Finite Group Databasebeta

← Group #243598

Character table — Group #243598

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444444444444444444888888888888888888888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111
χ911111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ1111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1111111-1-111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ1411111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ1511111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-111
χ1611111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-11111-1-1
χ172222222222222222-2-22222-2-2-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ182222222222222222-2-22222-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ19222222222222-2-2-2-222-2-2-2-222-2-2-2-2220000000022-2-200000000-2-22200000000000000000000
χ20222222222222-2-2-2-222-2-2-2-222-2-2-2-22200000000-2-2220000000022-2-200000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2322222222-2-2-2-2222222-2-2-2-22222-2-2-2-200000000222200000000-2-2-2-200000000000000000000
χ2422222222-2-2-2-2222222-2-2-2-22222-2-2-2-200000000-2-2-2-200000000222200000000000000000000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-222-2-22222-2-2-2-222000000000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-222-2-222-2-22222-2-2000000000000000000000000000000000000
χ2922-2-2-222-22i2i−2i−2i2i2i−2i−2i2-222-2-22-22i−2i2-22i−2i00000000000000000000000000000000000000002-22i−2i
χ3022-2-2-222-22i2i−2i−2i2i2i−2i−2i2-222-2-22-22i−2i2-22i−2i0000000000000000000000000000000000000000-22−2i2i
χ3122-2-2-222-22i2i−2i−2i2i2i−2i−2i-2222-2-2-22−2i2i-22−2i2i000000000000000000000000000000002i−2i00002-20000
χ3222-2-2-222-22i2i−2i−2i2i2i−2i−2i-2222-2-2-22−2i2i-22−2i2i00000000000000000000000000000000−2i2i0000-220000
χ3322-2-2-222-22i2i−2i−2i−2i−2i2i2i2-2-2-2222-2−2i2i-222i−2i0000000000002i2i−2i−2i22-2-2000000000000000000000000
χ3422-2-2-222-22i2i−2i−2i−2i−2i2i2i2-2-2-2222-2−2i2i-222i−2i000000000000−2i−2i2i2i-2-222000000000000000000000000
χ3522-2-2-222-22i2i−2i−2i−2i−2i2i2i-22-2-222-222i−2i2-2−2i2i00000000000000000000000000000000002-22i−2i000000
χ3622-2-2-222-22i2i−2i−2i−2i−2i2i2i-22-2-222-222i−2i2-2−2i2i0000000000000000000000000000000000-22−2i2i000000
χ3722-2-2-222-2−2i−2i2i2i2i2i−2i−2i2-2-2-2222-22i−2i-22−2i2i0000000000002i2i−2i−2i-2-222000000000000000000000000
χ3822-2-2-222-2−2i−2i2i2i2i2i−2i−2i2-2-2-2222-22i−2i-22−2i2i000000000000−2i−2i2i2i22-2-2000000000000000000000000
χ3922-2-2-222-2−2i−2i2i2i2i2i−2i−2i-22-2-222-22−2i2i2-22i−2i00000000000000000000000000000000002-2−2i2i000000
χ4022-2-2-222-2−2i−2i2i2i2i2i−2i−2i-22-2-222-22−2i2i2-22i−2i0000000000000000000000000000000000-222i−2i000000
χ4122-2-2-222-2−2i−2i2i2i−2i−2i2i2i2-222-2-22-2−2i2i2-2−2i2i00000000000000000000000000000000000000002-2−2i2i
χ4222-2-2-222-2−2i−2i2i2i−2i−2i2i2i2-222-2-22-2−2i2i2-2−2i2i0000000000000000000000000000000000000000-222i−2i
χ4322-2-2-222-2−2i−2i2i2i−2i−2i2i2i-2222-2-2-222i−2i-222i−2i000000000000000000000000000000002i−2i0000-220000
χ4422-2-2-222-2−2i−2i2i2i−2i−2i2i2i-2222-2-2-222i−2i-222i−2i00000000000000000000000000000000−2i2i00002-20000
