Finite Group Databasebeta

← Group #350523

Character table — Group #350523

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444224444444444444444444422444444444444444888888888888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ9111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ10111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ11111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ12111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ13111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ14111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ172222222222-2-2222222-2-222-2-22222222200000000-2-2-2-2-2-2-2000000000000000000000000000000
χ182222222222-2-2222222-2-222-2-2-2-2-2-2-2-2-2-200000000-2-222-222000000000000000000000000000000
χ192222222222-2-2-2-2-2-222-2-2-2-2222222-2-2-2-200000000-2-2-2-2222000000000000000000000000000000
χ202222222222-2-2-2-2-2-222-2-2-2-222-2-2-2-2222200000000-2-2222-2-2000000000000000000000000000000
χ2122222222-2-2222222-2-222-2-2220000000022222222-2-200-200-2-2-2-200000000000000000000000000
χ2222222222-2-2222222-2-222-2-22200000000-2-2-2-2-2-2-2-2-2-200-200222200000000000000000000000000
χ2322222222-2-222-2-2-2-2-2-22222-2-2000000002222-2-2-2-2-2-200200-2-22200000000000000000000000000
χ2422222222-2-222-2-2-2-2-2-22222-2-200000000-2-2-2-22222-2-20020022-2-200000000000000000000000000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-200000000000000002200200000022-2-222-2-2000000000000000000
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000022002000000-2-222-2-222000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002200-200000022-2-2-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002200-2000000-2-22222-2-2000000000000000000
χ292222-2-2-2-2002-22i2i−2i−2i002-2002i−2i0000000022-2-22i2i−2i−2i000000000000000000022−2−2i2i2−i2−i200002−2i2−i200
χ302222-2-2-2-2002-22i2i−2i−2i002-2002i−2i0000000022-2-22i2i−2i−2i0000000000000000000−2−222−i2−i2i2i20000−22−i2i200
χ312222-2-2-2-2002-22i2i−2i−2i002-2002i−2i00000000-2-222−2i−2i2i2i000000000000000000022−2−2i2i2−i2−i20000−22−i2i200
χ322222-2-2-2-2002-22i2i−2i−2i002-2002i−2i00000000-2-222−2i−2i2i2i0000000000000000000−2−222−i2−i2i2i200002−2i2−i200
χ332222-2-2-2-2002-2−2i−2i2i2i002-200−2i2i0000000022-2-2−2i−2i2i2i000000000000000000022−2−2−i2−i2i2i200002−2−i2i200
χ342222-2-2-2-2002-2−2i−2i2i2i002-200−2i2i0000000022-2-2−2i−2i2i2i0000000000000000000−2−222i2i2−i2−i20000−22i2−i200
χ352222-2-2-2-2002-2−2i−2i2i2i002-200−2i2i00000000-2-2222i2i−2i−2i000000000000000000022−2−2−i2−i2i2i20000−22i2−i200
χ362222-2-2-2-2002-2−2i−2i2i2i002-200−2i2i00000000-2-2222i2i−2i−2i0000000000000000000−2−222i2i2−i2−i200002−2−i2i200
χ3722-2-222-2-22-22-200002-2-220000000022-2-22i−2i2i−2i00002-20002-22i−2i0000002i−2i2i−2i000000000000000000
χ3822-2-222-2-22-22-200002-2-220000000022-2-2−2i2i−2i2i00002-20002-2−2i2i000000−2i2i−2i2i000000000000000000
χ3922-2-222-2-22-22-200002-2-2200000000-2-2222i−2i2i−2i00002-2000-222i−2i000000−2i2i−2i2i000000000000000000
χ4022-2-222-2-22-22-200002-2-2200000000-2-222−2i2i−2i2i00002-2000-22−2i2i0000002i−2i2i−2i000000000000000000
χ4122-2-222-2-22-2-2200002-22-20000000022-2-200002i−2i2i−2i-22000-22002i−2i2i−2i2i−2i0000000000000000000000
χ4222-2-222-2-22-2-2200002-22-20000000022-2-20000−2i2i−2i2i-22000-2200−2i2i−2i2i−2i2i0000000000000000000000
χ4322-2-222-2-22-2-2200002-22-200000000-2-22200002i−2i2i−2i-220002-2002i−2i−2i2i−2i2i0000000000000000000000
