Finite Group Databasebeta

← Group #239107

Character table — Group #239107

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444444444444444888888888888888844444444888888884444444488888888
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
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
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
χ19222222222222-2-2-2-22222222-2-2-2-22-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ20222222222222-2-2-2-22222222-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-22222-2-2-222000000000000000022-2-222-2-2000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-22222-2-2-2220000000000000000-2-222-2-222000000000000000000000000
χ2322222222-2-2-2-2222222-2-2-2-22-2-2-2-22-2-2222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2422222222-2-2-2-2222222-2-2-2-22-2-2-2-22-2-222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ2522222222-2-2-2-22222-2-22222-22222-2-2-2-2-2000000000000000022-2-2-2-222000000000000000000000000
χ2622222222-2-2-2-22222-2-22222-22222-2-2-2-2-20000000000000000-2-22222-2-2000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2922-2-22-22-200002i2i−2i−2i002i2i−2i−2i022-2-200000i2i2−i2−i222−2−2i2i2−i2−i222−2−2002i−2i2-2002−22−2i2−i2i2−i20000000000000000
χ3022-2-22-22-200002i2i−2i−2i002i2i−2i−2i022-2-200000i2i2−i2−i222−2−2i2i2−i2−i222−2−200−2i2i-2200−22−22−i2i2−i2i20000000000000000
χ3122-2-22-22-200002i2i−2i−2i002i2i−2i−2i022-2-200000−i2−i2i2i2−2−222−i2−i2i2i2−2−222002i−2i2-200−22−22−i2i2−i2i20000000000000000
χ3222-2-22-22-200002i2i−2i−2i002i2i−2i−2i022-2-200000−i2−i2i2i2−2−222−i2−i2i2i2−2−22200−2i2i-22002−22−2i2−i2i2−i20000000000000000
χ3322-2-22-22-200002i2i−2i−2i00−2i−2i2i2i0-2-22200000i2i2−i2−i2−2−222−i2−i2i2i222−2−22-200002i−2ii2−i2−i2i2−222−20000000000000000
χ3422-2-22-22-200002i2i−2i−2i00−2i−2i2i2i0-2-22200000i2i2−i2−i2−2−222−i2−i2i2i222−2−2-220000−2i2i−i2i2i2−i22−2−220000000000000000
χ3522-2-22-22-200002i2i−2i−2i00−2i−2i2i2i0-2-22200000−i2−i2i2i222−2−2i2i2−i2−i2−2−2222-200002i−2i−i2i2i2−i22−2−220000000000000000
χ3622-2-22-22-200002i2i−2i−2i00−2i−2i2i2i0-2-22200000−i2−i2i2i222−2−2i2i2−i2−i2−2−222-220000−2i2ii2−i2−i2i2−222−20000000000000000
χ3722-2-22-22-20000−2i−2i2i2i002i2i−2i−2i0-2-22200000i2i2−i2−i222−2−2−i2−i2i2i2−2−2222-20000−2i2ii2−i2−i2i22−2−220000000000000000
χ3822-2-22-22-20000−2i−2i2i2i002i2i−2i−2i0-2-22200000i2i2−i2−i222−2−2−i2−i2i2i2−2−222-2200002i−2i−i2i2i2−i2−222−20000000000000000
χ3922-2-22-22-20000−2i−2i2i2i002i2i−2i−2i0-2-22200000−i2−i2i2i2−2−222i2i2−i2−i222−2−22-20000−2i2i−i2i2i2−i2−222−20000000000000000
χ4022-2-22-22-20000−2i−2i2i2i002i2i−2i−2i0-2-22200000−i2−i2i2i2−2−222i2i2−i2−i222−2−2-2200002i−2ii2−i2−i2i22−2−220000000000000000
χ4122-2-22-22-20000−2i−2i2i2i00−2i−2i2i2i022-2-200000i2i2−i2−i2−2−222i2i2−i2−i2−2−222002i−2i-22002−22−2−i2i2−i2i20000000000000000
χ4222-2-22-22-20000−2i−2i2i2i00−2i−2i2i2i022-2-200000i2i2−i2−i2−2−222i2i2−i2−i2−2−22200−2i2i2-200−22−22i2−i2i2−i20000000000000000
χ4322-2-22-22-20000−2i−2i2i2i00−2i−2i2i2i022-2-200000−i2−i2i2i222−2−2−i2−i2i2i222−2−2002i−2i-2200−22−22i2−i2i2−i20000000000000000
χ4422-2-22-22-20000−2i−2i2i2i00−2i−2i2i2i022-2-200000−i2−i2i2i222−2−2−i2−i2i2i222−2−200−2i2i2-2002−22−2−i2i2−i2i20000000000000000
χ452-2-22-2-22222-2-22-22-2222-22-2-22-22-2-22-22-2000000000000000000000000000000000000000000002i−2i2i−2i
χ462-2-22-2-22222-2-22-22-2222-22-2-22-22-2-22-22-200000000000000000000000000000000000000000000−2i2i−2i2i
