Finite Group Databasebeta

← Group #295517

Character table — Group #295517

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444444444444444444444448888888888888888224444444488888888224444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ61111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1
χ91111111111-1-1-1-1111-1-1-1-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1111-1-11-1
χ101111111111-1-1-1-1111-1-1-1-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-11-1-1-111-11
χ111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-11111-1-111-11-1-111-11
χ121111111111-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1111111-1-11-111-1-11-1
χ131111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1111-1-1-11
χ141111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1111-1-1-1111-1
χ151111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-11111-1-1-1-111-1-1-11-1-1111-1
χ161111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1111111-1-1-1-1-1-1111-111-1-1-11
χ1722222222222222-2-2-2222222-2-2-2-2-20000-2-200000000000000000000002222000000000000-2-2000000
χ1822222222222222-2-2-2222222-2-2-2-2-20000-2-20000000000000000000000-2-2-2-200000000000022000000
χ192222222222-2-2-2-2-2-2-2-2-2-2-222-222220000-2-2000000000000000000000022-2-20000000000002-2000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-222-222220000-2-20000000000000000000000-2-222000000000000-22000000
χ2122222222-2-22222222-2-2-2-2-2-2222-2-22222-2-20000000000000000-2-2-2-222000000000000000000000000
χ2222222222-2-22222222-2-2-2-2-2-2222-2-2-2-2-2-2-2-200000000000000002222-2-2000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-22200002200000000000000000000000000000000002-22-200000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2220000220000000000000000000000000000000000-22-2200000000
χ2522222222-2-2-2-2-2-22222222-2-22-2-2222222-2-2000000000000000022-2-2-2-2000000000000000000000000
χ2622222222-2-2-2-2-2-22222222-2-22-2-222-2-2-2-2-2-20000000000000000-2-22222000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-22222-2-2-222-2-200002200000000000000000000000000000000002-2-2200000000
χ2822222222-2-2-2-2-2-2-2-2-22222-2-2-222-2-20000220000000000000000000000000000000000-222-200000000
χ2922-22-22-2-20022-2-22-2-200000022-2002i2i−2i−2i00i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i200002i−2i000022−2−222−2−2000000000000
χ3022-22-22-2-20022-2-22-2-200000022-2002i2i−2i−2i00−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200002i−2i0000−2−222−2−222000000000000
χ3122-22-22-2-20022-2-22-2-200000022-200−2i−2i2i2i00i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i20000−2i2i0000−2−222−2−222000000000000
χ3222-22-22-2-20022-2-22-2-200000022-200−2i−2i2i2i00−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000−2i2i000022−2−222−2−2000000000000
χ3322-22-22-2-200-2-2222-2-20000002-22002i2i−2i−2i00i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i20000−2i2i000022−2−2−2−222000000000000
χ3422-22-22-2-200-2-2222-2-20000002-22002i2i−2i−2i00−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i20000−2i2i0000−2−22222−2−2000000000000
χ3522-22-22-2-200-2-2222-2-20000002-2200−2i−2i2i2i00i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i200002i−2i0000−2−22222−2−2000000000000
χ3622-22-22-2-200-2-2222-2-20000002-2200−2i−2i2i2i00−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i200002i−2i000022−2−2−2−222000000000000
χ3722-2-22-22-22-22i−2i2i−2i0002i2i−2i−2i2-200000000000i2i2−i2−i2i2i2−i2−i222−2−222−2−20000002-22i−2i00000000000000i2−i22−200
χ3822-2-22-22-22-22i−2i2i−2i0002i2i−2i−2i2-200000000000i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000-22−2i2i00000000000000−i2i2−2200
χ3922-2-22-22-22-22i−2i2i−2i0002i2i−2i−2i2-200000000000−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000002-22i−2i00000000000000−i2i2−2200
χ4022-2-22-22-22-22i−2i2i−2i0002i2i−2i−2i2-200000000000−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000-22−2i2i00000000000000i2−i22−200
χ4122-2-22-22-22-2−2i2i−2i2i000−2i−2i2i2i2-200000000000i2i2−i2−i2i2i2−i2−i2−2−222−2−2220000002-2−2i2i00000000000000i2−i2−2200
χ4222-2-22-22-22-2−2i2i−2i2i000−2i−2i2i2i2-200000000000i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000-222i−2i00000000000000−i2i22−200