χ4422-2-222-2-22-2-2200002-22-200000000-2-2220000−2i2i−2i2i-220002-200−2i2i2i−2i2i−2i0000000000000000000000
χ4522-2-222-2-2-222-20000-22-22000022-2-200002i−2i2i−2i0000-222-2000−2i2i002i−2i−2i2i0000000000000000000000
χ4622-2-222-2-2-222-20000-22-22000022-2-20000−2i2i−2i2i0000-222-20002i−2i00−2i2i2i−2i0000000000000000000000
χ4722-2-222-2-2-222-20000-22-220000-2-22200002i−2i2i−2i0000-22-22000−2i2i00−2i2i2i−2i0000000000000000000000
χ4822-2-222-2-2-222-20000-22-220000-2-2220000−2i2i−2i2i0000-22-220002i−2i002i−2i−2i2i0000000000000000000000
χ4922-2-222-2-2-22-220000-222-2000022-2-2000000002i−2i2i−2i2-2-2200000−2i2i00002i−2i−2i2i000000000000000000
χ5022-2-222-2-2-22-220000-222-2000022-2-200000000−2i2i−2i2i2-2-22000002i−2i0000−2i2i2i−2i000000000000000000
χ5122-2-222-2-2-22-220000-222-20000-2-222000000002i−2i2i−2i2-22-200000−2i2i0000−2i2i2i−2i000000000000000000
χ5222-2-222-2-2-22-220000-222-20000-2-22200000000−2i2i−2i2i2-22-2000002i−2i00002i−2i−2i2i000000000000000000
χ532-22-22-2-2222002-22-2-2-2002-2002i−2i2i−2i2i−2i2i−2i0000000000000000000000000002−22−22−22−2i2−i2i2−i2000000
χ542-22-22-2-2222002-22-2-2-2002-2002i−2i2i−2i2i−2i2i−2i000000000000000000000000000−22−22−22−22−i2i2−i2i2000000
χ552-22-22-2-2222002-22-2-2-2002-200−2i2i−2i2i−2i2i−2i2i0000000000000000000000000002−22−22−22−2−i2i2−i2i2000000
χ562-22-22-2-2222002-22-2-2-2002-200−2i2i−2i2i−2i2i−2i2i000000000000000000000000000−22−22−22−22i2−i2i2−i2000000
χ572-22-22-2-222200-22-22-2-200-22002i−2i2i−2i−2i2i−2i2i0000000000000000000000000002−22−2−22−22i2−i2−i2i2000000
χ582-22-22-2-222200-22-22-2-200-22002i−2i2i−2i−2i2i−2i2i000000000000000000000000000−22−222−22−2−i2i2i2−i2000000
χ592-22-22-2-222200-22-22-2-200-2200−2i2i−2i2i2i−2i2i−2i0000000000000000000000000002−22−2−22−22−i2i2i2−i2000000
χ602-22-22-2-222200-22-22-2-200-2200−2i2i−2i2i2i−2i2i−2i000000000000000000000000000−22−222−22−2i2−i2−i2i2000000
χ614444-4-4-4-400-444i4i−4i−4i00-4400−4i4i00000000000000000000000000000000000000000000000000000
χ624444-4-4-4-400-44−4i−4i4i4i00-44004i−4i00000000000000000000000000000000000000000000000000000
χ6344-4-4-4-4440044000000-4-40000000000004i−4i−4i4i00000000000000000000000000000000000000000
χ6444-4-4-4-4440044000000-4-4000000000000−4i4i4i−4i00000000000000000000000000000000000000000
χ6544-4-4-4-44400-4-40000004400000000000000004-4-440000000000000000000000000000000000000
χ6644-4-4-4-44400-4-4000000440000000000000000-444-40000000000000000000000000000000000000
χ674-44-44-4-44-4-4004-44-44400-440000000000000000000000000000000000000000000000000000000
χ684-44-44-4-44-4-400-44-4444004-40000000000000000000000000000000000000000000000000000000
χ694-44-4-444-400004i−4i−4i4i00000000000000000000000000000000000000000002-2-222i−2i−2i2i0000000000
χ704-44-4-444-400004i−4i−4i4i0000000000000000000000000000000000000000000-222-2−2i2i2i−2i0000000000
χ714-44-4-444-40000−4i4i4i−4i00000000000000000000000000000000000000000002-2-22−2i2i2i−2i0000000000
χ724-44-4-444-40000−4i4i4i−4i0000000000000000000000000000000000000000000-222-22i−2i−2i2i0000000000
χ734-4-444-44-44-4000000-4400000000004i−4i−4i4i000000000000000000000000000000000000000000000
χ744-4-444-44-44-4000000-440000000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ754-4-444-44-4-440000004-40000004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ764-4-444-44-4-440000004-4000000−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ778-8-88-88-88000000000000000000000000000000000000000000000000000000000000000000000

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