Finite Group Databasebeta

← Group #348722

Character table — Group #348722

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444222244444444444444444444444444444444444888888888888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ91111111111-1-1-1-11111111111-1-1-1-1-1-11-1-11111-1-1-1-11-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111-1-1-1-11111111111-1-1-1-1-1-11-1-11111-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111-1-1-1-11111111111-1-1-1-1-1-11-1-1-1-1-1-111111-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ121111111111-1-1-1-11111111111-1-1-1-1-1-11-1-1-1-1-1-111111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ131111111111-1-1-1-1111111-1-1-1-1-1-111111-1-11111-1-1-1-11-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ141111111111-1-1-1-1111111-1-1-1-1-1-111111-1-11111-1-1-1-11-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ151111111111-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-1-1-111111-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ161111111111-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-1-1-111111-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ1722222222222222-2-222-2-22222222222-2-2-200000000-2-20000-2-2-2-200000000000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-222-2-2-2-2-2-2-200000000-2-20000222200000000000000000000000000
χ192222222222-2-2-2-2-2-222-2-22222-2-2-2-2-2-2-22200000000-220000-2-22200000000000000000000000000
χ202222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-22222-22200000000-22000022-2-200000000000000000000000000
χ2122222222-2-2222222-2-2220000-2-20000-22222222222-2-2-2-2-2-2000000000000000000000000000000
χ2222222222-2-2222222-2-2220000-2-20000-222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-20000-2-200002-2-200000000220000000022-2-222-2-2000000000000000000
χ2422222222-2-22222-2-2-2-2-2-20000-2-200002-2-2000000002200000000-2-222-2-222000000000000000000
χ2522222222-2-2-2-2-2-222-2-2220000220000-2-2-22222-2-2-2-2-22-2-222000000000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-2220000220000-2-2-2-2-2-2-22222-2222-2-2000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-20000220000222000000002-20000000022-2-2-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000220000222000000002-200000000-2-22222-2-2000000000000000000
χ2922-22-2-22-2002i2i−2i−2i2-2002-2000000000002i−2i2i2i−2i−2i22-2-2000000000000000000i2i2−i2−i222−2−200002−2i2−i200
χ3022-22-2-22-2002i2i−2i−2i2-2002-2000000000002i−2i2i2i−2i−2i22-2-2000000000000000000−i2−i2i2i2−2−2220000−22−i2i200
χ3122-22-2-22-2002i2i−2i−2i2-2002-2000000000002i−2i−2i−2i2i2i-2-222000000000000000000i2i2−i2−i222−2−20000−22−i2i200
χ3222-22-2-22-2002i2i−2i−2i2-2002-2000000000002i−2i−2i−2i2i2i-2-222000000000000000000−i2−i2i2i2−2−22200002−2i2−i200
χ3322-22-2-22-200−2i−2i2i2i2-2002-200000000000−2i2i2i2i−2i−2i-2-222000000000000000000i2i2−i2−i2−2−22200002−2−i2i200
χ3422-22-2-22-200−2i−2i2i2i2-2002-200000000000−2i2i2i2i−2i−2i-2-222000000000000000000−i2−i2i2i222−2−20000−22i2−i200
χ3522-22-2-22-200−2i−2i2i2i2-2002-200000000000−2i2i−2i−2i2i2i22-2-2000000000000000000i2i2−i2−i2−2−2220000−22i2−i200
χ3622-22-2-22-200−2i−2i2i2i2-2002-200000000000−2i2i−2i−2i2i2i22-2-2000000000000000000−i2−i2i2i222−2−200002−2−i2i200
χ372-222-2-2-222-22i−2i2i−2i002-20022-2-22i−2i2i2i−2i−2i000000000000000000000000000002−22−2i2−i2i2−i22−2i2−i2000000
χ382-222-2-2-222-22i−2i2i−2i002-20022-2-22i−2i2i2i−2i−2i00000000000000000000000000000−22−22−i2i2−i2i2−22−i2i2000000
χ392-222-2-2-222-22i−2i2i−2i002-200-2-2222i−2i−2i−2i2i2i000000000000000000000000000002−22−2i2−i2i2−i2−22−i2i2000000
χ402-222-2-2-222-22i−2i2i−2i002-200-2-2222i−2i−2i−2i2i2i00000000000000000000000000000−22−22−i2i2−i2i22−2i2−i2000000
