Finite Group Databasebeta

← Group #288784

Character table — Group #288784

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444448888888844888888888888888888882222444488888888444488882444
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-1-11
χ101111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-111-1
χ111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-111-1
χ121111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-1-11
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111111-1-1-1-1111-11-1
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-11111-1-1-11-11
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-111-1-1-1-111-11-11
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-11111-1-11-11-1
χ17222222222-2-22-222-200000000-2-200002222-2-2-2-20000000022-2-2-2-22200000000000000000000
χ18222222222-2-22-222-200000000-2-200002222-2-2-2-200000000-2-22222-2-200000000000000000000
χ19222222222-2-22-222-200000000-2-20000-2-2-2-22222000000002222-2-2-2-200000000000000000000
χ20222222222-2-22-222-200000000-2-20000-2-2-2-2222200000000-2-2-2-2222200000000000000000000
χ2122222222-222-22-2-2222222222-2-2-2-2-2-2000000000000000000000000000000002-22-200000000
χ2222222222-222-22-2-2222222222-2-2-2-2-2-200000000000000000000000000000000-22-2200000000
χ2322222222-222-22-2-22-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000002-2-2200000000
χ2422222222-222-22-2-22-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000-222-200000000
χ25222-22-2-2-2-200-202202222−2−2−2−20022−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i2002-22i−2i00i2i2−i2−i222−2−2000000000000
χ26222-22-2-2-2-200-202202222−2−2−2−20022−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i200-22−2i2i00−i2−i2i2i2−2−222000000000000
χ27222-22-2-2-2-200-202202222−2−2−2−20022−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i2002-2−2i2i00−i2−i2i2i222−2−2000000000000
χ28222-22-2-2-2-200-202202222−2−2−2−20022−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i200-222i−2i00i2i2−i2−i2−2−222000000000000
χ29222-22-2-2-2-200-20220−2−2−2−2222200−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i2002-22i−2i00−i2−i2i2i2−2−222000000000000
χ30222-22-2-2-2-200-20220−2−2−2−2222200−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i200-22−2i2i00i2i2−i2−i222−2−2000000000000
χ31222-22-2-2-2-200-20220−2−2−2−2222200−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i2002-2−2i2i00i2i2−i2−i2−2−222000000000000
χ32222-22-2-2-2-200-20220−2−2−2−2222200−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i200-222i−2i00−i2−i2i2i222−2−2000000000000
χ332-222-22-2-2200-20-220i2i2−i2−i2i2i2−i2−i200i2−i2i2−i22i−2i2i−2i000022−2−222−2−22-200002i−2ii2−i2i2−i22−22−2000000000000
χ342-222-22-2-2200-20-220i2i2−i2−i2i2i2−i2−i200i2−i2i2−i22i−2i2i−2i000022−2−222−2−2-220000−2i2i−i2i2−i2i2−22−22000000000000
χ352-222-22-2-2200-20-220i2i2−i2−i2i2i2−i2−i200i2−i2i2−i2−2i2i−2i2i0000−2−222−2−2222-20000−2i2ii2−i2i2−i2−22−22000000000000
χ362-222-22-2-2200-20-220i2i2−i2−i2i2i2−i2−i200i2−i2i2−i2−2i2i−2i2i0000−2−222−2−222-2200002i−2i−i2i2−i2i22−22−2000000000000
χ372-222-22-2-2200-20-220−i2−i2i2i2−i2−i2i2i200−i2i2−i2i22i−2i2i−2i0000−2−222−2−2222-200002i−2i−i2i2−i2i2−22−22000000000000
χ382-222-22-2-2200-20-220−i2−i2i2i2−i2−i2i2i200−i2i2−i2i22i−2i2i−2i0000−2−222−2−222-220000−2i2ii2−i2i2−i22−22−2000000000000
χ392-222-22-2-2200-20-220−i2−i2i2i2−i2−i2i2i200−i2i2−i2i2−2i2i−2i2i000022−2−222−2−22-20000−2i2i−i2i2−i2i22−22−2000000000000
χ402-222-22-2-2200-20-220−i2−i2i2i2−i2−i2i2i200−i2i2−i2i2−2i2i−2i2i000022−2−222−2−2-2200002i−2ii2−i2i2−i2−22−22000000000000
