Finite Group Databasebeta

← Group #507428

Character table — Group #507428

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order122222224444448888888888882444444444888888888816161616161616161616161616161616244488884444
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
χ5111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ6111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ8111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ91111-1-1111-1-1111-1-1-1-111111111-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11-1-1111-1-11
χ101111-1-1111-1-1111-1-1-1-111111111-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-111-1-1-111-1
χ111111-1-1111-1-1111-1-1-1-111111111-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11-1-111-111-1
χ121111-1-1111-1-1111-1-1-1-111111111-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-111-1-11-1-11
χ131111-1-1111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1111-1-111-1-1
χ141111-1-1111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-1-111-1-111
χ151111-1-1111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1111-1-1-1-111
χ161111-1-1111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-1
χ1722222222222222-2-2-2-22222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ19222222-2-22222-2-2222200002222-2-200000000-2-2-2-2000000000000000000000000002i−2i2i−2i0000
χ20222222-2-22222-2-2222200002222-2-200000000-2-2-2-200000000000000000000000000−2i2i−2i2i0000
χ21222222-2-22222-2-2-2-2-2-20000-2-2-2-2-2-2000000002222000000000000000000000022-2-200000000
χ22222222-2-22222-2-2-2-2-2-20000-2-2-2-2-2-20000000022220000000000000000000000-2-22200000000
χ23222222-2-2-2-2-2-222000022220000-22000000000000-2-222-2-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ24222222-2-2-2-2-2-222000022220000-22000000000000-2-222-2-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ25222222-2-2-2-2-2-2220000-2-2-2-20000-2200000000000022-2-222i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ26222222-2-2-2-2-2-2220000-2-2-2-20000-2200000000000022-2-222−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ272222-2-2222-2-222222222222-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2-2-20000000000000000000000000000
χ282222-2-2222-2-22222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-222-2-222220000000000000000000000000000
χ292222-2-2-2-22-2-22-2-222220000-2-2-2-2220000000022-2-200000000000000000000002-22-200000000
χ302222-2-2-2-22-2-22-2-222220000-2-2-2-2220000000022-2-20000000000000000000000-22-2200000000
χ312222-2-2-2-22-2-22-2-2-2-2-2-2000022222200000000-2-222000000000000000000000000002i−2i−2i2i0000
χ322222-2-2-2-22-2-22-2-2-2-2-2-2000022222200000000-2-22200000000000000000000000000−2i2i2i−2i0000
χ332222-2-2-2-2-222-2220000222200002-2000000000000-2-2-2-222i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ342222-2-2-2-2-222-2220000222200002-2000000000000-2-2-2-222−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ352222-2-2-2-2-222-2220000-2-2-2-200002-20000000000002222-2-2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ362222-2-2-2-2-222-2220000-2-2-2-200002-20000000000002222-2-2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ372-2-22002-2-20022-200002i2i−2i−2i22-2-2002i2i−2i−2i00002-2002i−2i000000002i−2i2i−2i00002-22-2000000000000
χ382-2-22002-2-20022-200002i2i−2i−2i22-2-2002i2i−2i−2i00002-2002i−2i00000000−2i2i−2i2i0000-22-22000000000000
χ392-2-22002-2-20022-200002i2i−2i−2i-2-22200−2i−2i2i2i0000-22002i−2i00002-22-200002i−2i2i−2i0000000000000000
χ402-2-22002-2-20022-200002i2i−2i−2i-2-22200−2i−2i2i2i0000-22002i−2i0000-22-220000−2i2i−2i2i0000000000000000
χ412-2-22002-2-20022-20000−2i−2i2i2i22-2-200−2i−2i2i2i00002-200−2i2i000000002i−2i2i−2i0000-22-22000000000000
