Finite Group Databasebeta

← Group #348768

Character table — Group #348768

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444444444444422222244444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-111-1-1-1-1111111111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ91111111111111-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111111-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ121111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ131111111111111-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-11
χ141111111111111-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-11-1
χ151111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ161111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ1722222222222-2-22222-2-22-2-2220000000022222222-2-2000000-2-2-200-2-20000000000000000000000
χ1822222222222-2-22222-2-22-2-22200000000-2-2-2-2-2-2-2-2-2-2000000-22200220000000000000000000000
χ1922222222222-2-2-2-2-2-2-2-2222-2-2000000002222-2-2-2-2-2-200000022200-2-20000000000000000000000
χ2022222222222-2-2-2-2-2-2-2-2222-2-200000000-2-2-2-22222-2-20000002-2-200220000000000000000000000
χ2122222222-2-2-222222222-222-2-22222222200000000-2-2-2-20000-200-2-2000000000000000000000000
χ2222222222-2-2-222222222-222-2-2-2-2-2-2-2-2-2-200000000-2-2220000-20022000000000000000000000000
χ2322222222-2-2-222-2-2-2-222-2-2-2222222-2-2-2-200000000-2-2-2-2000020022000000000000000000000000
χ2422222222-2-2-222-2-2-2-222-2-2-222-2-2-2-2222200000000-2-2220000200-2-2000000000000000000000000
χ2522222222-2-2-2-2-22222-2-2-2-2-2-2-20000000000000000220022-2-2200000022-2-2000000000000000000
χ2622222222-2-2-2-2-22222-2-2-2-2-2-2-200000000000000002200-2-2222000000-2-222000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000220022-2-2-2000000-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002200-2-222-200000022-2-2000000000000000000
χ292-2222-2-2-20002-22i2i−2i−2i2-202i−2i002i2i−2i−2i22-2-200000000000000000000000000022−2−2i2i2−i2−i20000i2−i22−200
χ302-2222-2-2-20002-22i2i−2i−2i2-202i−2i002i2i−2i−2i22-2-2000000000000000000000000000−2−222−i2−i2i2i20000−i2i2−2200
χ312-2222-2-2-20002-22i2i−2i−2i2-202i−2i00−2i−2i2i2i-2-22200000000000000000000000000022−2−2i2i2−i2−i20000−i2i2−2200
χ322-2222-2-2-20002-22i2i−2i−2i2-202i−2i00−2i−2i2i2i-2-222000000000000000000000000000−2−222−i2−i2i2i20000i2−i22−200
χ332-2222-2-2-20002-2−2i−2i2i2i2-20−2i2i002i2i−2i−2i-2-22200000000000000000000000000022−2−2−i2−i2i2i20000i2−i2−2200
χ342-2222-2-2-20002-2−2i−2i2i2i2-20−2i2i002i2i−2i−2i-2-222000000000000000000000000000−2−222i2i2−i2−i20000−i2i22−200
χ352-2222-2-2-20002-2−2i−2i2i2i2-20−2i2i00−2i−2i2i2i22-2-200000000000000000000000000022−2−2−i2−i2i2i20000−i2i22−200
χ362-2222-2-2-20002-2−2i−2i2i2i2-20−2i2i00−2i−2i2i2i22-2-2000000000000000000000000000−2−222i2i2−i2−i20000i2−i2−2200
χ372-2-22-222-222-2002-22-200-2002-20000000022-2-222-2-20000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000
χ382-2-22-222-222-2002-22-200-2002-20000000022-2-222-2-20000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000
χ392-2-22-222-222-2002-22-200-2002-200000000-2-222-2-2220000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000
χ402-2-22-222-222-2002-22-200-2002-200000000-2-222-2-2220000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000
χ412-2-22-222-222-200-22-2200-200-220000000022-2-2-2-2220000000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2000000
χ422-2-22-222-222-200-22-2200-200-220000000022-2-2-2-2220000000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2000000