χ472-2-22-2-22222-2-22-22-2-2-2-22-222-22-2222-2-22000000000000000000000000000000002-22-2000000000000
χ482-2-22-2-22222-2-22-22-2-2-2-22-222-22-2222-2-2200000000000000000000000000000000-22-22000000000000
χ492-2-22-2-22222-2-2-22-22222-22-2-2-22-22-2-22-2200000000000000000000000000000000000000002i−2i2i−2i0000
χ502-2-22-2-22222-2-2-22-22222-22-2-2-22-22-2-22-220000000000000000000000000000000000000000−2i2i−2i2i0000
χ512-2-22-2-22222-2-2-22-22-2-2-22-2222-22-22-222-20000000000000000000000000000000000002-22-200000000
χ522-2-22-2-22222-2-2-22-22-2-2-22-2222-22-22-222-2000000000000000000000000000000000000-22-2200000000
χ532-2-22-2-222-2-2222-22-222-22-22-2-22-22-2-222-200000000000000000000000000000000000000002i−2i−2i2i0000
χ542-2-22-2-222-2-2222-22-222-22-22-2-22-22-2-222-20000000000000000000000000000000000000000−2i2i2i−2i0000
χ552-2-22-2-222-2-2222-22-2-2-22-22-222-22-22-22-220000000000000000000000000000000000002-2-2200000000
χ562-2-22-2-222-2-2222-22-2-2-22-22-222-22-22-22-22000000000000000000000000000000000000-222-200000000
χ572-2-22-2-222-2-222-22-2222-22-22-22-22-2-22-2-22000000000000000000000000000000000000000000002i−2i−2i2i
χ582-2-22-2-222-2-222-22-2222-22-22-22-22-2-22-2-2200000000000000000000000000000000000000000000−2i2i2i−2i
χ592-2-22-2-222-2-222-22-22-2-22-22-22-22-2222-22-2000000000000000000000000000000002-2-22000000000000
χ602-2-22-2-222-2-222-22-22-2-22-22-22-22-2222-22-200000000000000000000000000000000-222-2000000000000
χ61444-4-4-4-44000000004-4000040000-4000000004-44-40000000000000000000000000000000000000000
χ62444-4-4-4-44000000004-4000040000-400000000-44-440000000000000000000000000000000000000000
χ63444-4-4-4-4400000000-440000-40000400004i−4i4i−4i00000000000000000000000000000000000000000000
χ64444-4-4-4-4400000000-440000-4000040000−4i4i−4i4i00000000000000000000000000000000000000000000
χ6544-44-44-4-44-44-40000000000000000000022−22−222222−22−22220000000000000000000000000000000000000000
χ6644-44-44-4-44-44-400000000000000000000−222222−22−222222−220000000000000000000000000000000000000000
χ6744-44-44-4-4-44-440000000000000000000022−22−2222−222222−220000000000000000000000000000000000000000
χ6844-44-44-4-4-44-4400000000000000000000−222222−2222−22−22220000000000000000000000000000000000000000
χ694-4444-4-4-44-4-44000000000000000000000000000022−2222−2222−2222−2200000000000000000000000000000000
χ704-4444-4-4-44-4-440000000000000000000000000000−2222−2222−2222−222200000000000000000000000000000000
χ714-4444-4-4-4-444-4000000000000000000000000000022−2222−22−2222−222200000000000000000000000000000000
χ724-4444-4-4-4-444-40000000000000000000000000000−2222−222222−2222−2200000000000000000000000000000000
χ734-44-4-444-400004i−4i−4i4i004i−4i−4i4i04-4-4400000000000000000000000000000000000000000000000000000
χ744-44-4-444-400004i−4i−4i4i00−4i4i4i−4i0-444-400000000000000000000000000000000000000000000000000000
χ754-44-4-444-40000−4i4i4i−4i004i−4i−4i4i0-444-400000000000000000000000000000000000000000000000000000
χ764-44-4-444-40000−4i4i4i−4i00−4i4i4i−4i04-4-4400000000000000000000000000000000000000000000000000000
χ774-4-4-444-44000000004-40000-40000400000000000000004-4-4400000000000000000000000000000000
χ784-4-4-444-44000000004-40000-4000040000000000000000-444-400000000000000000000000000000000
χ794-4-4-444-4400000000-44000040000-40000000000004i−4i−4i4i000000000000000000000000000000000000
χ804-4-4-444-4400000000-44000040000-4000000000000−4i4i4i−4i000000000000000000000000000000000000

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