Finite Group Databasebeta

← Group #252738

Character table — Group #252738

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444224444444422444444444888888888888888844444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1
χ4111111111111111111111111111111-1-11111-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111-1-1-1-1111-1-111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1111111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-11111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-11111-11111-1-1-1-1
χ91111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111111-1-111-1-1
χ101111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111111-1-111
χ111111111111-1-1-1-1111111-1-1-1-1111111-1-111-1-111-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-111
χ121111111111-1-1-1-1111111-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-1-11111-1-1
χ131111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1111111-1-1-1-11111-1-1-1-1-111-1-11-1-111-1-111
χ141111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-111-1-1-1-11111-1-1-1-11111-111111-1-1-1-111-1-1
χ151111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1111111-1-1-1-1-1-1-1-111111-1-1-1-1-1111111-1-1
χ161111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-111-1-1-1-111111111-1-1-1-11-1-111-111-1-1-1-111
χ1722222222222222-2-222-2-222-2-20000-2-222000022-2000000000000000000-20000-200000000
χ1822222222222222-2-222-2-222-2-20000-2-2-2-20000-2-2-200000000000000000020000200000000
χ192222222222-2-2-2-2-2-222-2-2-2-2220000-2-2220000-2-2200000000000000000020000-200000000
χ202222222222-2-2-2-2-2-222-2-2-2-2220000-2-2-2-20000222000000000000000000-20000200000000
χ2122222222-2-2222222-2-222-2-2222222-2-200-2-22200-2-2-2000000000000000000000000000000
χ2222222222-2-2222222-2-222-2-222-2-2-2-2-2-20022-2-200-222000000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-200002200000000200000000000000000002-20002-2000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-20000220000000020000000000000000000-22000-22000000
χ2522222222-2-2-2-2-2-222-2-22222-2-22222-2-200-2-2-2-200222000000000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-2-2-2-2-2-2002222002-2-2000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200000000-200000000000000000002-2000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200000000-20000000000000000000-220002-2000000
χ2922-2-2-2-222002i2i−2i−2i2-2002-2002i−2i22-2-20000002i−2i0000000000000i2i2−i2−i222−2−20000000000i2−i22−2
χ3022-2-2-2-222002i2i−2i−2i2-2002-2002i−2i22-2-20000002i−2i0000000000000−i2−i2i2i2−2−2220000000000−i2i2−22
χ3122-2-2-2-222002i2i−2i−2i2-2002-2002i−2i-2-222000000−2i2i0000000000000i2i2−i2−i222−2−20000000000−i2i2−22
χ3222-2-2-2-222002i2i−2i−2i2-2002-2002i−2i-2-222000000−2i2i0000000000000−i2−i2i2i2−2−2220000000000i2−i22−2
χ3322-2-2-2-22200−2i−2i2i2i2-2002-200−2i2i22-2-2000000−2i2i0000000000000i2i2−i2−i2−2−2220000000000i2−i2−22
χ3422-2-2-2-22200−2i−2i2i2i2-2002-200−2i2i22-2-2000000−2i2i0000000000000−i2−i2i2i222−2−20000000000−i2i22−2
χ3522-2-2-2-22200−2i−2i2i2i2-2002-200−2i2i-2-2220000002i−2i0000000000000i2i2−i2−i2−2−2220000000000−i2i22−2
χ3622-2-2-2-22200−2i−2i2i2i2-2002-200−2i2i-2-2220000002i−2i0000000000000−i2−i2i2i222−2−20000000000i2−i2−22
χ372-2-222-22-2222-22-200-2-2002-2000000002-200002-2000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i200000000000000
