2i22i2−2i22i200000000002i2−2i2−2i22i200002-22-2-22-22000000000000000000000000000000
χ764-4-44-44-44000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000−2i22i22i2−2i20000-22-222-22-2000000000000000000000000000000
χ774-4-44-44-4400000000−2i22i2−2i22i22i2−2i22i2−2i200000000002i2−2i2−2i22i20000-22-222-22-2000000000000000000000000000000
χ784-4-44-44-4400000000−2i22i2−2i22i22i2−2i22i2−2i20000000000−2i22i22i2−2i200002-22-2-22-22000000000000000000000000000000
χ794-4-4-4444-4400-400-442i22i2−2i2−2i2−2i2−2i22i22i20000002i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ804-4-4-4444-4400-400-44−2i2−2i22i22i22i22i2−2i2−2i2000000−2i22i22i2−2i20000000000000000000000000000000000000000000000

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