Finite Group Databasebeta

← Group #243333

Character table — Group #243333

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444444444444444888888888888888844444444888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ172222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ19222222222222-2-2-2-2222222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222000000000000000022-2-222-2-2000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2220000000000000000-2-222-2-222000000000000000000000000
χ2322222222-2-2-2-222222222-2-22222-2-2-2-2-2-2000000000000000022-2-2-2-222000000000000000000000000
χ2422222222-2-2-2-222222222-2-22222-2-2-2-2-2-20000000000000000-2-22222-2-2000000000000000000000000
χ2522222222-2-2-2-22222-2-2-2-222-2-2-2-222-2-2222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2622222222-2-2-2-22222-2-2-2-222-2-2-2-222-2-222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2922-22-2-2-2200002i2i−2i−2i2i2i−2i−2i0022-2-200000022−2−2i2i2−i2−i222−2−2i2i2−i2−i2002-22i−2i002−22−2i2−i2i2−i20000000000000000
χ3022-22-2-2-2200002i2i−2i−2i2i2i−2i−2i0022-2-200000022−2−2i2i2−i2−i222−2−2i2i2−i2−i200-22−2i2i00−22−22−i2i2−i2i20000000000000000
χ3122-22-2-2-2200002i2i−2i−2i2i2i−2i−2i0022-2-2000000−2−222−i2−i2i2i2−2−222−i2−i2i2i2002-22i−2i00−22−22−i2i2−i2i20000000000000000
χ3222-22-2-2-2200002i2i−2i−2i2i2i−2i−2i0022-2-2000000−2−222−i2−i2i2i2−2−222−i2−i2i2i200-22−2i2i002−22−2i2−i2i2−i20000000000000000
χ3322-22-2-2-2200002i2i−2i−2i−2i−2i2i2i00-2-22200000022−2−2−i2−i2i2i2−2−222i2i2−i2−i22i−2i00002-2i2−i2−i2i2−222−20000000000000000
χ3422-22-2-2-2200002i2i−2i−2i−2i−2i2i2i00-2-22200000022−2−2−i2−i2i2i2−2−222i2i2−i2−i2−2i2i0000-22−i2i2i2−i22−2−220000000000000000
χ3522-22-2-2-2200002i2i−2i−2i−2i−2i2i2i00-2-222000000−2−222i2i2−i2−i222−2−2−i2−i2i2i22i−2i00002-2−i2i2i2−i22−2−220000000000000000
χ3622-22-2-2-2200002i2i−2i−2i−2i−2i2i2i00-2-222000000−2−222i2i2−i2−i222−2−2−i2−i2i2i2−2i2i0000-22i2−i2−i2i2−222−20000000000000000
χ3722-22-2-2-220000−2i−2i2i2i2i2i−2i−2i00-2-22200000022−2−2i2i2−i2−i2−2−222−i2−i2i2i22i−2i0000-22i2−i2−i2i22−2−220000000000000000
χ3822-22-2-2-220000−2i−2i2i2i2i2i−2i−2i00-2-22200000022−2−2i2i2−i2−i2−2−222−i2−i2i2i2−2i2i00002-2−i2i2i2−i2−222−20000000000000000
χ3922-22-2-2-220000−2i−2i2i2i2i2i−2i−2i00-2-222000000−2−222−i2−i2i2i222−2−2i2i2−i2−i22i−2i0000-22−i2i2i2−i2−222−20000000000000000
χ4022-22-2-2-220000−2i−2i2i2i2i2i−2i−2i00-2-222000000−2−222−i2−i2i2i222−2−2i2i2−i2−i2−2i2i00002-2i2−i2−i2i22−2−220000000000000000
χ4122-22-2-2-220000−2i−2i2i2i−2i−2i2i2i0022-2-200000022−2−2−i2−i2i2i222−2−2−i2−i2i2i2002-2−2i2i002−22−2−i2i2−i2i20000000000000000
χ4222-22-2-2-220000−2i−2i2i2i−2i−2i2i2i0022-2-200000022−2−2−i2−i2i2i222−2−2−i2−i2i2i200-222i−2i00−22−22i2−i2i2−i20000000000000000
χ4322-22-2-2-220000−2i−2i2i2i−2i−2i2i2i0022-2-2000000−2−222i2i2−i2−i2−2−222i2i2−i2−i2002-2−2i2i00−22−22i2−i2i2−i20000000000000000
χ4422-22-2-2-220000−2i−2i2i2i−2i−2i2i2i0022-2-2000000−2−222i2i2−i2−i2−2−222i2i2−i2−i200-222i−2i002−22−2−i2i2−i2i20000000000000000
χ452-22-22-2-222i2i−2i−2i2i−2i2i−2i2i−2i2i−2i2-22-22-22-22-22i−2i00000000000000000000000000000000002i−2i002-200000000
χ462-22-22-2-222i2i−2i−2i2i−2i2i−2i2i−2i2i−2i2-22-22-22-22-22i−2i0000000000000000000000000000000000−2i2i00-2200000000
χ472-22-22-2-222i2i−2i−2i2i−2i2i−2i−2i2i−2i2i-22-22-22-222-2−2i2i00000000000000000000000000000000000000002-22i−2i0000
χ482-22-22-2-222i2i−2i−2i2i−2i2i−2i−2i2i−2i2i-22-22-22-222-2−2i2i0000000000000000000000000000000000000000-22−2i2i0000
