Finite Group Databasebeta

← Group #347702

Character table — Group #347702

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222222244444444444444444488888888888888884444444488888888888888882244
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ911111111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ1111111111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ1211111111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1
χ1311111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ1411111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ1511111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ1611111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ172222222222222222222-2-2-2-22-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-22222-2-2-222-2-2000000000000000022-2-222-2-200000000000000000000
χ20222222222222-2-2-2-2-2-2-22222-2-2-222-2-20000000000000000-2-222-2-22200000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2220000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2322222222-2-2-2-222-2-2-2-22-2-2-2-22-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2422222222-2-2-2-222-2-2-2-22-2-2-2-22-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-22222-22222-2-2-2-2-222000000000000000022-2-2-2-22200000000000000000000
χ2622222222-2-2-2-2-2-22222-22222-2-2-2-2-2220000000000000000-2-22222-2-200000000000000000000
χ2722222222-2-2-2-2-2-22222-2-2-2-2-2-22222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-22222-2-2-2-2-2-22222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ2922-2-22-2-2222-2-22-222-2-220000-200000022-2-222-2-2000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ3022-2-22-2-2222-2-22-222-2-220000-200000022-2-222-2-2000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ3122-2-22-2-2222-2-22-222-2-220000-2000000-2-222-2-222000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ3222-2-22-2-2222-2-22-222-2-220000-2000000-2-222-2-222000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ3322-2-22-2-22-2-2222-2-2-22220000-200000022-2-2-2-222000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ3422-2-22-2-22-2-2222-2-2-22220000-200000022-2-2-2-222000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ3522-2-22-2-22-2-2222-2-2-22220000-2000000-2-22222-2-2000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ3622-2-22-2-22-2-2222-2-2-22220000-2000000-2-22222-2-2000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ372-2-2-2222-20000220000-222-2-2-22-2000000002i−2i2i−2i00002i2i−2i−2i00002-22-22i−2i2i−2i0000000000000000
χ382-2-2-2222-20000220000-222-2-2-22-2000000002i−2i2i−2i00002i2i−2i−2i0000-22-22−2i2i−2i2i0000000000000000
χ392-2-2-2222-20000220000-222-2-2-22-200000000−2i2i−2i2i0000−2i−2i2i2i00002-22-2−2i2i−2i2i0000000000000000
χ402-2-2-2222-20000220000-222-2-2-22-200000000−2i2i−2i2i0000−2i−2i2i2i0000-22-222i−2i2i−2i0000000000000000
χ412-2-2-2222-20000220000-2-2-222-2-22000000002i−2i2i−2i0000−2i−2i2i2i2-22-2000000002i−2i2i−2i000000000000
χ422-2-2-2222-20000220000-2-2-222-2-22000000002i−2i2i−2i0000−2i−2i2i2i-22-2200000000−2i2i−2i2i000000000000
χ432-2-2-2222-20000220000-2-2-222-2-2200000000−2i2i−2i2i00002i2i−2i−2i2-22-200000000−2i2i−2i2i000000000000
χ442-2-2-2222-20000220000-2-2-222-2-2200000000−2i2i−2i2i00002i2i−2i−2i-22-22000000002i−2i2i−2i000000000000
χ452-2-2-2222-20000-2-20000222-2-22-2200002-22-2000022-2-2000000002-2-2200002-2-22000000000000
χ462-2-2-2222-20000-2-20000222-2-22-2200002-22-2000022-2-200000000-222-20000-222-2000000000000
χ472-2-2-2222-20000-2-20000222-2-22-220000-22-220000-2-222000000002-2-220000-222-2000000000000
χ482-2-2-2222-20000-2-20000222-2-22-220000-22-220000-2-22200000000-222-200002-2-22000000000000
χ492-2-2-2222-20000-2-200002-2-22222-200002-22-20000-2-22200002-2-2200002-2-220000000000000000
χ502-2-2-2222-20000-2-200002-2-22222-200002-22-20000-2-2220000-222-20000-222-20000000000000000
χ512-2-2-2222-20000-2-200002-2-22222-20000-22-22000022-2-200002-2-220000-222-20000000000000000
χ522-2-2-2222-20000-2-200002-2-22222-20000-22-22000022-2-20000-222-200002-2-220000000000000000
χ53444-4-44-4-40000004i−4i4i−4i0000000000000000000022−2222−222i2−2i22i2−2i20000000000000000000000000000
χ54444-4-44-4-40000004i−4i4i−4i00000000000000000000−2222−2222−2i22i2−2i22i20000000000000000000000000000
χ55444-4-44-4-4000000−4i4i−4i4i0000000000000000000022−2222−22−2i22i2−2i22i20000000000000000000000000000
χ56444-4-44-4-4000000−4i4i−4i4i00000000000000000000−2222−22222i2−2i22i2−2i20000000000000000000000000000
χ5744-44-4-44-40000004i−4i−4i4i04-44-4000004i−4i00000000000000000000000000000000000000000000
χ5844-44-4-44-40000004i−4i−4i4i0-44-4400000−4i4i00000000000000000000000000000000000000000000
χ5944-44-4-44-4000000−4i4i4i−4i04-44-400000−4i4i00000000000000000000000000000000000000000000
χ6044-44-4-44-4000000−4i4i4i−4i0-44-44000004i−4i00000000000000000000000000000000000000000000
χ6144-4-44-4-4444-4-4-44-4-444-40000400000000000000000000000000000000000000000000000000
χ6244-4-44-4-44-4-444-4444-4-4-40000400000000000000000000000000000000000000000000000000
χ634-4444-4-4-400004-40000-40000400000000004i−4i−4i4i000000000000000000000000000000000000
χ644-4444-4-4-400004-40000-4000040000000000−4i4i4i−4i000000000000000000000000000000000000
χ654-4444-4-4-40000-44000040000-40000004-4-440000000000000000000000000000000000000000
χ664-4444-4-4-40000-44000040000-4000000-444-40000000000000000000000000000000000000000
χ674-44-4-4-4444-44-400000004-4-440004-40000000000000000000000000000000000000000000000
χ684-44-4-4-4444-44-40000000-444-4000-440000000000000000000000000000000000000000000000
χ694-44-4-4-444-44-4400000004-4-44000-440000000000000000000000000000000000000000000000
χ704-44-4-4-444-44-440000000-444-40004-40000000000000000000000000000000000000000000000
χ714-4-44-44-444-4-440000000000000000000000000022−22−222222−22−22220000000000000000000000000000
χ724-4-44-44-444-4-4400000000000000000000000000−222222−22−222222−220000000000000000000000000000
χ734-4-44-44-44-444-40000000000000000000000000022−22−2222−222222−220000000000000000000000000000
χ744-4-44-44-44-444-400000000000000000000000000−222222−2222−22−22220000000000000000000000000000

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