Finite Group Databasebeta

← Group #325191

Character table — Group #325191

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
χ91111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-11-1
χ101111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-11-11
χ111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11-11
χ121111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-11-1
χ131111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ141111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ151111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ161111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ17222222222222222222-2-2-222-2-2-2-2-2-2-2000000000000000000000000000000002-22-200000000
χ18222222222222222222-2-2-222-2-2-2-2-2-2-200000000000000000000000000000000-22-2200000000
χ192222222222-2-2-2-2-2-2-2-2-2-2-222-2-2-22222000000000000000000000000000000002-2-2200000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-222-2-2-2222200000000000000000000000000000000-222-200000000
χ2122222222-2-22222-2-2-2-2222-2-22-2-222-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ2222222222-2-22222-2-2-2-2222-2-22-2-222-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-222-2-2220000000000000000000000000000000000002i−2i2i−2i0000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000−2i2i−2i2i0000
χ2522222222-2-2-2-2-2-22222222-2-22-2-2-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2622222222-2-2-2-2-2-22222222-2-22-2-2-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2722222222-2-2-2-2-2-22222-2-2-2-2-2-22222-2-20000000000000000000000000000000000002i−2i−2i2i0000
χ2822222222-2-2-2-2-2-22222-2-2-2-2-2-22222-2-2000000000000000000000000000000000000−2i2i2i−2i0000
χ292222-2-2-2-20022-2-2000022-200-2002-20022-2-2000022-2-2000022−2−222−2−222−2−222−2−2000000000000
χ302222-2-2-2-20022-2-2000022-200-2002-20022-2-2000022-2-20000−2−222−2−222−2−222−2−222000000000000
χ312222-2-2-2-20022-2-2000022-200-2002-200-2-2220000-2-222000022−2−222−2−2−2−222−2−222000000000000
χ322222-2-2-2-20022-2-2000022-200-2002-200-2-2220000-2-2220000−2−222−2−22222−2−222−2−2000000000000
χ332222-2-2-2-200-2-222000022-200-200-220022-2-20000-2-222000022−2−2−2−22222−2−2−2−222000000000000
χ342222-2-2-2-200-2-222000022-200-200-220022-2-20000-2-2220000−2−22222−2−2−2−22222−2−2000000000000
χ352222-2-2-2-200-2-222000022-200-200-2200-2-222000022-2-2000022−2−2−2−222−2−22222−2−2000000000000
χ362222-2-2-2-200-2-222000022-200-200-2200-2-222000022-2-20000−2−22222−2−222−2−2−2−222000000000000
χ3722-2-222-2-22-2000000002-222-2-22-200002-22-222-2-20000000000002-22-200002-22-2000000000000
χ3822-2-222-2-22-2000000002-222-2-22-200002-22-222-2-2000000000000-22-220000-22-22000000000000
χ3922-2-222-2-22-2000000002-222-2-22-20000-22-22-2-2220000000000002-22-20000-22-22000000000000
χ4022-2-222-2-22-2000000002-222-2-22-20000-22-22-2-222000000000000-22-2200002-22-2000000000000
χ4122-2-222-2-2-22000000002-22-22-2-2200002-22-2-2-222000000002-22-200002-22-20000000000000000
χ4222-2-222-2-2-22000000002-22-22-2-2200002-22-2-2-22200000000-22-220000-22-220000000000000000
χ4322-2-222-2-2-22000000002-22-22-2-220000-22-2222-2-2000000002-22-20000-22-220000000000000000
χ4422-2-222-2-2-22000000002-22-22-2-220000-22-2222-2-200000000-22-2200002-22-20000000000000000
χ4522-2-2-2-22200000022-2-22-2-200200002-22-2-220000000022-2-22−2−222−2−222−2−222−2−22000000000000
χ4622-2-2-2-22200000022-2-22-2-200200002-22-2-220000000022-2-2−222−2−222−2−222−2−222−2000000000000
χ4722-2-2-2-22200000022-2-22-2-200200002-2-222-200000000-2-2222−2−222−2−22−222−2−222−2000000000000
χ4822-2-2-2-22200000022-2-22-2-200200002-2-222-200000000-2-222−222−2−222−22−2−222−2−22000000000000
χ4922-2-2-2-222000000-2-2222-2-20020000-222-2-2200000000-2-2222−2−22−222−22−2−22−222−2000000000000
χ5022-2-2-2-222000000-2-2222-2-20020000-222-2-2200000000-2-222−222−22−2−22−222−22−2−22000000000000
χ5122-2-2-2-222000000-2-2222-2-20020000-22-222-20000000022-2-22−2−22−222−2−222−22−2−22000000000000
χ5222-2-2-2-222000000-2-2222-2-20020000-22-222-20000000022-2-2−222−22−2−222−2−22−222−2000000000000
χ534444-4-4-4-40044-4-40000-4-4400400-440000000000000000000000000000000000000000000000
χ544444-4-4-4-400-4-4440000-4-44004004-40000000000000000000000000000000000000000000000
χ5544-4-444-4-44-400000000-44-44-44-44000000000000000000000000000000000000000000000000
χ5644-4-444-4-4-4400000000-44-4-4444-4000000000000000000000000000000000000000000000000
χ5744-4-4-4-44400000044-4-4-44400-40000-4400000000000000000000000000000000000000000000
χ5844-4-4-4-444000000-4-444-44400-400004-400000000000000000000000000000000000000000000
χ594-44-44-44-40000004i−4i4i−4i00000000000000002i2−2i22i2−2i222−2222−2200000000000000000000000000000000
χ604-44-44-44-40000004i−4i4i−4i0000000000000000−2i22i2−2i22i2−2222−222200000000000000000000000000000000
χ614-44-44-44-4000000−4i4i−4i4i00000000000000002i2−2i22i2−2i2−2222−222200000000000000000000000000000000
χ624-44-44-44-4000000−4i4i−4i4i0000000000000000−2i22i2−2i22i222−2222−2200000000000000000000000000000000
χ634-44-4-44-444400000000000-4-400000000000000022−22−222222−2222−220000000000000000000000000000
χ644-44-4-44-444400000000000-4-4000000000000000−222222−22−2222−22220000000000000000000000000000
χ654-44-4-44-44-4-4000000000004400000000000000022−22−2222−2222−22220000000000000000000000000000
χ664-44-4-44-44-4-40000000000044000000000000000−222222−2222−2222−220000000000000000000000000000
χ674-4-444-4-44004i−4i4i−4i000000000000000000002i2−2i2−2i22i2000022−22−22220000000000000000000000000000
χ684-4-444-4-44004i−4i4i−4i00000000000000000000−2i22i22i2−2i20000−222222−220000000000000000000000000000
χ694-4-444-4-4400−4i4i−4i4i000000000000000000002i2−2i2−2i22i20000−222222−220000000000000000000000000000
χ704-4-444-4-4400−4i4i−4i4i00000000000000000000−2i22i22i2−2i2000022−22−22220000000000000000000000000000
χ714-4-44-444-44-44i−4i−4i4i−4i4i4i−4i000-44000000000000000000000000000000000000000000000000000
χ724-4-44-444-44-4−4i4i4i−4i4i−4i−4i4i000-44000000000000000000000000000000000000000000000000000
χ734-4-44-444-4-444i−4i−4i4i4i−4i−4i4i0004-4000000000000000000000000000000000000000000000000000
χ744-4-44-444-4-44−4i4i4i−4i−4i4i4i−4i0004-4000000000000000000000000000000000000000000000000000

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