Finite Group Databasebeta

← Group #98987

Character table — Group #98987

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444888888884444444488888888888844444444888888888888888888888888
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
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-222220000000022-2-2-2-2-2-200000000000022-2-222-2-2000000000000000000000000
χ18222222222222-2-2-2-222220000000022-2-2-2-2-2-2000000000000-2-222-2-222000000000000000000000000
χ192222222222-2-2222222-2-222222222-2-2-2-222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ202222222222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-2222200000000000000000000000000000000
χ212222222222-2-2-2-2-2-222-2-200000000-2-222-2-222000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ222222222222-2-2-2-2-2-222-2-200000000-2-222-2-22200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-2222222-2-22222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2422222222-2-2222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
χ2522222222-2-222-2-2-2-2-2-22200000000-2-22222-2-2000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2622222222-2-222-2-2-2-2-2-22200000000-2-22222-2-200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-2222200000000000022-2-2-2-222000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-22222000000000000-2-22222-2-2000000000000000000000000
χ2922-2-222-2-2002i−2i2-22-2002i−2i2222-2-2-2-20000002i−2i000000002i2i−2i−2i00000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ3022-2-222-2-2002i−2i2-22-2002i−2i2222-2-2-2-20000002i−2i000000002i2i−2i−2i0000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ3122-2-222-2-2002i−2i2-22-2002i−2i-2-2-2-222220000002i−2i00000000−2i−2i2i2i00000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ3222-2-222-2-2002i−2i2-22-2002i−2i-2-2-2-222220000002i−2i00000000−2i−2i2i2i0000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ3322-2-222-2-200−2i2i2-22-200−2i2i2222-2-2-2-2000000−2i2i00000000−2i−2i2i2i00000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ3422-2-222-2-200−2i2i2-22-200−2i2i2222-2-2-2-2000000−2i2i00000000−2i−2i2i2i0000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ3522-2-222-2-200−2i2i2-22-200−2i2i-2-2-2-22222000000−2i2i000000002i2i−2i−2i00000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ3622-2-222-2-200−2i2i2-22-200−2i2i-2-2-2-22222000000−2i2i000000002i2i−2i−2i0000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ3722-2-2-2-2222i−2i002-2-222i−2i0022-2-222-2-200002i−2i0000002i2i−2i−2i00000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ3822-2-2-2-2222i−2i002-2-222i−2i0022-2-222-2-200002i−2i0000002i2i−2i−2i0000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ3922-2-2-2-2222i−2i002-2-222i−2i00-2-222-2-22200002i−2i000000−2i−2i2i2i00000000000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i
χ4022-2-2-2-2222i−2i002-2-222i−2i00-2-222-2-22200002i−2i000000−2i−2i2i2i0000000000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i
χ4122-2-2-2-222−2i2i002-2-22−2i2i0022-2-222-2-20000−2i2i000000−2i−2i2i2i00000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ4222-2-2-2-222−2i2i002-2-22−2i2i0022-2-222-2-20000−2i2i000000−2i−2i2i2i0000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ4322-2-2-2-222−2i2i002-2-22−2i2i00-2-222-2-2220000−2i2i0000002i2i−2i−2i00000000000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i
χ4422-2-2-2-222−2i2i002-2-22−2i2i00-2-222-2-2220000−2i2i0000002i2i−2i−2i0000000000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i
χ452-22-22-22-222220000-2-2-2-22−22−22−22−22-200000022−2−22−22−22−22−2002-2002-22−22−22−22−20000000000000000
χ462-22-22-22-222220000-2-2-2-22−22−22−22−22-200000022−2−22−22−22−22−200-2200-22−22−22−22−220000000000000000
