Finite Group Databasebeta

← Group #348718

Character table — Group #348718

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444444444444444444444444444444888888888888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-11
χ1111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-111-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ1211111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-11
χ1722222222222222-2-222-2-222-2-20000000022222222-2-2-200-2-2000000-2-20000000000000000000000
χ1822222222222222-2-222-2-222-2-200000000-2-2-2-2-2-2-2-2-2-2-20022000000220000000000000000000000
χ19222222222222-2-222-2-222-2-2222222222200000000-2-2-2-2-2000000-2-2000000000000000000000000
χ20222222222222-2-222-2-222-2-222-2-2-2-2-2-2-2-200000000-2-2-22200000022000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000222000022-2-2000022-2-2000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000002220000-2-2220000-2-222000000000000000000
χ2322222222-2-2-2-222-2-222-2-2-2-222000000002222-2-2-2-2-2-2200-2-2000000220000000000000000000000
χ2422222222-2-2-2-222-2-222-2-2-2-22200000000-2-2-2-22222-2-220022000000-2-20000000000000000000000
χ2522222222-2-2-2-2-2-222-2-22222-2-22222-2-2-2-200000000-2-22-2-200000022000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-2-2-2-2222200000000-2-2222000000-2-2000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000022-2000022-2-20000-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000022-20000-2-222000022-2-2000000000000000000
χ292-222-2-22-22i2i−2i−2i002-2002-2002i−2i2i2i−2i−2i22-2-2000000000000000000000000000i2i2−i2−i222−2−22−2i2−i2000000
χ302-222-2-22-22i2i−2i−2i002-2002-2002i−2i2i2i−2i−2i22-2-2000000000000000000000000000−i2−i2i2i2−2−222−22−i2i2000000
χ312-222-2-22-22i2i−2i−2i002-2002-2002i−2i−2i−2i2i2i-2-222000000000000000000000000000i2i2−i2−i222−2−2−22−i2i2000000
χ322-222-2-22-22i2i−2i−2i002-2002-2002i−2i−2i−2i2i2i-2-222000000000000000000000000000−i2−i2i2i2−2−2222−2i2−i2000000
χ332-222-2-22-2−2i−2i2i2i002-2002-200−2i2i2i2i−2i−2i-2-222000000000000000000000000000i2i2−i2−i2−2−2222−2−i2i2000000
χ342-222-2-22-2−2i−2i2i2i002-2002-200−2i2i2i2i−2i−2i-2-222000000000000000000000000000−i2−i2i2i222−2−2−22i2−i2000000
χ352-222-2-22-2−2i−2i2i2i002-2002-200−2i2i−2i−2i2i2i22-2-2000000000000000000000000000i2i2−i2−i2−2−222−22i2−i2000000
χ362-222-2-22-2−2i−2i2i2i002-2002-200−2i2i−2i−2i2i2i22-2-2000000000000000000000000000−i2−i2i2i222−2−22−2−i2i2000000
χ372-22-22-2-2200002222-2-2-2-200002i−2i2i−2i00002i2i−2i−2i0000-2202i−2i2i−2i000000002-22-2000000000000000000
χ382-22-22-2-2200002222-2-2-2-200002i−2i2i−2i0000−2i−2i2i2i0000-2202i−2i−2i2i00000000-22-22000000000000000000
χ392-22-22-2-2200002222-2-2-2-20000−2i2i−2i2i00002i2i−2i−2i0000-220−2i2i2i−2i00000000-22-22000000000000000000
χ402-22-22-2-2200002222-2-2-2-20000−2i2i−2i2i0000−2i−2i2i2i0000-220−2i2i−2i2i000000002-22-2000000000000000000
χ412-22-22-2-22000022-2-2-2-222000000002-22-22i2i−2i−2i00002-2000−2i2i2i−2i2i−2i2-2000000000000000000000000
χ422-22-22-2-22000022-2-2-2-222000000002-22-2−2i−2i2i2i00002-20002i−2i−2i2i−2i2i2-2000000000000000000000000
χ432-22-22-2-22000022-2-2-2-22200000000-22-222i2i−2i−2i00002-2000−2i2i−2i2i−2i2i-22000000000000000000000000
χ442-22-22-2-22000022-2-2-2-22200000000-22-22−2i−2i2i2i00002-20002i−2i2i−2i2i−2i-22000000000000000000000000
