Finite Group Databasebeta

← Group #315161

Character table — Group #315161

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444448888888844888888888888888888882244444488888888444488884444
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-11-11
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111-11-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11-11-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-11-11
χ91111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-11-1-11
χ101111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-111-1
χ111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-111-1
χ121111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-1111-1-11
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-11-11-1-1-111-1-111
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-11-1111-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111-11-1-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-11-1111-1-1-1-111
χ17222222222-222-2-2-2200000000-2-200002222-2-2-2-2000000002222-2-2-2-200000000000000000000
χ18222222222-222-2-2-2200000000-2-200002222-2-2-2-200000000-2-2-2-2222200000000000000000000
χ19222222222-222-2-2-2200000000-2-20000-2-2-2-222220000000022-2-222-2-200000000000000000000
χ20222222222-222-2-2-2200000000-2-20000-2-2-2-2222200000000-2-222-2-22200000000000000000000
χ2122222222-22-2-2222-222222222-2-2-2-2-2-2000000000000000000000000000000002-2-2200000000
χ2222222222-22-2-2222-222222222-2-2-2-2-2-200000000000000000000000000000000-222-200000000
χ2322222222-22-2-2222-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000022-2-200000000
χ2422222222-22-2-2222-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000-2-22200000000
χ25222-2-22-2-2-202-200022222−2−2−2−20022−2−200002i2i−2i−2ii2i2i2i2−i2−i2−i2−i22-2002i−2i00i2i2−i2−i222−2−2000000000000
χ26222-2-22-2-2-202-200022222−2−2−2−20022−2−200002i2i−2i−2ii2i2i2i2−i2−i2−i2−i2-2200−2i2i00−i2−i2i2i2−2−222000000000000
χ27222-2-22-2-2-202-200022222−2−2−2−20022−2−20000−2i−2i2i2i−i2−i2−i2−i2i2i2i2i22-200−2i2i00−i2−i2i2i222−2−2000000000000
χ28222-2-22-2-2-202-200022222−2−2−2−20022−2−20000−2i−2i2i2i−i2−i2−i2−i2i2i2i2i2-22002i−2i00i2i2−i2−i2−2−222000000000000
χ29222-2-22-2-2-202-20002−2−2−2−2222200−2−22200002i2i−2i−2i−i2−i2−i2−i2i2i2i2i22-2002i−2i00−i2−i2i2i2−2−222000000000000
χ30222-2-22-2-2-202-20002−2−2−2−2222200−2−22200002i2i−2i−2i−i2−i2−i2−i2i2i2i2i2-2200−2i2i00i2i2−i2−i222−2−2000000000000
χ31222-2-22-2-2-202-20002−2−2−2−2222200−2−2220000−2i−2i2i2ii2i2i2i2−i2−i2−i2−i22-200−2i2i00i2i2−i2−i2−2−222000000000000
χ32222-2-22-2-2-202-20002−2−2−2−2222200−2−2220000−2i−2i2i2ii2i2i2i2−i2−i2−i2−i2-22002i−2i00−i2−i2i2i222−2−2000000000000
χ3322-22-2-22-2-20-22000222−2−222−2−2002−22−200002-22-222−2−222−2−2002i−2i002i−2ii2−i2i2−i2i2−i2i2−i2000000000000
χ3422-22-2-22-2-20-22000222−2−222−2−2002−22−200002-22-222−2−222−2−200−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i2000000000000
χ3522-22-2-22-2-20-22000222−2−222−2−2002−22−20000-22-22−2−222−2−222002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i2000000000000
χ3622-22-2-22-2-20-22000222−2−222−2−2002−22−20000-22-22−2−222−2−22200−2i2i002i−2i−i2i2−i2i2i2−i2i2−i2000000000000
χ3722-22-2-22-2-20-220002−2−222−2−22200−22−2200002-22-2−2−222−2−222002i−2i002i−2i−i2i2−i2i2−i2i2−i2i2000000000000
χ3822-22-2-22-2-20-220002−2−222−2−22200−22−2200002-22-2−2−222−2−22200−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i2000000000000
χ3922-22-2-22-2-20-220002−2−222−2−22200−22−220000-22-2222−2−222−2−2002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i2000000000000
χ4022-22-2-22-2-20-220002−2−222−2−22200−22−220000-22-2222−2−222−2−200−2i2i002i−2ii2−i2i2−i2−i2i2−i2i2000000000000