χ4322-2-22-22-22-2−2i2i−2i2i000−2i−2i2i2i2-200000000000−i2−i2i2i2−i2−i2i2i222−2−222−2−20000002-2−2i2i00000000000000−i2i22−200
χ4422-2-22-22-22-2−2i2i−2i2i000−2i−2i2i2i2-200000000000−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000-222i−2i00000000000000i2−i2−2200
χ452-22-222-2-22-20000-22-20000-22200002i−2i2i−2i2-2000000002i−2i2i−2i2i−2i2i−2i002i−2i00000000002-22-2000000000000
χ462-22-222-2-22-20000-22-20000-22200002i−2i2i−2i2-200000000−2i2i−2i2i−2i2i−2i2i002i−2i0000000000-22-22000000000000
χ472-22-222-2-22-20000-22-20000-2220000−2i2i−2i2i2-2000000002i−2i2i−2i2i−2i2i−2i00−2i2i0000000000-22-22000000000000
χ482-22-222-2-22-20000-22-20000-2220000−2i2i−2i2i2-200000000−2i2i−2i2i−2i2i−2i2i00−2i2i00000000002-22-2000000000000
χ492-22-222-2-2-220000-22-200002-2200002i−2i2i−2i-222i−2i2i−2i2i−2i2i−2i0000000000−2i2i0000002-22-20000000000000000
χ502-22-222-2-2-220000-22-200002-2200002i−2i2i−2i-22−2i2i−2i2i−2i2i−2i2i0000000000−2i2i000000-22-220000000000000000
χ512-22-222-2-2-220000-22-200002-220000−2i2i−2i2i-222i−2i2i−2i2i−2i2i−2i00000000002i−2i000000-22-220000000000000000
χ522-22-222-2-2-220000-22-200002-220000−2i2i−2i2i-22−2i2i−2i2i−2i2i−2i2i00000000002i−2i0000002-22-20000000000000000
χ532-2-2-2-2222000000-2-222-22-2002002-22-2-22002−22−2−22−222−22−2−22−222-2000000002−2−222−2−22000000000000
χ542-2-2-2-2222000000-2-222-22-2002002-22-2-2200−22−222−22−2−22−222−22−22-200000000−222−2−222−2000000000000
χ552-2-2-2-2222000000-2-222-22-2002002-2-222-2002−22−2−22−222−22−2−22−22-2200000000−222−2−222−2000000000000
χ562-2-2-2-2222000000-2-222-22-2002002-2-222-200−22−222−22−2−22−222−22−2-22000000002−2−222−2−22000000000000
χ572-2-2-2-2222000000-2-22-22-2200200-222-2-22002−22−2−22−22−22−222−22−2-22000000002−2−22−222−2000000000000
χ582-2-2-2-2222000000-2-22-22-2200200-222-2-2200−22−222−22−22−22−2−22−22-2200000000−222−22−2−22000000000000
χ592-2-2-2-2222000000-2-22-22-2200200-22-222-2002−22−2−22−22−22−222−22−22-200000000−222−22−2−22000000000000
χ602-2-2-2-2222000000-2-22-22-2200200-22-222-200−22−222−22−22−22−2−22−222-2000000002−2−22−222−2000000000000
χ61444-4-4-4-44004i−4i−4i4i0000000000000000000022-2-2-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ62444-4-4-4-44004i−4i−4i4i00000000000000000000-2-22222-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ63444-4-4-4-4400−4i4i4i−4i0000000000000000000022-2-2-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ64444-4-4-4-4400−4i4i4i−4i00000000000000000000-2-22222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6544-44-44-4-40044-4-4-444000000-4-44000000000000000000000000000000000000000000000000000000
χ6644-44-44-4-400-4-444-444000000-44-4000000000000000000000000000000000000000000000000000000
χ6744-4-44-44-4-444i−4i4i−4i000−4i−4i4i4i-44000000000000000000000000000000000000000000000000000000000
χ6844-4-44-44-4-44−4i4i−4i4i0004i4i−4i−4i-44000000000000000000000000000000000000000000000000000000000
χ694-444-4-44-40000000004i−4i−4i4i00000000000002i−2i−2i2i−2i2i2i−2i2-2-22-222-2000000000000000000000000000000
χ704-444-4-44-40000000004i−4i−4i4i0000000000000−2i2i2i−2i2i−2i−2i2i-222-22-2-22000000000000000000000000000000
χ714-444-4-44-4000000000−4i4i4i−4i00000000000002i−2i−2i2i−2i2i2i−2i-222-22-2-22000000000000000000000000000000
χ724-444-4-44-4000000000−4i4i4i−4i0000000000000−2i2i2i−2i2i−2i−2i2i2-2-22-222-2000000000000000000000000000000
χ734-44-444-4-44-400004-440000-44-400000000-440000000000000000000000000000000000000000000000
χ744-44-444-4-4-4400004-4400004-4-4000000004-40000000000000000000000000000000000000000000000
χ754-4-444-4-444400000000000-4-400000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ764-4-444-4-444400000000000-4-40000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000
χ774-4-444-4-44-4-400000000000440000000000022−22−222222−22−222200000000000000000000000000000000000000
χ784-4-444-4-44-4-4000000000004400000000000−222222−22−222222−2200000000000000000000000000000000000000
χ794-4-4-4-444400000044-44-44-400-400-440000000000000000000000000000000000000000000000000000
χ804-4-4-4-444400000044-4-44-4400-4004-40000000000000000000000000000000000000000000000000000

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