Finite Group Databasebeta

← Group #347698

Character table — Group #347698

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222222244444444444444444488888888888888882222444488888888888888882444
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
χ911111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-11-11-1
χ1011111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-11-11
χ1111111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1111111-1-111-1-1-11-11
χ1211111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-111-1-1111-11-1
χ1311111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ1411111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-11111-1-1-111-1
χ1511111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111111-1-1-1-111-1-1-1-111-111-1
χ1611111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ1722222222222222-2-2-2-2-2-2-222-2-2-222-2-200000000000000002222-2-2-2-200000000000000000000
χ1822222222222222-2-2-2-2-2-2-222-2-2-222-2-20000000000000000-2-2-2-2222200000000000000000000
χ19222222222222-2-22222222-2-22-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ20222222222222-2-22222222-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
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
χ2322222222-2-2-2-222-2-22222-222-2-2-2-2-222000000000000000022-2-2-2-22200000000000000000000
χ2422222222-2-2-2-222-2-22222-222-2-2-2-2-2220000000000000000-2-22222-2-200000000000000000000
χ2522222222-2-2-2-2-2-222-2-2-2-22-2-22-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-2-2-22-2-22-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ292-2-222-2-2200002-2220000-22-2-22-200002i2i−2i−2i00002i2i−2i−2i0000002-2002-200002i−2i2i−2i000000000000
χ302-2-222-2-2200002-2220000-22-2-22-200002i2i−2i−2i00002i2i−2i−2i000000-2200-220000−2i2i−2i2i000000000000
χ312-2-222-2-2200002-2220000-22-2-22-20000−2i−2i2i2i0000−2i−2i2i2i0000002-2002-20000−2i2i−2i2i000000000000
χ322-2-222-2-2200002-2220000-22-2-22-20000−2i−2i2i2i0000−2i−2i2i2i000000-2200-2200002i−2i2i−2i000000000000
χ332-2-222-2-2200002-2-2-2000022-22-220000000022-2-2000022-2-2002-200-222-22-20000000000000000
χ342-2-222-2-2200002-2-2-2000022-22-220000000022-2-2000022-2-200-22002-2-22-220000000000000000
χ352-2-222-2-2200002-2-2-2000022-22-2200000000-2-2220000-2-222002-200-22-22-220000000000000000
χ362-2-222-2-2200002-2-2-2000022-22-2200000000-2-2220000-2-22200-22002-22-22-20000000000000000
χ372-2-222-2-220000-22220000-2-22-2-2200002i2i−2i−2i0000−2i−2i2i2i00002-2002-2002i−2i−2i2i0000000000000000
χ382-2-222-2-220000-22220000-2-22-2-2200002i2i−2i−2i0000−2i−2i2i2i0000-2200-2200−2i2i2i−2i0000000000000000
χ392-2-222-2-220000-22220000-2-22-2-220000−2i−2i2i2i00002i2i−2i−2i00002-2002-200−2i2i2i−2i0000000000000000
χ402-2-222-2-220000-22220000-2-22-2-220000−2i−2i2i2i00002i2i−2i−2i0000-2200-22002i−2i−2i2i0000000000000000
χ412-2-222-2-220000-22-2-200002-2222-20000000022-2-20000-2-2222-200-220000002-2-22000000000000
χ422-2-222-2-220000-22-2-200002-2222-20000000022-2-20000-2-222-22002-2000000-222-2000000000000
χ432-2-222-2-220000-22-2-200002-2222-200000000-2-222000022-2-22-200-22000000-222-2000000000000
χ442-2-222-2-220000-22-2-200002-2222-200000000-2-222000022-2-2-22002-20000002-2-22000000000000
χ452-2-2-2-222222-2-2002-222-2-2-2002000000000000002-22-22-22-200000000000000002−22−22−22−20000
χ462-2-2-2-222222-2-2002-222-2-2-2002000000000000002-22-22-22-20000000000000000−22−22−22−220000
χ472-2-2-2-222222-2-2002-222-2-2-200200000000000000-22-22-22-2200000000000000002−22−2−22−220000
χ482-2-2-2-222222-2-2002-222-2-2-200200000000000000-22-22-22-220000000000000000−22−222−22−20000
χ492-2-2-2-2222-2-222002-2-2-222-2002000000000000002-22-2-22-2200000000000000002−2−222−2−220000
χ502-2-2-2-2222-2-222002-2-2-222-2002000000000000002-22-2-22-220000000000000000−222−2−222−20000
χ512-2-2-2-2222-2-222002-2-2-222-200200000000000000-22-222-22-200000000000000002−2−22−222−20000
χ522-2-2-2-2222-2-222002-2-2-222-200200000000000000-22-222-22-20000000000000000−222−22−2−220000
χ53444-4-4-4-440000004-40000400-4000000000000004i−4i−4i4i00000000000000000000000000000000
χ54444-4-4-4-440000004-40000400-400000000000000−4i4i4i−4i00000000000000000000000000000000
χ55444-4-4-4-44000000-440000-40040000000000000000004-4-440000000000000000000000000000
χ56444-4-4-4-44000000-440000-4004000000000000000000-444-40000000000000000000000000000
χ5744-44-44-4-4000000004i−4i4i−4i000000000022−2222−222i2−2i22i2−2i2000000000000000000000000000000000000
χ5844-44-44-4-4000000004i−4i4i−4i0000000000−2222−2222−2i22i2−2i22i2000000000000000000000000000000000000
χ5944-44-44-4-400000000−4i4i−4i4i000000000022−2222−22−2i22i2−2i22i2000000000000000000000000000000000000
χ6044-44-44-4-400000000−4i4i−4i4i0000000000−2222−22222i2−2i22i2−2i2000000000000000000000000000000000000
χ6144-4-44-44-44-44-4440000000-4-40004-40000000000000000000000000000000000000000000000
χ6244-4-44-44-44-44-4-4-4000000044000-440000000000000000000000000000000000000000000000
χ6344-4-44-44-4-44-44440000000-4-4000-440000000000000000000000000000000000000000000000
χ6444-4-44-44-4-44-44-4-40000000440004-40000000000000000000000000000000000000000000000
χ654-444-4-44-44-4-440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000
χ664-444-4-44-44-4-44000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000
χ674-444-4-44-4-444-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000
χ684-444-4-44-4-444-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000
χ694-44-444-4-400004-4004i−4i−4i4i0-44000004i−4i00000000000000000000000000000000000000000000
χ704-44-444-4-400004-400−4i4i4i−4i0-4400000−4i4i00000000000000000000000000000000000000000000
χ714-44-444-4-40000-44004i−4i−4i4i04-400000−4i4i00000000000000000000000000000000000000000000
χ724-44-444-4-40000-4400−4i4i4i−4i04-4000004i−4i00000000000000000000000000000000000000000000
χ734-4-4-4-444444-4-400-44-4-444400-400000000000000000000000000000000000000000000000000
χ744-4-4-4-4444-4-44400-4444-4-4400-400000000000000000000000000000000000000000000000000

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