χ422-2-22002-2-20022-20000−2i−2i2i2i22-2-200−2i−2i2i2i00002-200−2i2i00000000−2i2i−2i2i00002-22-2000000000000
χ432-2-22002-2-20022-20000−2i−2i2i2i-2-222002i2i−2i−2i0000-2200−2i2i00002-22-20000−2i2i−2i2i0000000000000000
χ442-2-22002-2-20022-20000−2i−2i2i2i-2-222002i2i−2i−2i0000-2200−2i2i0000-22-2200002i−2i2i−2i0000000000000000
χ452-2-2200-22200-22-22i2i−2i−2i2i2i−2i−2i000000000022-2-2002i−2i−2i2i0000i2−i2−i2i22−2−22−222−2−i2i2i2−i2000000000000
χ462-2-2200-22200-22-22i2i−2i−2i2i2i−2i−2i000000000022-2-2002i−2i−2i2i0000−i2i2i2−i2−222−22−2−22i2−i2−i2i2000000000000
χ472-2-2200-22200-22-22i2i−2i−2i−2i−2i2i2i0000000000-2-222002i−2i2i−2i0000i2−i2−i2i22−2−222−2−22i2−i2−i2i2000000000000
χ482-2-2200-22200-22-22i2i−2i−2i−2i−2i2i2i0000000000-2-222002i−2i2i−2i0000−i2i2i2−i2−222−2−222−2−i2i2i2−i2000000000000
χ492-2-2200-22200-22-2−2i−2i2i2i2i2i−2i−2i0000000000-2-22200−2i2i−2i2i0000i2−i2−i2i2−222−2−222−2i2−i2−i2i2000000000000
χ502-2-2200-22200-22-2−2i−2i2i2i2i2i−2i−2i0000000000-2-22200−2i2i−2i2i0000−i2i2i2−i22−2−222−2−22−i2i2i2−i2000000000000
χ512-2-2200-22200-22-2−2i−2i2i2i−2i−2i2i2i000000000022-2-200−2i2i2i−2i0000i2−i2−i2i2−222−22−2−22−i2i2i2−i2000000000000
χ522-2-2200-22200-22-2−2i−2i2i2i−2i−2i2i2i000000000022-2-200−2i2i2i−2i0000−i2i2i2−i22−2−22−222−2i2−i2−i2i2000000000000
χ5344444444-4-4-4-4-4-40000000000004-40000000000000000000000000000000000000000000000
χ544444-4-444-444-4-4-4000000000000-440000000000000000000000000000000000000000000000
χ5544-4-4000004i−4i00022−2222−222i2−2i22i2−2i22i2−2i22i2−2i2002-22-22i−2i2i−2i0000000022−220000000000000000000000000000
χ5644-4-4000004i−4i00022−2222−22−2i22i2−2i22i22i2−2i22i2−2i200-22-22−2i2i−2i2i00000000−22220000000000000000000000000000
χ5744-4-4000004i−4i000−2222−22222i2−2i22i2−2i2−2i22i2−2i22i200-22-22−2i2i−2i2i0000000022−220000000000000000000000000000
χ5844-4-4000004i−4i000−2222−2222−2i22i2−2i22i2−2i22i2−2i22i2002-22-22i−2i2i−2i00000000−22220000000000000000000000000000
χ5944-4-400000−4i4i00022−2222−222i2−2i22i2−2i2−2i22i2−2i22i200-22-222i−2i2i−2i00000000−22220000000000000000000000000000
χ6044-4-400000−4i4i00022−2222−22−2i22i2−2i22i2−2i22i2−2i22i2002-22-2−2i2i−2i2i0000000022−220000000000000000000000000000
χ6144-4-400000−4i4i000−2222−22222i2−2i22i2−2i22i2−2i22i2−2i2002-22-2−2i2i−2i2i00000000−22220000000000000000000000000000
χ6244-4-400000−4i4i000−2222−2222−2i22i2−2i22i22i2−2i22i2−2i200-22-222i−2i2i−2i0000000022−220000000000000000000000000000
χ634-44-44-4000000002i2−2i2−2i22i222−22−22222i2−2i2−2i22i200−2i2i2i−2i−2i2i2i−2i00000022−22000000000000000000000000000000
χ644-44-44-4000000002i2−2i2−2i22i2−222222−222i2−2i2−2i22i2002i−2i−2i2i2i−2i−2i2i000000−2222000000000000000000000000000000
χ654-44-44-400000000−2i22i22i2−2i222−22−2222−2i22i22i2−2i2002i−2i−2i2i2i−2i−2i2i00000022−22000000000000000000000000000000
χ664-44-44-400000000−2i22i22i2−2i2−222222−22−2i22i22i2−2i200−2i2i2i−2i−2i2i2i−2i000000−2222000000000000000000000000000000
χ674-44-4-44000000002i2−2i2−2i22i222−22−2222−2i22i22i2−2i2002i−2i−2i2i−2i2i2i−2i000000−2222000000000000000000000000000000
χ684-44-4-44000000002i2−2i2−2i22i2−222222−22−2i22i22i2−2i200−2i2i2i−2i2i−2i−2i2i00000022−22000000000000000000000000000000
χ694-44-4-4400000000−2i22i22i2−2i222−22−22222i2−2i2−2i22i200−2i2i2i−2i2i−2i−2i2i000000−2222000000000000000000000000000000
χ704-44-4-4400000000−2i22i22i2−2i2−222222−222i2−2i2−2i22i2002i−2i−2i2i−2i2i2i−2i00000022−22000000000000000000000000000000
χ714-4-44004-4400-4-444i4i−4i−4i00000000000000000000−4i4i0000000000000000000000000000000000
χ724-4-44004-4400-4-44−4i−4i4i4i000000000000000000004i−4i0000000000000000000000000000000000
χ734-4-4400-44-4004-440000000044-4-40000000000-44000000000000000000000000000000000000
χ744-4-4400-44-4004-4400000000-4-44400000000004-4000000000000000000000000000000000000

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