χ492-22-22-2-222i2i−2i−2i−2i2i−2i2i2i−2i2i−2i2-2-22-222-2-22−2i2i000000000000000000000000000000002i−2i002-20000000000
χ502-22-22-2-222i2i−2i−2i−2i2i−2i2i2i−2i2i−2i2-2-22-222-2-22−2i2i00000000000000000000000000000000−2i2i00-220000000000
χ512-22-22-2-222i2i−2i−2i−2i2i−2i2i−2i2i−2i2i-222-22-2-22-222i−2i000000000000000000000000000000000000000000002-22i−2i
χ522-22-22-2-222i2i−2i−2i−2i2i−2i2i−2i2i−2i2i-222-22-2-22-222i−2i00000000000000000000000000000000000000000000-22−2i2i
χ532-22-22-2-22−2i−2i2i2i2i−2i2i−2i2i−2i2i−2i-222-22-2-22-22−2i2i000000000000000000000000000000000000000000002-2−2i2i
χ542-22-22-2-22−2i−2i2i2i2i−2i2i−2i2i−2i2i−2i-222-22-2-22-22−2i2i00000000000000000000000000000000000000000000-222i−2i
χ552-22-22-2-22−2i−2i2i2i2i−2i2i−2i−2i2i−2i2i2-2-22-222-2-222i−2i000000000000000000000000000000002i−2i00-220000000000
χ562-22-22-2-22−2i−2i2i2i2i−2i2i−2i−2i2i−2i2i2-2-22-222-2-222i−2i00000000000000000000000000000000−2i2i002-20000000000
χ572-22-22-2-22−2i−2i2i2i−2i2i−2i2i2i−2i2i−2i-22-22-22-222-22i−2i00000000000000000000000000000000000000002-2−2i2i0000
χ582-22-22-2-22−2i−2i2i2i−2i2i−2i2i2i−2i2i−2i-22-22-22-222-22i−2i0000000000000000000000000000000000000000-222i−2i0000
χ592-22-22-2-22−2i−2i2i2i−2i2i−2i2i−2i2i−2i2i2-22-22-22-22-2−2i2i00000000000000000000000000000000002i−2i00-2200000000
χ602-22-22-2-22−2i−2i2i2i−2i2i−2i2i−2i2i−2i2i2-22-22-22-22-2−2i2i0000000000000000000000000000000000−2i2i002-200000000
χ61444-4-4-44-4000000000000440000-4-400004-44-400000000000000000000000000000000000000000000
χ62444-4-4-44-4000000000000440000-4-40000-44-4400000000000000000000000000000000000000000000
χ63444-4-4-44-4000000000000-4-4000044000000004i−4i4i−4i0000000000000000000000000000000000000000
χ64444-4-4-44-4000000000000-4-400004400000000−4i4i−4i4i0000000000000000000000000000000000000000
χ6544-4-444-4-44-44-40000000000000000000022−22−222222−22−22220000000000000000000000000000000000000000
χ6644-4-444-4-44-44-400000000000000000000−222222−22−222222−220000000000000000000000000000000000000000
χ6744-4-444-4-4-44-440000000000000000000022−22−2222−222222−220000000000000000000000000000000000000000
χ6844-4-444-4-4-44-4400000000000000000000−222222−2222−22−22220000000000000000000000000000000000000000
χ694-444-44-4-40000000000004-40000-4400000000000000004-44-400000000000000000000000000000000
χ704-444-44-4-40000000000004-40000-440000000000000000-44-4400000000000000000000000000000000
χ714-444-44-4-4000000000000-4400004-40000000000004-44-4000000000000000000000000000000000000
χ724-444-44-4-4000000000000-4400004-4000000000000-44-44000000000000000000000000000000000000
χ734-4-444-44-44i−4i−4i4i000000000000000000000000000022−22−22222i2−2i2−2i22i200000000000000000000000000000000
χ744-4-444-44-44i−4i−4i4i0000000000000000000000000000−222222−22−2i22i22i2−2i200000000000000000000000000000000
χ754-4-444-44-4−4i4i4i−4i000000000000000000000000000022−22−2222−2i22i22i2−2i200000000000000000000000000000000
χ764-4-444-44-4−4i4i4i−4i0000000000000000000000000000−222222−222i2−2i2−2i22i200000000000000000000000000000000
χ774-4-4-4-444400004-4-444-4-44004-4-44000000000000000000000000000000000000000000000000000000
χ784-4-4-4-444400004-4-44-444-400-444-4000000000000000000000000000000000000000000000000000000
χ794-4-4-4-44440000-444-44-4-4400-444-4000000000000000000000000000000000000000000000000000000
χ804-4-4-4-44440000-444-4-444-4004-4-44000000000000000000000000000000000000000000000000000000

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