χ432-2-22-222-222-200-22-2200-200-2200000000-2-22222-2-20000000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2i2−i2000000
χ442-2-22-222-222-200-22-2200-200-2200000000-2-22222-2-20000000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2−i2i2000000
χ452-2-2-222-222-22220000-2-2-2000000002i−2i2i−2i00002i−2i2i−2i-22002-22-202i−2i2i−2i000000000000000000000000
χ462-2-2-222-222-22220000-2-2-2000000002i−2i2i−2i0000−2i2i−2i2i-2200-22-220−2i2i2i−2i000000000000000000000000
χ472-2-2-222-222-22220000-2-2-200000000−2i2i−2i2i00002i−2i2i−2i-2200-22-2202i−2i−2i2i000000000000000000000000
χ482-2-2-222-222-22220000-2-2-200000000−2i2i−2i2i0000−2i2i−2i2i-22002-22-20−2i2i−2i2i000000000000000000000000
χ492-2-2-222-222-22-2-2000022-200002-22-2000000002i−2i2i−2i2-22-200000−2i2i00002i−2i2i−2i000000000000000000
χ502-2-2-222-222-22-2-2000022-200002-22-200000000−2i2i−2i2i2-22-2000002i−2i0000−2i2i−2i2i000000000000000000
χ512-2-2-222-222-22-2-2000022-20000-22-22000000002i−2i2i−2i2-2-2200000−2i2i0000−2i2i−2i2i000000000000000000
χ522-2-2-222-222-22-2-2000022-20000-22-2200000000−2i2i−2i2i2-2-22000002i−2i00002i−2i2i−2i000000000000000000
χ532-2-2-222-22-22-2220000-2-22000000002i−2i2i−2i2-22-200002-2000000000−2i2i2-22i−2i−2i2i000000000000000000
χ542-2-2-222-22-22-2220000-2-22000000002i−2i2i−2i-22-2200002-2000000000−2i2i-22−2i2i2i−2i000000000000000000
χ552-2-2-222-22-22-2220000-2-2200000000−2i2i−2i2i2-22-200002-20000000002i−2i2-2−2i2i2i−2i000000000000000000
χ562-2-2-222-22-22-2220000-2-2200000000−2i2i−2i2i-22-2200002-20000000002i−2i-222i−2i−2i2i000000000000000000
χ572-2-2-222-22-22-2-2-2000022200002-22-200002-22-20000-22-222-2-2200000-220000000000000000000000
χ582-2-2-222-22-22-2-2-2000022200002-22-20000-22-220000-22-22-222-2000002-20000000000000000000000
χ592-2-2-222-22-22-2-2-200002220000-22-2200002-22-20000-222-2-222-200000-220000000000000000000000
χ602-2-2-222-22-22-2-2-200002220000-22-220000-22-220000-222-22-2-22000002-20000000000000000000000
χ61444-4-44-4-44-4-400000000400000000000000004i−4i−4i4i0000000000000000000000000000000000000
χ62444-4-44-4-44-4-40000000040000000000000000−4i4i4i−4i0000000000000000000000000000000000000
χ63444-4-44-4-4-44400000000-40000000000004-4-4400000000000000000000000000000000000000000
χ64444-4-44-4-4-44400000000-4000000000000-444-400000000000000000000000000000000000000000
χ6544-44-4-4-44000004i−4i−4i4i0000000000000000000000000000000000000000002i−2i−2i2i-222-20000000000
χ6644-44-4-4-44000004i−4i−4i4i000000000000000000000000000000000000000000−2i2i2i−2i2-2-220000000000
χ6744-44-4-4-4400000−4i4i4i−4i0000000000000000000000000000000000000000002i−2i−2i2i2-2-220000000000
χ6844-44-4-4-4400000−4i4i4i−4i000000000000000000000000000000000000000000−2i2i2i−2i-222-20000000000
χ6944-4-44-44-40004-40000-440000000004i−4i−4i4i000000000000000000000000000000000000000000000
χ7044-4-44-44-40004-40000-44000000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ7144-4-44-44-4000-4400004-4000004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ7244-4-44-44-4000-4400004-400000−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ734-4444-4-4-4000-444i4i−4i−4i-440−4i4i0000000000000000000000000000000000000000000000000000000
χ744-4444-4-4-4000-44−4i−4i4i4i-4404i−4i0000000000000000000000000000000000000000000000000000000
χ754-4-44-444-4-4-44004-44-400400-4400000000000000000000000000000000000000000000000000000
χ764-4-44-444-4-4-4400-44-44004004-400000000000000000000000000000000000000000000000000000
χ778-88-8-8-888000000000000000000000000000000000000000000000000000000000000000000000

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