Finite Group Databasebeta

← Group #325666

Character table — Group #325666

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444444444444444444488888888888888888888888888888888444488884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ911111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-11-1
χ1011111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-11-11
χ1111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11-11
χ1211111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-11-1
χ1311111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ1411111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ1511111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ1611111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ172222222222222222-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000002-22-200000000
χ182222222222222222-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000-22-2200000000
χ19222222222222-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ20222222222222-2-2-2-222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000002i−2i2i−2i0000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000−2i2i−2i2i0000
χ2322222222-2-2-2-2222222-2-2-2-222-2-222-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2422222222-2-2-2-2222222-2-2-2-222-2-222-2-2-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-2220000000000000000000000000000000000002i−2i−2i2i0000
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000−2i2i2i−2i0000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2000000000000000000000000000000002-2-2200000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-22222-2-200000000000000000000000000000000-222-200000000
χ2922-2-2-2-222000000002222-2-2-2-200002-222-2-222-2-20000000000002i2i−2i−2i00002i2i−2i−2i000000000000
χ3022-2-2-2-222000000002222-2-2-2-200002-222-2-222-2-2000000000000−2i−2i2i2i0000−2i−2i2i2i000000000000
χ3122-2-2-2-222000000002222-2-2-2-200002-2-2-222-2-2220000000000002i2i−2i−2i0000−2i−2i2i2i000000000000
χ3222-2-2-2-222000000002222-2-2-2-200002-2-2-222-2-222000000000000−2i−2i2i2i00002i2i−2i−2i000000000000
χ3322-2-2-2-2220000000022-2-222-2-20000-2222-2-2-2-222000000002i2i−2i−2i00002i2i−2i−2i0000000000000000
χ3422-2-2-2-2220000000022-2-222-2-20000-2222-2-2-2-22200000000−2i−2i2i2i0000−2i−2i2i2i0000000000000000
χ3522-2-2-2-2220000000022-2-222-2-20000-22-2-22222-2-2000000002i2i−2i−2i0000−2i−2i2i2i0000000000000000
χ3622-2-2-2-2220000000022-2-222-2-20000-22-2-22222-2-200000000−2i−2i2i2i00002i2i−2i−2i0000000000000000
χ372-222-2-22-200002i2i−2i−2i2-200002-2002i−2i0000002-22-22i2i−2i−2i0000i2−i2i2−i22−22−2i2−i2i2−i22−22−2000000000000
χ382-222-2-22-200002i2i−2i−2i2-200002-2002i−2i0000002-22-22i2i−2i−2i0000−i2i2−i2i2−22−22−i2i2−i2i2−22−22000000000000
χ392-222-2-22-200002i2i−2i−2i2-200002-2002i−2i000000-22-22−2i−2i2i2i0000i2−i2i2−i22−22−2−i2i2−i2i2−22−22000000000000
χ402-222-2-22-200002i2i−2i−2i2-200002-2002i−2i000000-22-22−2i−2i2i2i0000−i2i2−i2i2−22−22i2−i2i2−i22−22−2000000000000
χ412-222-2-22-20000−2i−2i2i2i2-200002-200−2i2i0000002-22-2−2i−2i2i2i0000i2−i2i2−i2−22−22i2−i2i2−i2−22−22000000000000
χ422-222-2-22-20000−2i−2i2i2i2-200002-200−2i2i0000002-22-2−2i−2i2i2i0000−i2i2−i2i22−22−2−i2i2−i2i22−22−2000000000000
χ432-222-2-22-20000−2i−2i2i2i2-200002-200−2i2i000000-22-222i2i−2i−2i0000i2−i2i2−i2−22−22−i2i2−i2i22−22−2000000000000