χ452-2-2222-2-22-22-22-22-2002-22-200000000002i−2i002i−2ii2−i2i2−i200000000i2−i2i2−i22−22−22−22−2000000000000
χ462-2-2222-2-22-22-22-22-2002-22-200000000002i−2i002i−2i−i2i2−i2i200000000−i2i2−i2i2−22−22−22−22000000000000
χ472-2-2222-2-22-22-22-22-2002-22-20000000000−2i2i00−2i2ii2−i2i2−i200000000i2−i2i2−i2−22−22−22−22000000000000
χ482-2-2222-2-22-22-22-22-2002-22-20000000000−2i2i00−2i2i−i2i2−i2i200000000−i2i2−i2i22−22−22−22−2000000000000
χ492-2-2222-2-22-22-2-22-2200-22-22000000002-2002-200i2−i2−i2i200000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ502-2-2222-2-22-22-2-22-2200-22-22000000002-2002-200−i2i2i2−i200000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ512-2-2222-2-22-22-2-22-2200-22-2200000000-2200-2200i2−i2−i2i200000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ522-2-2222-2-22-22-2-22-2200-22-2200000000-2200-2200−i2i2i2−i200000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ532-2-2222-2-2-22-222-22-200-22-22000000002-200-2200i2−i2i2−i200000000−i2i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ542-2-2222-2-2-22-222-22-200-22-22000000002-200-2200−i2i2−i2i200000000i2−i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ552-2-2222-2-2-22-222-22-200-22-2200000000-22002-200i2−i2i2−i200000000−i2i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ562-2-2222-2-2-22-222-22-200-22-2200000000-22002-200−i2i2−i2i200000000i2−i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ572-2-2222-2-2-22-22-22-22002-22-200000000002i−2i00−2i2ii2−i2−i2i200000000i2−i2−i2i22−22−2−22−22000000000000
χ582-2-2222-2-2-22-22-22-22002-22-200000000002i−2i00−2i2i−i2i2i2−i200000000−i2i2i2−i2−22−222−22−2000000000000
χ592-2-2222-2-2-22-22-22-22002-22-20000000000−2i2i002i−2ii2−i2−i2i200000000i2−i2−i2i2−22−222−22−2000000000000
χ602-2-2222-2-2-22-22-22-22002-22-20000000000−2i2i002i−2i−i2i2i2−i200000000−i2i2i2−i22−22−2−22−22000000000000
χ61444-44-4-4-4000000004-40000-44000000000000000000000022−2222−22000000000000000000000000
χ62444-44-4-4-4000000004-40000-440000000000000000000000−2222−2222000000000000000000000000
χ63444-44-4-4-400000000-4400004-400000000000000000022−2222−220000000000000000000000000000
χ64444-44-4-4-400000000-4400004-4000000000000000000−2222−22220000000000000000000000000000
χ6544-44-4-4-4400000000440000-4-4000000000000000000000022−22−2222000000000000000000000000
χ6644-44-4-4-4400000000440000-4-40000000000000000000000−222222−22000000000000000000000000
χ6744-44-4-4-4400000000-4-40000440000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ6844-44-4-4-4400000000-4-4000044000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ694-44-4-44-444i−4i−4i4i4i−4i−4i4i004-4-440000000000000000000000000000000000000000000000000000
χ704-44-4-44-444i−4i−4i4i−4i4i4i−4i00-444-40000000000000000000000000000000000000000000000000000
χ714-44-4-44-44−4i4i4i−4i4i−4i−4i4i00-444-40000000000000000000000000000000000000000000000000000
χ724-44-4-44-44−4i4i4i−4i−4i4i4i−4i004-4-440000000000000000000000000000000000000000000000000000
χ738-888-8-88-8000000000000000000000000000000000000000000000000000000000000000000
χ748-8-8-88-888000000000000000000000000000000000000000000000000000000000000000000

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