χ452-22-22-2-220000-2-22222-2-200002i−2i2i−2i0000000022-2-22-20−2i2i002i−2i−2i2i002-20000000000000000000000
χ462-22-22-2-220000-2-22222-2-200002i−2i2i−2i00000000-2-2222-20−2i2i00−2i2i2i−2i00-220000000000000000000000
χ472-22-22-2-220000-2-22222-2-20000−2i2i−2i2i0000000022-2-22-202i−2i00−2i2i2i−2i002-20000000000000000000000
χ482-22-22-2-220000-2-22222-2-20000−2i2i−2i2i00000000-2-2222-202i−2i002i−2i−2i2i00-220000000000000000000000
χ492-22-22-2-220000-2-2-2-22222000000002-22-2000022-2-2-22000000000-22-222-2-22000000000000000000
χ502-22-22-2-220000-2-2-2-22222000000002-22-20000-2-222-22000000000-222-2-222-2000000000000000000
χ512-22-22-2-220000-2-2-2-2222200000000-22-22000022-2-2-220000000002-2-22-222-2000000000000000000
χ522-22-22-2-220000-2-2-2-2222200000000-22-220000-2-222-220000000002-22-22-2-22000000000000000000
χ532-2-2-2222-22i−2i2i−2i2-2002-2002i−2i00000000002i−2i2i−2i2-22-20000000000000000000i2−i2i2−i22−22−200002−2i2−i200
χ542-2-2-2222-22i−2i2i−2i2-2002-2002i−2i00000000002i−2i2i−2i2-22-20000000000000000000−i2i2−i2i2−22−220000−22−i2i200
χ552-2-2-2222-22i−2i2i−2i2-2002-2002i−2i0000000000−2i2i−2i2i-22-220000000000000000000i2−i2i2−i22−22−20000−22−i2i200
χ562-2-2-2222-22i−2i2i−2i2-2002-2002i−2i0000000000−2i2i−2i2i-22-220000000000000000000−i2i2−i2i2−22−2200002−2i2−i200
χ572-2-2-2222-2−2i2i−2i2i2-2002-200−2i2i00000000002i−2i2i−2i-22-220000000000000000000i2−i2i2−i2−22−2200002−2−i2i200
χ582-2-2-2222-2−2i2i−2i2i2-2002-200−2i2i00000000002i−2i2i−2i-22-220000000000000000000−i2i2−i2i22−22−20000−22i2−i200
χ592-2-2-2222-2−2i2i−2i2i2-2002-200−2i2i0000000000−2i2i−2i2i2-22-20000000000000000000i2−i2i2−i2−22−220000−22i2−i200
χ602-2-2-2222-2−2i2i−2i2i2-2002-200−2i2i0000000000−2i2i−2i2i2-22-20000000000000000000−i2i2−i2i22−22−200002−2−i2i200
χ61444-4-44-4-40000004-400-4400004-4-440000000000000000000000000000000000000000000000000
χ62444-4-44-4-40000004-400-440000-444-40000000000000000000000000000000000000000000000000
χ63444-4-44-4-4000000-44004-4000000004-4-44000000000000000000000000000000000000000000000
χ64444-4-44-4-4000000-44004-400000000-444-4000000000000000000000000000000000000000000000
χ6544-444-4-4-400004-400-44000000000000004-4-4400000000000000000000000000000000000000000
χ6644-444-4-4-400004-400-4400000000000000-444-400000000000000000000000000000000000000000
χ6744-444-4-4-40000-44004-40000000000000000004-4-440000000000000000000000000000000000000
χ6844-444-4-4-40000-44004-4000000000000000000-444-40000000000000000000000000000000000000
χ6944-4-4-4-4444-4-44000000000000000000000000000000000000000000000002-2-222-2-220000000000
χ7044-4-4-4-4444-4-4400000000000000000000000000000000000000000000000-222-2-222-20000000000
χ7144-4-4-4-444-444-4000000000000000000000000000000000000000000000002-2-22-222-20000000000
χ7244-4-4-4-444-444-400000000000000000000000000000000000000000000000-222-22-2-220000000000
χ734-444-4-44-44i4i−4i−4i00-4400-4400−4i4i00000000000000000000000000000000000000000000000000000
χ744-444-4-44-4−4i−4i4i4i00-4400-44004i−4i00000000000000000000000000000000000000000000000000000
χ754-4-4-4444-44i−4i4i−4i-4400-4400−4i4i0000000000000000000000000000000000000000000000000000000
χ764-4-4-4444-4−4i4i−4i4i-4400-44004i−4i0000000000000000000000000000000000000000000000000000000
χ778-8-88-88-88000000000000000000000000000000000000000000000000000000000000000000000

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