χ4122-2-22-2-2222-2-2-22-2200000000-2200002i2i−2i−2i2i−2i−2i2i00000000000000002-2-22−2i2i2i−2i000000000000
χ4222-2-22-2-2222-2-2-22-2200000000-2200002i2i−2i−2i2i−2i−2i2i0000000000000000-222-22i−2i−2i2i000000000000
χ4322-2-22-2-2222-2-2-22-2200000000-220000−2i−2i2i2i−2i2i2i−2i00000000000000002-2-222i−2i−2i2i000000000000
χ4422-2-22-2-2222-2-2-22-2200000000-220000−2i−2i2i2i−2i2i2i−2i0000000000000000-222-2−2i2i2i−2i000000000000
χ4522-2-22-2-222-2-2-22-22222-2-2-2-2222-22-2-222i2i−2i−2i−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ4622-2-22-2-222-2-2-22-22222-2-2-2-2222-22-2-22−2i−2i2i2i2i−2i−2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ4722-2-22-2-222-2-2-22-222-2-22222-2-22-2-222-22i2i−2i−2i−2i2i2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ4822-2-22-2-222-2-2-22-222-2-22222-2-22-2-222-2−2i−2i2i2i2i−2i−2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ4922-2-22-2-22-2-2222-22-222-2-2-2-222-22-222-20000000000000000000000000000000000002i−2i2i−2i0000
χ5022-2-22-2-22-2-2222-22-222-2-2-2-222-22-222-2000000000000000000000000000000000000−2i2i−2i2i0000
χ5122-2-22-2-22-2-2222-22-2-2-22222-2-2-222-2-220000000000000000000000000000000000002i−2i−2i2i0000
χ5222-2-22-2-22-2-2222-22-2-2-22222-2-2-222-2-22000000000000000000000000000000000000−2i2i2i−2i0000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000000
χ54444-4-44-4-440-44000-422222222−22−22−22−2200−22−22222200000000000000000000000000000000000000000000
χ55444-4-44-4-440-44000-4−22−22−22−2222222222002222−22−2200000000000000000000000000000000000000000000
χ5644-44-4-44-4404-4000-42222−22−222222−22−2200−2222−222200000000000000000000000000000000000000000000
χ5744-44-4-44-4404-4000-4−22−222222−22−2222220022−2222−2200000000000000000000000000000000000000000000
χ5844-4-44-4-44-4444-44-4-4000000004-4000000000000000000000000000000000000000000000000
χ594-444-4-4-440400-4-44000000000000000000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000000000
χ604-444-4-4-440400-4-4400000000000000000000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000000000
χ614-444-4-4-440-40044-404i−4i4i−4i4i−4i4i−4i00000000000000000000000000000000000000000000000000
χ624-444-4-4-440-40044-40−4i4i−4i4i−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ634-44-44-44-4000000002i2−2i22i2−2i2−2i22i2−2i22i20000002i2−2i22i2−2i200002-22-2-22-220000000000000000000000000000
χ644-44-44-44-4000000002i2−2i22i2−2i2−2i22i2−2i22i2000000−2i22i2−2i22i20000-22-222-22-20000000000000000000000000000
χ654-44-44-44-400000000−2i22i2−2i22i22i2−2i22i2−2i20000002i2−2i22i2−2i20000-22-222-22-20000000000000000000000000000
χ664-44-44-44-400000000−2i22i2−2i22i22i2−2i22i2−2i2000000−2i22i2−2i22i200002-22-2-22-220000000000000000000000000000
χ674-4-4444-4-4000000002i2−2i2−2i22i22i2−2i2−2i22i200000022−22−222200002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ684-4-4444-4-4000000002i2−2i2−2i22i22i2−2i2−2i22i2000000−222222−220000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ694-4-4444-4-400000000−2i22i22i2−2i2−2i22i22i2−2i200000022−22−22220000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ704-4-4444-4-400000000−2i22i22i2−2i2−2i22i22i2−2i2000000−222222−2200002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ714-4-4-4-444404004-4-404i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ724-4-4-4-444404004-4-40−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000
χ734-4-4-4-44440-400-4440000000000000000000000022−22−2222−222222−220000000000000000000000000000
χ744-4-4-4-44440-400-44400000000000000000000000−222222−2222−22−22220000000000000000000000000000

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