Finite Group Databasebeta

← Group #275837

Character table — Group #275837

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444448888888822444888888888888888888884444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
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
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-11-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ911111111-1-1-1-11111111111-1-111111111-1-11111-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-11
χ1011111111-1-1-1-11111111111-1-111111111-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-1
χ1111111111-1-1-1-11111111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1111-1
χ1211111111-1-1-1-11111111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-11
χ1311111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11-1
χ1411111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-11
χ1511111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-11
χ1611111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-11-1
χ172222222222222-222-2-22-2-2-2-2-22222-2-2-2-2220000000022-2-2-2000000000000000000000000000000
χ182222222222222-222-2-22-2-2-2-2-2-2-2-2-222222200000000-2-2-222000000000000000000000000000000
χ19222222222222-22-2-222-22-2-22200000000-2-22222222200-200-2-2-2-200000000000000000000000000
χ20222222222222-22-2-222-22-2-22200000000-2-2-2-2-2-2-2-2-2-200-200222200000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-200000000-2-20000000000200000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ22222222222222-2-2-2-2-2-2-2-222-2-200000000-2-2000000000020000000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2322222222-2-2-2-22-222-2-22-2-2-2222222-2-2-2-2-2-200000000-2-2222000000000000000000000000000000
χ2422222222-2-2-2-22-222-2-22-2-2-222-2-2-2-22222-2-200000000222-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-22-2-222-22-2-2-2-200000000222222-2-2-2-200200-2-22200000000000000000000000000
χ2622222222-2-2-2-2-22-2-222-22-2-2-2-20000000022-2-2-2-222220020022-2-200000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000220000000000-200000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000220000000000-20000000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ2922-22-22-2-22i2i−2i−2i20-2-200200000000022-2-22i−2i22−2−2i2i2−i2−i20002i−2i2−2i2−i200002−22−2i2−i2i2−i200000000000000
χ3022-22-22-2-22i2i−2i−2i20-2-200200000000022-2-22i−2i−2−222−i2−i2i2i20002i−2i−22−i2i20000−22−22−i2i2−i2i200000000000000
χ3122-22-22-2-22i2i−2i−2i20-2-2002000000000-2-2222i−2i22−2−2i2i2−i2−i2000−2i2i2−2i2−i20000−22−22−i2i2−i2i200000000000000
χ3222-22-22-2-22i2i−2i−2i20-2-2002000000000-2-2222i−2i−2−222−i2−i2i2i2000−2i2i−22−i2i200002−22−2i2−i2i2−i200000000000000
χ3322-22-22-2-22i2i−2i−2i-202200-2000002i2i−2i−2i0000−2i2i22−2−2i2i2−i2−i22-2000−22−i2i20000i2−i2−i2i2−222−200000000000000
χ3422-22-22-2-22i2i−2i−2i-202200-2000002i2i−2i−2i0000−2i2i−2−222−i2−i2i2i22-20002−2i2−i20000−i2i2i2−i22−2−2200000000000000
χ3522-22-22-2-22i2i−2i−2i-202200-200000−2i−2i2i2i0000−2i2i22−2−2i2i2−i2−i2-22000−22−i2i20000−i2i2i2−i22−2−2200000000000000
χ3622-22-22-2-22i2i−2i−2i-202200-200000−2i−2i2i2i0000−2i2i−2−222−i2−i2i2i2-220002−2i2−i20000i2−i2−i2i2−222−200000000000000
χ3722-22-22-2-2−2i−2i2i2i20-2-200200000000022-2-2−2i2i22−2−2−i2−i2i2i2000−2i2i2−2−i2i200002−22−2−i2i2−i2i200000000000000
χ3822-22-22-2-2−2i−2i2i2i20-2-200200000000022-2-2−2i2i−2−222i2i2−i2−i2000−2i2i−22i2−i20000−22−22i2−i2i2−i200000000000000
χ3922-22-22-2-2−2i−2i2i2i20-2-2002000000000-2-222−2i2i22−2−2−i2−i2i2i20002i−2i2−2−i2i20000−22−22i2−i2i2−i200000000000000
χ4022-22-22-2-2−2i−2i2i2i20-2-2002000000000-2-222−2i2i−2−222i2i2−i2−i20002i−2i−22i2−i200002−22−2−i2i2−i2i200000000000000
χ4122-22-22-2-2−2i−2i2i2i-202200-2000002i2i−2i−2i00002i−2i22−2−2−i2−i2i2i2-22000−22i2−i20000i2−i2−i2i22−2−2200000000000000
