Finite Group Databasebeta

← Group #274713

Character table — Group #274713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444448888888822244888888888888888888884444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ9111111111-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-11-1
χ10111111111-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-111-11
χ11111111111-1-1-1-1111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ12111111111-1-1-1-1111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-11-1
χ13111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ14111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1111-1
χ15111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1111-1
χ16111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-111-1-1-11
χ172222222222222-2-222-2-22-2-222-2-22222-2-2-2-200000000-222-2-2000000000000000000000000000000
χ182222222222222-2-222-2-22-2-222-2-2-2-2-2-2222200000000-2-2-222000000000000000000000000000000
χ19222222222-2-2-2-2-2-222-2-22-2-2-2-2222222-2-2-2-2000000002-2-222000000000000000000000000000000
χ20222222222-2-2-2-2-2-222-2-22-2-2-2-222-2-2-2-2222200000000222-2-2000000000000000000000000000000
χ2122222222-2222222-2-222-2-2-2-2-2220000000022222222-200000000-2-2-2-20000000000000000000000
χ2222222222-2222222-2-222-2-2-2-2-22200000000-2-2-2-2-2-2-2-2-20000000022220000000000000000000000
χ2322222222-22222-2-2-2-2-2-2-222-2-2-2-2000000000000000020000000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2422222222-22222-2-2-2-2-2-2-222-2-2-2-200000000000000002000000000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2522222222-2-2-2-2-222-2-222-2-2-222-2-2000000002222-2-2-2-2200000000-2-2220000000000000000000000
χ2622222222-2-2-2-2-222-2-222-2-2-222-2-200000000-2-2-2-2222220000000022-2-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000-20000000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000-2000000000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ292222-2-2-2-202i2i−2i−2i2-2002-2000002i−2i000000002i2i−2i−2i22-2-20000022−2−2000000000000i2i2−i2−i20000i2−i22−200
χ302222-2-2-2-202i2i−2i−2i2-2002-2000002i−2i000000002i2i−2i−2i22-2-200000−2−222000000000000−i2−i2i2i20000−i2i2−2200
χ312222-2-2-2-202i2i−2i−2i2-2002-2000002i−2i00000000−2i−2i2i2i-2-2220000022−2−2000000000000i2i2−i2−i20000−i2i2−2200
χ322222-2-2-2-202i2i−2i−2i2-2002-2000002i−2i00000000−2i−2i2i2i-2-22200000−2−222000000000000−i2−i2i2i20000i2−i22−200
χ332222-2-2-2-20−2i−2i2i2i2-2002-200000−2i2i000000002i2i−2i−2i-2-2220000022−2−2000000000000−i2−i2i2i20000i2−i2−2200
χ342222-2-2-2-20−2i−2i2i2i2-2002-200000−2i2i000000002i2i−2i−2i-2-22200000−2−222000000000000i2i2−i2−i20000−i2i22−200
χ352222-2-2-2-20−2i−2i2i2i2-2002-200000−2i2i00000000−2i−2i2i2i22-2-20000022−2−2000000000000−i2−i2i2i20000−i2i22−200
χ362222-2-2-2-20−2i−2i2i2i2-2002-200000−2i2i00000000−2i−2i2i2i22-2-200000−2−222000000000000i2i2−i2−i20000i2−i2−2200
χ3722-2-222-2-222i−2i2i−2i00-2-2002002i−2i002i2i−2i−2i00002−22−2i2−i2i2−i202-20000002−2i2−i2i2−i2i2−i22−22−200000000000000
χ3822-2-222-2-222i−2i2i−2i00-2-2002002i−2i002i2i−2i−2i0000−22−22−i2i2−i2i202-2000000−22−i2i2−i2i2−i2i2−22−2200000000000000
χ3922-2-222-2-222i−2i2i−2i00-2-2002002i−2i00−2i−2i2i2i00002−22−2i2−i2i2−i20-220000002−2i2−i2−i2i2−i2i2−22−2200000000000000
χ4022-2-222-2-222i−2i2i−2i00-2-2002002i−2i00−2i−2i2i2i0000−22−22−i2i2−i2i20-22000000−22−i2i2i2−i2i2−i22−22−200000000000000
χ4122-2-222-2-22−2i2i−2i2i00-2-200200−2i2i002i2i−2i−2i00002−22−2−i2i2−i2i20-220000002−2−i2i2i2−i2i2−i2−22−2200000000000000
χ4222-2-222-2-22−2i2i−2i2i00-2-200200−2i2i002i2i−2i−2i0000−22−22i2−i2i2−i20-22000000−22i2−i2−i2i2−i2i22−22−200000000000000
