Finite Group Databasebeta

← Group #276452

Character table — Group #276452

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444448888888844444888888888888888888884444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
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
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-11111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-11111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ1111111111-1-1-1-11111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ1211111111-1-1-1-11111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ1311111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ1411111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ1511111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ172222222222222-2-2-2-2222-2-2-2-2222222-2-2-2-20000000022-2-2-2000000000000000000000000000000
χ182222222222222-2-2-2-2222-2-2-2-222-2-2-2-2222200000000-2-2-222000000000000000000000000000000
χ19222222222222-22222-2-2-2-2-222-2-2000000002222222200-200-2-2-2-200000000000000000000000000
χ20222222222222-22222-2-2-2-2-222-2-200000000-2-2-2-2-2-2-2-200-200222200000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000000020000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ22222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000002000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ2322222222-2-2-2-22-2-2-2-2222-2-222-2-22222-2-2-2-200000000-2-2222000000000000000000000000000000
χ2422222222-2-2-2-22-2-2-2-2222-2-222-2-2-2-2-2-2222200000000222-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-22222-2-2-2-2-2-2-222000000002222-2-2-2-200200-2-22200000000000000000000000000
χ2622222222-2-2-2-2-22222-2-2-2-2-2-2-22200000000-2-2-2-222220020022-2-200000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000-20000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000-2000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ2922-22-22-2-20000-222-2-22-222-200002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000022-2-2002i−2i000000
χ3022-22-22-2-20000-222-2-22-222-200002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000-2-22200−2i2i000000
χ3122-22-22-2-20000-222-2-22-222-20000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000022-2-200−2i2i000000
χ3222-22-22-2-20000-222-2-22-222-20000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000-2-222002i−2i000000
χ3322-22-22-2-20000-2-2-2222-22-2200002i2i−2i−2i−2i−2i2i2i00000000000000000000000002i2i−2i−2i00002-200000000
χ3422-22-22-2-20000-2-2-2222-22-2200002i2i−2i−2i−2i−2i2i2i0000000000000000000000000−2i−2i2i2i0000-2200000000
χ3522-22-22-2-20000-2-2-2222-22-220000−2i−2i2i2i2i2i−2i−2i00000000000000000000000002i2i−2i−2i0000-2200000000
χ3622-22-22-2-20000-2-2-2222-22-220000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000−2i−2i2i2i00002-200000000
χ3722-2-2-2-2222i2i−2i−2i02-22-2000002i−2i000000000022-2-22i2i−2i−2i00000000000000000i2−i2i2−i22−22−20000i2−i22−200
χ3822-2-2-2-2222i2i−2i−2i02-22-2000002i−2i000000000022-2-22i2i−2i−2i00000000000000000−i2i2−i2i2−22−220000−i2i2−2200
χ3922-2-2-2-2222i2i−2i−2i02-22-2000002i−2i0000000000-2-222−2i−2i2i2i00000000000000000i2−i2i2−i22−22−20000−i2i2−2200
χ4022-2-2-2-2222i2i−2i−2i02-22-2000002i−2i0000000000-2-222−2i−2i2i2i00000000000000000−i2i2−i2i2−22−220000i2−i22−200
χ4122-2-2-2-222−2i−2i2i2i02-22-200000−2i2i000000000022-2-2−2i−2i2i2i00000000000000000i2−i2i2−i2−22−220000i2−i2−2200
χ4222-2-2-2-222−2i−2i2i2i02-22-200000−2i2i000000000022-2-2−2i−2i2i2i00000000000000000−i2i2−i2i22−22−20000−i2i22−200
χ4322-2-2-2-222−2i−2i2i2i02-22-200000−2i2i0000000000-2-2222i2i−2i−2i00000000000000000i2−i2i2−i2−22−220000−i2i22−200
χ4422-2-2-2-222−2i−2i2i2i02-22-200000−2i2i0000000000-2-2222i2i−2i−2i00000000000000000−i2i2−i2i22−22−20000i2−i2−2200