χ412-222-2-2-222-2−2i2i−2i2i002-20022-2-2−2i2i−2i−2i2i2i000000000000000000000000000002−22−2−i2i2−i2i22−2−i2i2000000
χ422-222-2-2-222-2−2i2i−2i2i002-20022-2-2−2i2i−2i−2i2i2i00000000000000000000000000000−22−22i2−i2i2−i2−22i2−i2000000
χ432-222-2-2-222-2−2i2i−2i2i002-200-2-222−2i2i2i2i−2i−2i000000000000000000000000000002−22−2−i2i2−i2i2−22i2−i2000000
χ442-222-2-2-222-2−2i2i−2i2i002-200-2-222−2i2i2i2i−2i−2i00000000000000000000000000000−22−22i2−i2i2−i22−2−i2i2000000
χ452-22-2-222-222000022-2-2-2-20000002i−2i2i−2i-2002i−2i2i−2i0000202i−2i00002i−2i00002-22-2000000000000000000
χ462-22-2-222-222000022-2-2-2-20000002i−2i2i−2i-200−2i2i−2i2i000020−2i2i00002i−2i0000-22-22000000000000000000
χ472-22-2-222-222000022-2-2-2-2000000−2i2i−2i2i-2002i−2i2i−2i0000202i−2i0000−2i2i0000-22-22000000000000000000
χ482-22-2-222-222000022-2-2-2-2000000−2i2i−2i2i-200−2i2i−2i2i000020−2i2i0000−2i2i00002-22-2000000000000000000
χ492-22-2-222-2220000-2-2-2-2220000002i−2i2i−2i20000002-22-2-20002-200−2i2i2i−2i2i−2i0000000000000000000000
χ502-22-2-222-2220000-2-2-2-2220000002i−2i2i−2i2000000-22-22-2000-2200−2i2i−2i2i−2i2i0000000000000000000000
χ512-22-2-222-2220000-2-2-2-222000000−2i2i−2i2i20000002-22-2-20002-2002i−2i−2i2i−2i2i0000000000000000000000
χ522-22-2-222-2220000-2-2-2-222000000−2i2i−2i2i2000000-22-22-2000-22002i−2i2i−2i2i−2i0000000000000000000000
χ532-22-2-222-2-2-200002222-2-22-22-20000002002i−2i2i−2i0000-20−2i2i002-2002i−2i−2i2i0000000000000000000000
χ542-22-2-222-2-2-200002222-2-22-22-2000000200−2i2i−2i2i0000-202i−2i002-200−2i2i2i−2i0000000000000000000000
χ552-22-2-222-2-2-200002222-2-2-22-220000002002i−2i2i−2i0000-20−2i2i00-2200−2i2i2i−2i0000000000000000000000
χ562-22-2-222-2-2-200002222-2-2-22-22000000200−2i2i−2i2i0000-202i−2i00-22002i−2i−2i2i0000000000000000000000
χ572-22-2-222-2-2-20000-2-222222-22-2000000-20000002-22-22000-22-220000002-2-22000000000000000000
χ582-22-2-222-2-2-20000-2-222222-22-2000000-2000000-22-2220002-2-22000000-222-2000000000000000000
χ592-22-2-222-2-2-20000-2-22222-22-22000000-20000002-22-22000-222-2000000-222-2000000000000000000
χ602-22-2-222-2-2-20000-2-22222-22-22000000-2000000-22-2220002-22-20000002-2-22000000000000000000
χ61444-44-4-4-44-4000000-44000000004-4-4400000000000000000000000000000000000000000000000
χ62444-44-4-4-44-4000000-4400000000-444-400000000000000000000000000000000000000000000000
χ63444-44-4-4-4-440000004-4004-4-4400000000000000000000000000000000000000000000000000000
χ64444-44-4-4-4-440000004-400-444-400000000000000000000000000000000000000000000000000000
χ6544-44-4-44-4004i4i−4i−4i-4400-4400000000000−4i4i00000000000000000000000000000000000000000000
χ6644-44-4-44-400−4i−4i4i4i-4400-44000000000004i−4i00000000000000000000000000000000000000000000
χ674-444-4-4-44-444i−4i4i−4i00-44000000−4i4i000000000000000000000000000000000000000000000000000
χ684-444-4-4-44-44−4i4i−4i4i00-440000004i−4i000000000000000000000000000000000000000000000000000
χ694-4-4444-4-4004-4-440000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ704-4-4444-4-4004-4-44000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ714-4-4444-4-400-444-40000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000
χ724-4-4444-4-400-444-4000000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000
χ734-4-4-44-4440000004-400-4400000000000004-4-440000000000000000000000000000000000000000
χ744-4-4-44-4440000004-400-440000000000000-444-40000000000000000000000000000000000000000
χ754-4-4-44-444000000-44004-4000000000000000004-4-44000000000000000000000000000000000000
χ764-4-4-44-444000000-44004-400000000000000000-444-4000000000000000000000000000000000000
χ7788-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000000

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