χ382-2-222-22-2222-22-200-2-2002-2000000002-200002-2000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i200000000000000
χ392-2-222-22-2222-22-200-2-2002-200000000-220000-22000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i200000000000000
χ402-2-222-22-2222-22-200-2-2002-200000000-220000-22000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i200000000000000
χ412-2-222-22-222-22-2200-2-200-22000000002-20000-22000i2i2−i2−i2−i2−i2i2i2i2−i2i2−i2−i2i2−i2i200000000000000
χ422-2-222-22-222-22-2200-2-200-22000000002-20000-22000−i2−i2i2i2i2i2−i2−i2−i2i2−i2i2i2−i2i2−i200000000000000
χ432-2-222-22-222-22-2200-2-200-2200000000-2200002-2000i2i2−i2−i2−i2−i2i2i2−i2i2−i2i2i2−i2i2−i200000000000000
χ442-2-222-22-222-22-2200-2-200-2200000000-2200002-2000−i2−i2i2i2i2i2−i2−i2i2−i2i2−i2−i2i2−i2i200000000000000
χ452-2-22-22-222-20000222-2-2-200002i−2i2i−2i2-2002i−2i000000000002i−2i2i−2i00000000000000002-20000
χ462-2-22-22-222-20000222-2-2-200002i−2i2i−2i2-2002i−2i00000000000−2i2i−2i2i0000000000000000-220000
χ472-2-22-22-222-20000222-2-2-20000−2i2i−2i2i2-200−2i2i000000000002i−2i2i−2i0000000000000000-220000
χ482-2-22-22-222-20000222-2-2-20000−2i2i−2i2i2-200−2i2i00000000000−2i2i−2i2i00000000000000002-20000
χ492-2-22-22-22-22000022-22-2-200002i−2i2i−2i-2200−2i2i00000002i−2i2i−2i0000000000000002-2000000000
χ502-2-22-22-22-22000022-22-2-200002i−2i2i−2i-2200−2i2i0000000−2i2i−2i2i000000000000000-22000000000
χ512-2-22-22-22-22000022-22-2-20000−2i2i−2i2i-22002i−2i00000002i−2i2i−2i000000000000000-22000000000
χ522-2-22-22-22-22000022-22-2-20000−2i2i−2i2i-22002i−2i0000000−2i2i−2i2i0000000000000002-2000000000
χ534444-4-4-4-44-4000000-4400000000000000000000000000022−22−22220000000000000000000000
χ544444-4-4-4-44-4000000-44000000000000000000000000000−222222−220000000000000000000000
χ554444-4-4-4-4-440000004-40000000000000000000000022−22−222200000000000000000000000000
χ564444-4-4-4-4-440000004-400000000000000000000000−222222−2200000000000000000000000000
χ5744-4-4-4-444004i4i−4i−4i-4400-4400−4i4i00000000000000000000000000000000000000000000000
χ5844-4-4-4-44400−4i−4i4i4i-4400-44004i−4i00000000000000000000000000000000000000000000000
χ594-44-44-4-440000004-400-4400004i−4i−4i4i0000000000000000000000000000000000000000000
χ604-44-44-4-440000004-400-440000−4i4i4i−4i0000000000000000000000000000000000000000000
χ614-44-44-4-44000000-44004-400000000000000000004i−4i000000000000000000000000000000
χ624-44-44-4-44000000-44004-40000000000000000000−4i4i000000000000000000000000000000
χ634-44-4-444-4004i−4i−4i4i000000000000000000000000000000000002-2-22−2i2i2i−2i00000000000000
χ644-44-4-444-4004i−4i−4i4i00000000000000000000000000000000000-222-22i−2i−2i2i00000000000000
χ654-44-4-444-400−4i4i4i−4i000000000000000000000000000000000002-2-222i−2i−2i2i00000000000000
χ664-44-4-444-400−4i4i4i−4i00000000000000000000000000000000000-222-2−2i2i2i−2i00000000000000
χ674-4-444-44-4-4-44-44-4004400-440000000000000000000000000000000000000000000000000
χ684-4-444-44-4-4-4-44-440044004-40000000000000000000000000000000000000000000000000
χ694-4-44-44-444-40000-4-44-44400000000-4400000000000000000000000000000000000000000
χ704-4-44-44-44-440000-4-4-4444000000004-400000000000000000000000000000000000000000
χ7188-8-888-8-8000000000000000000000000000000000000000000000000000000000000000

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