χ442-222-2-22-20000−2i−2i2i2i2-200002-200−2i2i000000-22-222i2i−2i−2i0000−i2i2−i2i22−22−2i2−i2i2−i2−22−22000000000000
χ452-2-2-2222-22i2i−2i−2i00002-20000-222i−2i000000002-2-2200002i2i−2i−2i2−2−22i2−i2−i2i2−222−2i2−i2−i2i2000000000000
χ462-2-2-2222-22i2i−2i−2i00002-20000-222i−2i000000002-2-2200002i2i−2i−2i−222−2−i2i2i2−i22−2−22−i2i2i2−i2000000000000
χ472-2-2-2222-22i2i−2i−2i00002-20000-222i−2i00000000-222-20000−2i−2i2i2i2−2−22i2−i2−i2i22−2−22−i2i2i2−i2000000000000
χ482-2-2-2222-22i2i−2i−2i00002-20000-222i−2i00000000-222-20000−2i−2i2i2i−222−2−i2i2i2−i2−222−2i2−i2−i2i2000000000000
χ492-2-2-2222-2−2i−2i2i2i00002-20000-22−2i2i000000002-2-220000−2i−2i2i2i2−2−22−i2i2i2−i2−222−2−i2i2i2−i2000000000000
χ502-2-2-2222-2−2i−2i2i2i00002-20000-22−2i2i000000002-2-220000−2i−2i2i2i−222−2i2−i2−i2i22−2−22i2−i2−i2i2000000000000
χ512-2-2-2222-2−2i−2i2i2i00002-20000-22−2i2i00000000-222-200002i2i−2i−2i2−2−22−i2i2i2−i22−2−22i2−i2−i2i2000000000000
χ522-2-2-2222-2−2i−2i2i2i00002-20000-22−2i2i00000000-222-200002i2i−2i−2i−222−2i2−i2−i2i2−222−2−i2i2i2−i2000000000000
χ53444-44-4-4-400000000004-44-4000000000000000022−2222−2222−2222−220000000000000000000000000000
χ54444-44-4-4-400000000004-44-40000000000000000−2222−2222−2222−22220000000000000000000000000000
χ55444-44-4-4-40000000000-44-44000000000000000022−2222−22−2222−22220000000000000000000000000000
χ56444-44-4-4-40000000000-44-440000000000000000−2222−222222−2222−220000000000000000000000000000
χ5744-44-44-4-44-44-44-44-4004-4-440000000000000000000000000000000000000000000000000000
χ5844-44-44-4-44-44-4-44-4400-444-40000000000000000000000000000000000000000000000000000
χ5944-44-44-4-4-44-444-44-400-444-40000000000000000000000000000000000000000000000000000
χ6044-44-44-4-4-44-44-44-44004-4-440000000000000000000000000000000000000000000000000000
χ6144-4-4-4-44400000000-4-444-4-4440000-4400000000000000000000000000000000000000000000
χ6244-4-4-4-44400000000-4-4-4-4444400004-400000000000000000000000000000000000000000000
χ634-444-4-44-400004i4i−4i−4i-440000-4400−4i4i0000000000000000000000000000000000000000000000
χ644-444-4-44-40000−4i−4i4i4i-440000-44004i−4i0000000000000000000000000000000000000000000000
χ654-44-4-44-444i−4i−4i4i00000000000000000022−2222−2200002i2−2i2−2i22i200000000000000000000000000000000
χ664-44-4-44-444i−4i−4i4i000000000000000000−2222−22220000−2i22i22i2−2i200000000000000000000000000000000
χ674-44-4-44-44−4i4i4i−4i00000000000000000022−2222−220000−2i22i22i2−2i200000000000000000000000000000000
χ684-44-4-44-44−4i4i4i−4i000000000000000000−2222−222200002i2−2i2−2i22i200000000000000000000000000000000
χ694-4-444-4-4400004i−4i−4i4i0000000000000022−22−222200000000−2i22i22i2−2i20000000000000000000000000000
χ704-4-444-4-4400004i−4i−4i4i00000000000000−222222−22000000002i2−2i2−2i22i20000000000000000000000000000
χ714-4-444-4-440000−4i4i4i−4i0000000000000022−22−2222000000002i2−2i2−2i22i20000000000000000000000000000
χ724-4-444-4-440000−4i4i4i−4i00000000000000−222222−2200000000−2i22i22i2−2i20000000000000000000000000000
χ734-4-4-4444-44i4i−4i−4i0000-4400004-4−4i4i000000000000000000000000000000000000000000000000
χ744-4-4-4444-4−4i−4i4i4i0000-4400004-44i−4i000000000000000000000000000000000000000000000000

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