χ4322-2-222-2-22−2i2i−2i2i00-2-200200−2i2i00−2i−2i2i2i00002−22−2−i2i2−i2i202-20000002−2−i2i2−i2i2−i2i22−22−200000000000000
χ4422-2-222-2-22−2i2i−2i2i00-2-200200−2i2i00−2i−2i2i2i0000−22−22i2−i2i2−i202-2000000−22i2−i2i2−i2i2−i2−22−2200000000000000
χ4522-2-222-2-2-22i−2i2i−2i002200-200−2i2i00000022-2-22−22−2i2−i2i2−i20002i−2i0000−22−i2i22−2−22−i2i2i2−i200000000000000
χ4622-2-222-2-2-22i−2i2i−2i002200-200−2i2i00000022-2-2−22−22−i2i2−i2i20002i−2i00002−2i2−i2−222−2i2−i2−i2i200000000000000
χ4722-2-222-2-2-22i−2i2i−2i002200-200−2i2i000000-2-2222−22−2i2−i2i2−i2000−2i2i0000−22−i2i2−222−2i2−i2−i2i200000000000000
χ4822-2-222-2-2-22i−2i2i−2i002200-200−2i2i000000-2-222−22−22−i2i2−i2i2000−2i2i00002−2i2−i22−2−22−i2i2i2−i200000000000000
χ4922-2-222-2-2-2−2i2i−2i2i002200-2002i−2i00000022-2-22−22−2−i2i2−i2i2000−2i2i0000−22i2−i22−2−22i2−i2−i2i200000000000000
χ5022-2-222-2-2-2−2i2i−2i2i002200-2002i−2i00000022-2-2−22−22i2−i2i2−i2000−2i2i00002−2−i2i2−222−2−i2i2i2−i200000000000000
χ5122-2-222-2-2-2−2i2i−2i2i002200-2002i−2i000000-2-2222−22−2−i2i2−i2i20002i−2i0000−22i2−i2−222−2−i2i2i2−i200000000000000
χ5222-2-222-2-2-2−2i2i−2i2i002200-2002i−2i000000-2-222−22−22i2−i2i2−i20002i−2i00002−2−i2i22−2−22i2−i2−i2i200000000000000
χ532-22-22-22-2200002-22-2-22-22-200002-22-22-22-200000000000002i−2i2i−2i00000000000000002i−2i00000000
χ542-22-22-22-2200002-22-2-22-22-200002-22-22-22-20000000000000−2i2i−2i2i0000000000000000−2i2i00000000
χ552-22-22-22-2200002-22-2-22-22-20000-22-22-22-2200000000000002i−2i2i−2i0000000000000000−2i2i00000000
χ562-22-22-22-2200002-22-2-22-22-20000-22-22-22-220000000000000−2i2i−2i2i00000000000000002i−2i00000000
χ572-22-22-22-220000-222-22-2-2-2200002-22-2-22-22000000000000000000000000000002i−2i2i−2i002i−2i000000
χ582-22-22-22-220000-222-22-2-2-2200002-22-2-22-2200000000000000000000000000000−2i2i−2i2i00−2i2i000000
χ592-22-22-22-220000-222-22-2-2-220000-22-222-22-2000000000000000000000000000002i−2i2i−2i00−2i2i000000
χ602-22-22-22-220000-222-22-2-2-220000-22-222-22-200000000000000000000000000000−2i2i−2i2i002i−2i000000
χ614444-4-4-4-404i4i−4i−4i-4400-4400000−4i4i000000000000000000000000000000000000000000000000000
χ624444-4-4-4-40−4i−4i4i4i-4400-44000004i−4i000000000000000000000000000000000000000000000000000
χ6344-4-4-4-44404-4-440000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000
χ6444-4-4-4-44404-4-44000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000
χ6544-4-4-4-4440-444-40000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ6644-4-4-4-4440-444-4000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ674-44-44-44-4-400004-4-44-444-440000000000000000000000000000000000000000000000000000000
χ684-44-44-44-4-40000-44-444-444-40000000000000000000000000000000000000000000000000000000
χ694-44-4-44-44000004400-4-400000000000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ704-44-4-44-44000004400-4-40000000000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ714-44-4-44-4400000-4-400440000000000000000000000000000000000000000000022−22−22220000000000
χ724-44-4-44-4400000-4-4004400000000000000000000000000000000000000000000−222222−220000000000
χ734-4-444-4-444000000-4400-40000004i−4i−4i4i00000000000000000000000000000000000000000000000
χ744-4-444-4-444000000-4400-4000000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ754-4-444-4-44-40000004-400400000000004-4-440000000000000000000000000000000000000000000
χ764-4-444-4-44-40000004-40040000000000-444-40000000000000000000000000000000000000000000
χ778-8-88-888-8000000000000000000000000000000000000000000000000000000000000000000000

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