χ412-22-2-2-222222-2-22-2-22i2i−2i−2i−2i−2i2i2i-22−2i2i2i−2i0000000000000000000000000000000000002-22i−2i0000
χ422-22-2-2-222222-2-22-2-22i2i−2i−2i−2i−2i2i2i-22−2i2i2i−2i000000000000000000000000000000000000-22−2i2i0000
χ432-22-2-2-222222-2-22-2-2−2i−2i2i2i2i2i−2i−2i-222i−2i−2i2i0000000000000000000000000000000000002-2−2i2i0000
χ442-22-2-2-222222-2-22-2-2−2i−2i2i2i2i2i−2i−2i-222i−2i−2i2i000000000000000000000000000000000000-222i−2i0000
χ452-22-2-2-222-2222-2-22-22i2i−2i−2i−2i−2i2i2i2-22i−2i−2i2i2-2-2222-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ462-22-2-2-222-2222-2-22-22i2i−2i−2i−2i−2i2i2i2-22i−2i−2i2i-222-2-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ472-22-2-2-222-2222-2-22-2−2i−2i2i2i2i2i−2i−2i2-2−2i2i2i−2i2-2-2222-2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ482-22-2-2-222-2222-2-22-2−2i−2i2i2i2i2i−2i−2i2-2−2i2i2i−2i-222-2-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ492-22-2-2-222-2-2-222-22200000000-2200002-2-22-2-22200000000000000002-2-222-2-22000000000000
χ502-22-2-2-222-2-2-222-22200000000-2200002-2-22-2-2220000000000000000-222-2-222-2000000000000
χ512-22-2-2-222-2-2-222-22200000000-220000-222-222-2-200000000000000002-2-22-222-2000000000000
χ522-22-2-2-222-2-2-222-22200000000-220000-222-222-2-20000000000000000-222-22-2-22000000000000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000000
χ54444-44-4-4-440040-4-4022222222−22−22−22−2200−22−22222200000000000000000000000000000000000000000000
χ55444-44-4-4-440040-4-40−22−22−22−2222222222002222−22−2200000000000000000000000000000000000000000000
χ5644-44-4-44-4000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000022−2222−222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ5744-44-4-44-4000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000−2222−2222−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ5844-44-4-44-400000000−2i22i2−2i22i2−2i22i2−2i22i2000000000022−2222−22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ5944-44-4-44-400000000−2i22i2−2i22i2−2i22i2−2i22i20000000000−2222−22222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ6044-4-4-44-4404-40400-44i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ6144-4-4-44-4404-40400-4−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000
χ6244-4-4-44-440-440-4004000000000000000000000022−2222−22−2222−22220000000000000000000000000000
χ6344-4-4-44-440-440-40040000000000000000000000−2222−222222−2222−220000000000000000000000000000
χ644-444-44-4-4-400404-402i22i2−2i2−2i22i22i2−2i2−2i200−2i22i2−2i22i200000000000000000000000000000000000000000000
χ654-444-44-4-4-400404-40−2i2−2i22i22i2−2i2−2i22i22i2002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ664-44-4-4-4444-4-4-444-44000000004-4000000000000000000000000000000000000000000000000
χ674-4-444-4-4404-40-40044-4-444-4-4400000000000000000000000000000000000000000000000000
χ684-4-444-4-4404-40-4004-444-4-444-400000000000000000000000000000000000000000000000000
χ694-4-444-4-440-440400-400000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000
χ704-4-444-4-440-440400-40000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000
χ714-4-4-4444-40000000022−22−2222−222222−22000000000022−22−2222-222-22-2-220000000000000000000000000000
χ724-4-4-4444-40000000022−22−2222−222222−220000000000−222222−222-2-22-222-20000000000000000000000000000
χ734-4-4-4444-400000000−222222−2222−22−2222000000000022−22−22222-2-22-222-20000000000000000000000000000
χ744-4-4-4444-400000000−222222−2222−22−22220000000000−222222−22-222-22-2-220000000000000000000000000000

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