Finite Group Databasebeta

← Group #271088

Character table — Group #271088

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444442244444444444444444444448888888888888888222444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-11111-1-1
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1111111-1-1
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-111-1-1-1-111
χ91111111111111111-1-1-1-1-1-111111-1-1111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-111111-1-11-1
χ101111111111111111-1-1-1-1-1-111111-1-1111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1111-1-111-11
χ111111111111111111-1-1-1-1-1-111111-1-11-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1111-1-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-111111-1-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111111-1-1-111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1111-1-1-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1111-1-111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1111111-1-1-1-1-1-1-1-111111-1-1-11111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-111-1-1-1-111111111-1-1-1-11-1-1-111-1-1111-1
χ172222222222-2-222-2-22222-2-20000-2-2-2-222002200000000000000000000-200-200000000
χ182222222222-2-222-2-22222-2-20000-2-2-2-2-2-200-2-200000000000000000000200200000000
χ192222222222-2-222-2-2-2-2-2-2220000-222-22200-2-200000000000000000000200-200000000
χ202222222222-2-222-2-2-2-2-2-2220000-222-2-2-2002200000000000000000000-200200000000
χ2122222222-2-222-2-22222-2-2222222-2-2-2-2002200-2-2-2-20000000000000000000000000000
χ2222222222-2-222-2-22222-2-222-2-2-2-2-2-2-2-200-2-20022220000000000000000000000000000
χ2322222222-2-222-2-222-2-222-2-22222-222-200-2-200-2-2220000000000000000000000000000
χ2422222222-2-222-2-222-2-222-2-2-2-2-2-2-222-200220022-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-2000022220000000000000000000000000002-202-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-200002222000000000000000000000000000-220-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222200002-2-220000000000000000000000000002-20-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222200002-2-22000000000000000000000000000-2202-2000000
χ2922-2-22-22-2002-2002-2002i−2i0022-2-202i−2i0000000002i−2ii2i2−i2−i222−2−2i2i2−i2−i222−2−2000000000000
χ3022-2-22-22-2002-2002-2002i−2i0022-2-202i−2i0000000002i−2i−i2−i2i2i2−2−222−i2−i2i2i2−2−222000000000000
χ3122-2-22-22-2002-2002-2002i−2i00-2-22202i−2i000000000−2i2ii2i2−i2−i222−2−2−i2−i2i2i2−2−222000000000000
χ3222-2-22-22-2002-2002-2002i−2i00-2-22202i−2i000000000−2i2i−i2−i2i2i2−2−222i2i2−i2−i222−2−2000000000000
χ3322-2-22-22-2002-2002-200−2i2i0022-2-20−2i2i000000000−2i2ii2i2−i2−i2−2−222i2i2−i2−i2−2−222000000000000
χ3422-2-22-22-2002-2002-200−2i2i0022-2-20−2i2i000000000−2i2i−i2−i2i2i222−2−2−i2−i2i2i222−2−2000000000000
χ3522-2-22-22-2002-2002-200−2i2i00-2-2220−2i2i0000000002i−2ii2i2−i2−i2−2−222−i2−i2i2i222−2−2000000000000
χ3622-2-22-22-2002-2002-200−2i2i00-2-2220−2i2i0000000002i−2i−i2−i2i2i222−2−2i2i2−i2−i2−2−222000000000000
χ372-22-2-222-2002200-2-22-2002-22-22-20000002-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ382-22-2-222-2002200-2-22-2002-22-22-20000002-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ392-22-2-222-2002200-2-22-2002-2-22-22000000-22000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ402-22-2-222-2002200-2-22-2002-2-22-22000000-22000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ412-22-2-222-2002200-2-2-2200-222-22-2000000-22000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ422-22-2-222-2002200-2-2-2200-222-22-2000000-22000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ432-22-2-222-2002200-2-2-2200-22-22-220000002-2000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ442-22-2-222-2002200-2-2-2200-22-22-220000002-2000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ452-2-22-2-222222-2-2-2-220000002-2-22200-20000002-20000002i−2i−2i2i00002i−2i−2i2i000000000000
χ462-2-22-2-222222-2-2-2-220000002-2-22200-20000002-2000000−2i2i2i−2i0000−2i2i2i−2i000000000000
χ472-2-22-2-222222-2-2-2-22000000-222-2200-2000000-220000002i−2i−2i2i0000−2i2i2i−2i000000000000
χ482-2-22-2-222222-2-2-2-22000000-222-2200-2000000-22000000−2i2i2i−2i00002i−2i−2i2i000000000000
χ492-2-22-2-222-2-22-222-220000002-2-22-2002000000-22002-2-2200002-2-220000000000000000
χ502-2-22-2-222-2-22-222-220000002-2-22-2002000000-2200-222-20000-222-20000000000000000
χ512-2-22-2-222-2-22-222-22000000-222-2-20020000002-2002-2-220000-222-20000000000000000
χ522-2-22-2-222-2-22-222-22000000-222-2-20020000002-200-222-200002-2-220000000000000000
χ534444-4-4-4-44-4004-40000000000000000000000000000000000000000000000000022−2200
χ544444-4-4-4-44-4004-400000000000000000000000000000000000000000000000000−222200
χ554444-4-4-4-4-4400-4400000000000000000000000000000000000000000000000022−220000
χ564444-4-4-4-4-4400-44000000000000000000000000000000000000000000000000−22220000
χ5744-4-44-44-400-4400-44004i−4i0000000−4i4i000000000000000000000000000000000000000
χ5844-4-44-44-400-4400-4400−4i4i00000004i−4i000000000000000000000000000000000000000
χ594-44-4-444-400-4-400444-400-440000000000000000000000000000000000000000000000
χ604-44-4-444-400-4-40044-44004-40000000000000000000000000000000000000000000000
χ614-4-4444-4-44-400-4400000000000000004i−4i000000000000000000000000000000000000
χ624-4-4444-4-44-400-440000000000000000−4i4i000000000000000000000000000000000000
χ634-4-4444-4-4-44004-4000000000000000000004i−4i00000000000000000000000000000000
χ644-4-4444-4-4-44004-400000000000000000000−4i4i00000000000000000000000000000000
χ654-4-44-4-44444-44-4-44-40000000000-400400000000000000000000000000000000000000
χ664-4-44-4-444-4-4-44444-40000000000400-400000000000000000000000000000000000000
χ6788-8-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-88-88-8-88000000000000000000000000000000000000000000000000000000000000

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