Finite Group Databasebeta

← Group #264215

Character table — Group #264215

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822444444448888888888888888222444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
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
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-111111-1-11-1
χ911111111111111111-1-1-1-111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-111
χ1011111111111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1111111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111-1-11-1-11111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-111-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-111111-1-1-111-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1111-1-111-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-11-1-1-11111-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1111-1-1-1-1111-1
χ172222222222-2-22-2-22-20000-22222-2-2-2-200002222000000000000000000-200-200000000
χ182222222222-2-22-2-22-20000-22222-2-2-2-20000-2-2-2-2000000000000000000200200000000
χ192222222222-2-22-2-22-20000-2-2-2-2-22222000022-2-2000000000000000000-200200000000
χ202222222222-2-22-2-22-20000-2-2-2-2-222220000-2-222000000000000000000200-200000000
χ2122222222-2-222-222-2-22222-20000000022-2-20000-2-222-2-2000000000000000000000000
χ2222222222-2-222-222-2-22222-200000000-2-2-2-2000022-2-222000000000000000000000000
χ2322222222-2-222-222-2-2-2-2-2-2-20000000022220000-2-2-2-222000000000000000000000000
χ2422222222-2-222-222-2-2-2-2-2-2-200000000-2-22200002222-2-2000000000000000000000000
χ2522-22-22-2-2002-202-20022-2-20i2i2−i2−i2i2i2−i2−i2000000002i−2i002i−2ii2i2−i2−i222−2−222−2−2000000000000
χ2622-22-22-2-2002-202-20022-2-20i2i2−i2−i2i2i2−i2−i200000000−2i2i00−2i2ii2i2−i2−i2−2−222−2−222000000000000
χ2722-22-22-2-2002-202-20022-2-20−i2−i2i2i2−i2−i2i2i2000000002i−2i002i−2i−i2−i2i2i2−2−222−2−222000000000000
χ2822-22-22-2-2002-202-20022-2-20−i2−i2i2i2−i2−i2i2i200000000−2i2i00−2i2i−i2−i2i2i222−2−222−2−2000000000000
χ2922-22-22-2-2002-202-200-2-2220i2i2−i2−i2i2i2−i2−i2000000002i−2i00−2i2i−i2−i2i2i222−2−2−2−222000000000000
χ3022-22-22-2-2002-202-200-2-2220i2i2−i2−i2i2i2−i2−i200000000−2i2i002i−2i−i2−i2i2i2−2−22222−2−2000000000000
χ3122-22-22-2-2002-202-200-2-2220−i2−i2i2i2−i2−i2i2i2000000002i−2i00−2i2ii2i2−i2−i2−2−22222−2−2000000000000
χ3222-22-22-2-2002-202-200-2-2220−i2−i2i2i2−i2−i2i2i200000000−2i2i002i−2ii2i2−i2−i222−2−2−2−222000000000000
χ332-22-222-2-2002-20-22002-22-20i2−i2i2−i2i2−i2i2−i22-2000000002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ342-22-222-2-2002-20-22002-22-20i2−i2i2−i2i2−i2i2−i2-2200000000-2200i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ352-22-222-2-2002-20-22002-22-20−i2i2−i2i2−i2i2−i2i22-2000000002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ362-22-222-2-2002-20-22002-22-20−i2i2−i2i2−i2i2−i2i2-2200000000-2200−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ372-22-222-2-2002-20-2200-22-220i2−i2i2−i2i2−i2i2−i22-200000000-2200−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ382-22-222-2-2002-20-2200-22-220i2−i2i2−i2i2−i2i2−i2-22000000002-200−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ392-22-222-2-2002-20-2200-22-220−i2i2−i2i2−i2i2−i2i22-200000000-2200i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ402-22-222-2-2002-20-2200-22-220−i2i2−i2i2−i2i2−i2i2-22000000002-200i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ412-2-2-2-22222222-2-2-2-222-2-22-200000000002-2000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ422-2-2-2-22222222-2-2-2-222-2-22-200000000002-200000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ432-2-2-2-22222222-2-2-2-22-222-2-20000000000-22000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ442-2-2-2-22222222-2-2-2-22-222-2-20000000000-2200000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ452-2-2-2-2222-2-2222-2-22-22-2-2222-2-222-2-2200-2200000000002-2-2200000000000000000000
χ462-2-2-2-2222-2-2222-2-22-22-2-222-222-2-222-200-220000000000-222-200000000000000000000
χ472-2-2-2-2222-2-2222-2-22-2-222-222-2-222-2-22002-20000000000-222-200000000000000000000
χ482-2-2-2-2222-2-2222-2-22-2-222-22-222-2-222-2002-200000000002-2-2200000000000000000000
χ492-2-2-2-2222-2-2-2-2222220000-22-2-22-222-20000000000000000000000000002-202-2000000
χ502-2-2-2-2222-2-2-2-2222220000-22-2-22-222-2000000000000000000000000000-220-22000000
χ512-2-2-2-2222-2-2-2-2222220000-2-222-22-2-220000000000000000000000000002-20-22000000
χ522-2-2-2-2222-2-2-2-2222220000-2-222-22-2-22000000000000000000000000000-2202-2000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ5444-44-44-4-400-440-4400000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ5544-44-44-4-400-440-440000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ5644-4-44-4-444-400400-4000000000000000000004i−4i000000000000000000000000000000
χ5744-4-44-4-444-400400-400000000000000000000−4i4i000000000000000000000000000000
χ5844-4-44-4-44-4400-400400000000000000000000000000000000000000000000000022−2200
χ5944-4-44-4-44-4400-4004000000000000000000000000000000000000000000000000−222200
χ604-444-4-4-444-400-4004000000000000000000000000000000000000000000000022−220000
χ614-444-4-4-444-400-40040000000000000000000000000000000000000000000000−22220000
χ624-444-4-4-44-4400400-40000000000000000004i−4i00000000000000000000000000000000
χ634-444-4-4-44-4400400-4000000000000000000−4i4i00000000000000000000000000000000
χ644-44-444-4-400-4404-400000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ654-44-444-4-400-4404-40000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ664-4-4-4-444444-4-4-444-4-4000040000000000000000000000000000000000000000000000
χ67888-8-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-8-888-88-8000000000000000000000000000000000000000000000000000000000000

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