χ4222-22-22-2-2−2i−2i2i2i-202200-2000002i2i−2i−2i00002i−2i−2−222i2i2−i2−i2-220002−2−i2i20000−i2i2i2−i2−222−200000000000000
χ4322-22-22-2-2−2i−2i2i2i-202200-200000−2i−2i2i2i00002i−2i22−2−2−i2−i2i2i22-2000−22i2−i20000−i2i2i2−i2−222−200000000000000
χ4422-22-22-2-2−2i−2i2i2i-202200-200000−2i−2i2i2i00002i−2i−2−222i2i2−i2−i22-20002−2−i2i20000i2−i2−i2i22−2−2200000000000000
χ452-22-2-22-220000222-2-2-2-222-2002i−2i2i−2i2i−2i2i−2i000000000000000000022-2-20000000000002i−2i00000000
χ462-22-2-22-220000222-2-2-2-222-2002i−2i2i−2i2i−2i2i−2i0000000000000000000-2-222000000000000−2i2i00000000
χ472-22-2-22-220000222-2-2-2-222-200−2i2i−2i2i−2i2i−2i2i000000000000000000022-2-2000000000000−2i2i00000000
χ482-22-2-22-220000222-2-2-2-222-200−2i2i−2i2i−2i2i−2i2i0000000000000000000-2-2220000000000002i−2i00000000
χ492-22-2-22-2200002-22-222-2-2-22002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000002i2i−2i−2i002-2000000
χ502-22-2-22-2200002-22-222-2-2-22002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000−2i−2i2i2i00-22000000
χ512-22-2-22-2200002-22-222-2-2-2200−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000002i2i−2i−2i00-22000000
χ522-22-2-22-2200002-22-222-2-2-2200−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000−2i−2i2i2i002-2000000
χ532-2-222-2-222-22-202002-20-2002-200000000002i−2i2i−2i2i−2i2i−2i000000000i2−i2i2−i200000000i2−i2i2−i200002−22−200
χ542-2-222-2-222-22-202002-20-2002-200000000002i−2i2i−2i2i−2i2i−2i000000000−i2i2−i2i200000000−i2i2−i2i20000−22−2200
χ552-2-222-2-222-22-202002-20-2002-20000000000−2i2i−2i2i−2i2i−2i2i000000000i2−i2i2−i200000000i2−i2i2−i20000−22−2200
χ562-2-222-2-222-22-202002-20-2002-20000000000−2i2i−2i2i−2i2i−2i2i000000000−i2i2−i2i200000000−i2i2−i2i200002−22−200
χ572-2-222-2-22-22-2202002-20-200-2200000000002i−2i2i−2i−2i2i−2i2i000000000i2−i2i2−i200000000−i2i2−i2i200002−2−2200
χ582-2-222-2-22-22-2202002-20-200-2200000000002i−2i2i−2i−2i2i−2i2i000000000−i2i2−i2i200000000i2−i2i2−i20000−222−200
χ592-2-222-2-22-22-2202002-20-200-220000000000−2i2i−2i2i2i−2i2i−2i000000000i2−i2i2−i200000000−i2i2−i2i20000−222−200
χ602-2-222-2-22-22-2202002-20-200-220000000000−2i2i−2i2i2i−2i2i−2i000000000−i2i2−i2i200000000i2−i2i2−i200002−2−2200
χ6144-4-4-4-44400000400-440-400000000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ6244-4-4-4-44400000400-440-40000000000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ6344-4-4-4-44400000-4004-404000000000000000000000000000000000000000000022−22−22220000000000
χ6444-4-4-4-44400000-4004-4040000000000000000000000000000000000000000000−222222−220000000000
χ654-444-4-44-44i−4i−4i4i00000000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000000000000000000
χ664-444-4-44-44i−4i−4i4i0000000000000000000000−2i22i22i2−2i222−22−222200000000000000000000000000000000000
χ674-444-4-44-4−4i4i4i−4i00000000000000000000002i2−2i2−2i22i222−22−222200000000000000000000000000000000000
χ684-444-4-44-4−4i4i4i−4i0000000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000000000000000000
χ694-44-4-44-440000-44-44-4-444-440000000000000000000000000000000000000000000000000000000
χ704-44-4-44-440000-4-4-44444-44-40000000000000000000000000000000000000000000000000000000
χ714-4-444-4-444-44-40-400-440400-4400000000000000000000000000000000000000000000000000000
χ724-4-444-4-44-44-440-400-4404004-400000000000000000000000000000000000000000000000000000
χ734-4-4-4444-4000040-4400-40000000004i−4i−4i4i000000000000000000000000000000000000000000000
χ744-4-4-4444-4000040-4400-4000000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ754-4-4-4444-40000-404-4004000004-4-440000000000000000000000000000000000000000000000000
χ764-4-4-4444-40000-404-400400000-444-40000000000000000000000000000000000000000000000000
χ77888-88-8-8-8000000000000000000000000000000000000000000000000000000000000000000000

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