χ452-22-2-222-22-22-220000-2-2200002-22i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i22i−2i000i2−i2i2−i22−22−22−22−2000000000000000000
χ462-22-2-222-22-22-220000-2-2200002-22i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i22i−2i000−i2i2−i2i2−22−22−22−22000000000000000000
χ472-22-2-222-22-22-220000-2-2200002-2−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i2−2i2i000i2−i2i2−i2−22−22−22−22000000000000000000
χ482-22-2-222-22-22-220000-2-2200002-2−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i2−2i2i000−i2i2−i2i22−22−22−22−2000000000000000000
χ492-22-2-222-22-22-2-2000022-20000-2200002-22-2i2−i2i2−i2i2−i2i2−i20002-2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ502-22-2-222-22-22-2-2000022-20000-2200002-22-2−i2i2−i2i2−i2i2−i2i20002-2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ512-22-2-222-22-22-2-2000022-20000-220000-22-22i2−i2i2−i2i2−i2i2−i2000-22−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ522-22-2-222-22-22-2-2000022-20000-220000-22-22−i2i2−i2i2−i2i2−i2i2000-22i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ532-22-2-222-2-22-2220000-2-220000-222i−2i2i−2i0000i2−i2i2−i2−i2i2−i2i2−2i2i000i2−i2−i2i22−22−2−22−22000000000000000000
χ542-22-2-222-2-22-2220000-2-220000-222i−2i2i−2i0000−i2i2−i2i2i2−i2i2−i2−2i2i000−i2i2i2−i2−22−222−22−2000000000000000000
χ552-22-2-222-2-22-2220000-2-220000-22−2i2i−2i2i0000i2−i2i2−i2−i2i2−i2i22i−2i000i2−i2−i2i2−22−222−22−2000000000000000000
χ562-22-2-222-2-22-2220000-2-220000-22−2i2i−2i2i0000−i2i2−i2i2i2−i2i2−i22i−2i000−i2i2i2−i22−22−2−22−22000000000000000000
χ572-22-2-222-2-22-22-2000022-200002-200002-22-2i2−i2i2−i2−i2i2−i2i2000-22−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000000000
χ582-22-2-222-2-22-22-2000022-200002-200002-22-2−i2i2−i2i2i2−i2i2−i2000-22i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000000000
χ592-22-2-222-2-22-22-2000022-200002-20000-22-22i2−i2i2−i2−i2i2−i2i20002-2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000000000
χ602-22-2-222-2-22-22-2000022-200002-20000-22-22−i2i2−i2i2i2−i2i2−i20002-2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000000000
χ61444-44-4-4-4000004-4-44000000000000000000000000000000000000000000000022−22−22220000000000
χ62444-44-4-4-4000004-4-440000000000000000000000000000000000000000000000−222222−220000000000
χ63444-44-4-4-400000-444-400000000000000000000000000000000000000000022−22−222200000000000000
χ64444-44-4-4-400000-444-4000000000000000000000000000000000000000000−222222−2200000000000000
χ6544-44-44-4-40000444-4-4-44-4-440000000000000000000000000000000000000000000000000000000
χ6644-44-44-4-400004-4-444-44-44-40000000000000000000000000000000000000000000000000000000
χ6744-4-4-4-4444i4i−4i−4i0-44-4400000−4i4i00000000000000000000000000000000000000000000000000000
χ6844-4-4-4-444−4i−4i4i4i0-44-44000004i−4i00000000000000000000000000000000000000000000000000000
χ694-4-444-44-44i−4i−4i4i00000000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000000000000000000
χ704-4-444-44-44i−4i−4i4i0000000000000000000000−2i22i22i2−2i222−22−222200000000000000000000000000000000000
χ714-4-444-44-4−4i4i4i−4i00000000000000000000002i2−2i2−2i22i222−22−222200000000000000000000000000000000000
χ724-4-444-44-4−4i4i4i−4i0000000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000000000000000000
χ734-4-4-444-440000400004-4-400000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ744-4-4-444-440000400004-4-40000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ754-4-4-444-440000-40000-4440000004-4-4400000000000000000000000000000000000000000000000
χ764-4-4-444-440000-40000-444000000-444-400000000000000000000000000000000000000000000000
χ778-888-8-8-88000000000000000000000000000000000000000000000000000000000000000000000

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