χ472-22-22-22-222220000-2-2-2-2−22−22−22−222-2000000−2−222−22−22−22−22002-2002-2−22−22−22−220000000000000000
χ482-22-22-22-222220000-2-2-2-2−22−22−22−222-2000000−2−222−22−22−22−2200-2200-222−22−22−22−20000000000000000
χ492-22-22-22-222-2-20000-2-2222−22−22−22−2-22000000−2−2222−22−2−22−222i−2i002i−2i00i2−i2−i2i2i2−i2−i2i20000000000000000
χ502-22-22-22-222-2-20000-2-2222−22−22−22−2-22000000−2−2222−22−2−22−22−2i2i00−2i2i00−i2i2i2−i2−i2i2i2−i20000000000000000
χ512-22-22-22-222-2-20000-2-222−22−22−22−22-2200000022−2−2−22−222−22−22i−2i002i−2i00−i2i2i2−i2−i2i2i2−i20000000000000000
χ522-22-22-22-222-2-20000-2-222−22−22−22−22-2200000022−2−2−22−222−22−2−2i2i00−2i2i00i2−i2−i2i2i2−i2−i2i20000000000000000
χ532-22-22-22-2-2-222000022-2-22−22−22−22−2-22000000−2−222−22−222−22−22i−2i00−2i2i00i2−i2−i2i2−i2i2i2−i20000000000000000
χ542-22-22-22-2-2-222000022-2-22−22−22−22−2-22000000−2−222−22−222−22−2−2i2i002i−2i00−i2i2i2−i2i2−i2−i2i20000000000000000
χ552-22-22-22-2-2-222000022-2-2−22−22−22−22-2200000022−2−22−22−2−22−222i−2i00−2i2i00−i2i2i2−i2i2−i2−i2i20000000000000000
χ562-22-22-22-2-2-222000022-2-2−22−22−22−22-2200000022−2−22−22−2−22−22−2i2i002i−2i00i2−i2−i2i2−i2i2i2−i20000000000000000
χ572-22-22-22-2-2-2-2-2000022222−22−22−22−22-200000022−2−2−22−22−22−22002-200-222−22−2−22−220000000000000000
χ582-22-22-22-2-2-2-2-2000022222−22−22−22−22-200000022−2−2−22−22−22−2200-22002-2−22−222−22−20000000000000000
χ592-22-22-22-2-2-2-2-200002222−22−22−22−222-2000000−2−2222−22−22−22−2002-200-22−22−222−22−20000000000000000
χ602-22-22-22-2-2-2-2-200002222−22−22−22−222-2000000−2−2222−22−22−22−200-22002-22−22−2−22−220000000000000000
χ614444-4-4-4-4000044-4-4000044-4-4-4-4440000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4000044-4-40000-4-44444-4-40000000000000000000000000000000000000000000000000000
χ634444-4-4-4-40000-4-444000000000000000000004i−4i4i−4i0000000000000000000000000000000000000000
χ644444-4-4-4-40000-4-44400000000000000000000−4i4i−4i4i0000000000000000000000000000000000000000
χ6544-4-444-4-4004i−4i-44-44004i−4i00000000000000−4i4i00000000000000000000000000000000000000000000
χ6644-4-444-4-400−4i4i-44-4400−4i4i000000000000004i−4i00000000000000000000000000000000000000000000
χ6744-4-4-4-4444i−4i00-444-44i−4i00000000000000−4i4i0000000000000000000000000000000000000000000000
χ6844-4-4-4-444−4i4i00-444-4−4i4i000000000000004i−4i0000000000000000000000000000000000000000000000
χ694-44-4-44-4400000000000022−22−2222−222222−22004i−4i00002i2−2i2−2i22i20000000000000000000000000000000000000000
χ704-44-4-44-4400000000000022−22−2222−222222−2200−4i4i0000−2i22i22i2−2i20000000000000000000000000000000000000000
χ714-44-4-44-44000000000000−222222−2222−22−2222004i−4i0000−2i22i22i2−2i20000000000000000000000000000000000000000
χ724-44-4-44-44000000000000−222222−2222−22−222200−4i4i00002i2−2i2−2i22i20000000000000000000000000000000000000000
χ734-4-444-4-44004i−4i000000−4i4i22−2222−22−2222−222200000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ744-4-444-4-44004i−4i000000−4i4i−2222−222222−2222−220000000000000000−2i22i22i2−2i200000000000000000000000000000000
χ754-4-444-4-4400−4i4i0000004i−4i22−2222−22−2222−22220000000000000000−2i22i22i2−2i200000000000000000000000000000000
χ764-4-444-4-4400−4i4i0000004i−4i−2222−222222−2222−2200000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ774-4-44-444-44i−4i000000−4i4i0022−22−222222−22−22220000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ784-4-44-444-44i−4i000000−4i4i00−222222−22−222222−22000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ794-4-44-444-4−4i4i0000004i−4i0022−22−222222−22−2222000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ804-4-44-444-4−4i4i0000004i−4i00−222222−22−222222−220000000000002i2−2i2−2i22i2000000000000000000000000000000000000

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