Finite Group Databasebeta

← Group #288221

Character table — Group #288221

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888224444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1111-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-111-1-11-1
χ91111111111111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111
χ101111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-11-1-1-1-1111-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-11-1-111-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-11-11111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-11-111-1-1111-1
χ17222222222-2-2222-2-20000-2-22222-2-2-2-22200-2-200000000000000000000002-200000000
χ18222222222-2-2222-2-20000-2-22222-2-2-2-2-2-200220000000000000000000000-2200000000
χ19222222222-2-2222-2-20000-2-2-2-2-2-222222200220000000000000000000000-2-200000000
χ20222222222-2-2222-2-20000-2-2-2-2-2-22222-2-200-2-200000000000000000000002200000000
χ2122222222-222-2-2-2222222-2-20000000000-2-20022-2-2000022-2-200000000000000000000
χ2222222222-222-2-2-2222222-2-20000000000-2-200-2-2220000-2-22200000000000000000000
χ2322222222-222-2-2-222-2-2-2-2-2-20000000000220022-2-20000-2-22200000000000000000000
χ2422222222-222-2-2-222-2-2-2-2-2-200000000002200-2-222000022-2-200000000000000000000
χ2522-2-2-2-222222-22-2-2-22i2i−2i−2i-2200000000002i−2i000000000000002i2i−2i−2i22-2-2000000000000
χ2622-2-2-2-222222-22-2-2-22i2i−2i−2i-2200000000002i−2i00000000000000−2i−2i2i2i-2-222000000000000
χ2722-2-2-2-222222-22-2-2-2−2i−2i2i2i-220000000000−2i2i000000000000002i2i−2i−2i-2-222000000000000
χ2822-2-2-2-222222-22-2-2-2−2i−2i2i2i-220000000000−2i2i00000000000000−2i−2i2i2i22-2-2000000000000
χ2922-2-2-2-222-2222-22-2-22i2i−2i−2i2-222-2-222-2-200−2i2i0000002i2i−2i−2i000000000000000000000000
χ3022-2-2-2-222-2222-22-2-22i2i−2i−2i2-2-2-222-2-22200−2i2i000000−2i−2i2i2i000000000000000000000000
χ3122-2-2-2-222-2222-22-2-2−2i−2i2i2i2-222-2-222-2-2002i−2i000000−2i−2i2i2i000000000000000000000000
χ3222-2-2-2-222-2222-22-2-2−2i−2i2i2i2-2-2-222-2-222002i−2i0000002i2i−2i−2i000000000000000000000000
χ3322-2-2-2-222-2-2-22-22220000-2222-2-2-2-222000000000000000000000000002-2002-2000000
χ3422-2-2-2-222-2-2-22-22220000-2222-2-2-2-22200000000000000000000000000-2200-22000000
χ3522-2-2-2-222-2-2-22-22220000-22-2-22222-2-2000000000000000000000000002-200-22000000
χ3622-2-2-2-222-2-2-22-22220000-22-2-22222-2-200000000000000000000000000-22002-2000000
χ372-22-22-22-202-20002-22-22-200i2−i2i2−i2i2−i2i2−i2000000002i−2ii2−i2i2−i2002i−2i2−22−22−22−2000000000000
χ382-22-22-22-202-20002-22-22-200i2−i2i2−i2i2−i2i2−i200000000−2i2ii2−i2i2−i200−2i2i−22−22−22−22000000000000
χ392-22-22-22-202-20002-22-22-200−i2i2−i2i2−i2i2−i2i2000000002i−2i−i2i2−i2i2002i−2i−22−22−22−22000000000000
χ402-22-22-22-202-20002-22-22-200−i2i2−i2i2−i2i2−i2i200000000−2i2i−i2i2−i2i200−2i2i2−22−22−22−2000000000000
χ412-22-22-22-202-20002-2-22-2200i2−i2i2−i2i2−i2i2−i2000000002i−2i−i2i2−i2i200−2i2i2−22−2−22−22000000000000
χ422-22-22-22-202-20002-2-22-2200i2−i2i2−i2i2−i2i2−i200000000−2i2i−i2i2−i2i2002i−2i−22−222−22−2000000000000
χ432-22-22-22-202-20002-2-22-2200−i2i2−i2i2−i2i2−i2i2000000002i−2ii2−i2i2−i200−2i2i−22−222−22−2000000000000
χ442-22-22-22-202-20002-2-22-2200−i2i2−i2i2−i2i2−i2i200000000−2i2ii2−i2i2−i2002i−2i2−22−2−22−22000000000000
χ452-2-22-222-202-2000-222i−2i−2i2i00i2−i2−i2i2i2−i2−i2i20000002-200−222−22i−2i00i2−i2−i2i22−2−22000000000000
χ462-2-22-222-202-2000-222i−2i−2i2i00i2−i2−i2i2i2−i2−i2i2000000-2200−222−2−2i2i00−i2i2i2−i2−222−2000000000000
χ472-2-22-222-202-2000-222i−2i−2i2i00−i2i2i2−i2−i2i2i2−i20000002-2002−2−222i−2i00−i2i2i2−i2−222−2000000000000
χ482-2-22-222-202-2000-222i−2i−2i2i00−i2i2i2−i2−i2i2i2−i2000000-22002−2−22−2i2i00i2−i2−i2i22−2−22000000000000
χ492-2-22-222-202-2000-22−2i2i2i−2i00i2−i2−i2i2i2−i2−i2i20000002-2002−2−22−2i2i00i2−i2−i2i2−222−2000000000000
χ502-2-22-222-202-2000-22−2i2i2i−2i00i2−i2−i2i2i2−i2−i2i2000000-22002−2−222i−2i00−i2i2i2−i22−2−22000000000000
χ512-2-22-222-202-2000-22−2i2i2i−2i00−i2i2i2−i2−i2i2i2−i20000002-200−222−2−2i2i00−i2i2i2−i22−2−22000000000000
χ522-2-22-222-202-2000-22−2i2i2i−2i00−i2i2i2−i2−i2i2i2−i2000000-2200−222−22i−2i00i2−i2−i2i2−222−2000000000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ544444-4-4-4-4400-4-4400000000000000000000000000000000000000000000000022−220000
χ554444-4-4-4-4400-4-44000000000000000000000000000000000000000000000000−22220000
χ564444-4-4-4-4-40044-400000000000000004-4000000000000000000000000000000000000
χ574444-4-4-4-4-40044-40000000000000000-44000000000000000000000000000000000000
χ5844-4-444-4-44004-4-4000000000000000000004-400000000000000000000000000000000
χ5944-4-444-4-44004-4-400000000000000000000-4400000000000000000000000000000000
χ6044-4-444-4-4-400-444000000000000000000000000000000000000000000000000002i2−2i200
χ6144-4-444-4-4-400-44400000000000000000000000000000000000000000000000000−2i22i200
χ6244-4-4-4-4444-4-4-44-44400004-40000000000000000000000000000000000000000000000
χ634-44-44-44-40-44000-440000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ644-44-44-44-40-44000-44000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ654-4-44-444-40-440004-40000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ664-4-44-444-40-440004-4000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ678-88-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-8-888-8-88000000000000000000000000000000000000000000000000000000000000

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