Finite Group Databasebeta

← Group #310190

Character table — Group #310190

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-111-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1-11111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-111-1-1111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111-1-1-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1111111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111111-1-1111-1-1-1-1-1-11
χ17222222222-22-2-222-20000-22222-2000022220000-2-22200-2-2000000000000-2000000000000
χ18222222222-22-2-222-20000-22222-20000-2-2-2-20000-2-2-2-200220000000000002000000000000
χ19222222222-22-2-222-20000-2-2-2-2-2-200002222000022-2-200-2-20000000000002000000000000
χ20222222222-22-2-222-20000-2-2-2-2-2-20000-2-2-2-2000022220022000000000000-2000000000000
χ2122222222-22-222-2-222222-20000-222220000-2-2220000-2-20000000000000000000-20000000
χ2222222222-22-222-2-222222-20000-2-2-2-2-20000-2-2-2-2000022000000000000000000020000000
χ2322222222-22-222-2-22-2-2-2-2-20000-22222000022-2-20000-2-2000000000000000000020000000
χ2422222222-22-222-2-22-2-2-2-2-20000-2-2-2-2-2000022220000220000000000000000000-20000000
χ2522-2-22-2-22-202002-200000022-2-20i2i2−i2−i22i2i−2i−2i0000002i−2ii2−i2000000i2i2−i2−i222−2−200000000002−20
χ2622-2-22-2-22-202002-200000022-2-20i2i2−i2−i2−2i−2i2i2i000000−2i2ii2−i2000000i2i2−i2−i2−2−2220000000000−220
χ2722-2-22-2-22-202002-200000022-2-20−i2−i2i2i22i2i−2i−2i0000002i−2i−i2i2000000−i2−i2i2i2−2−2220000000000−220
χ2822-2-22-2-22-202002-200000022-2-20−i2−i2i2i2−2i−2i2i2i000000−2i2i−i2i2000000−i2−i2i2i222−2−200000000002−20
χ2922-2-22-2-22-202002-2000000-2-2220i2i2−i2−i22i2i−2i−2i000000−2i2ii2−i2000000−i2−i2i2i222−2−20000000000−220
χ3022-2-22-2-22-202002-2000000-2-2220i2i2−i2−i2−2i−2i2i2i0000002i−2ii2−i2000000−i2−i2i2i2−2−22200000000002−20
χ3122-2-22-2-22-202002-2000000-2-2220−i2−i2i2i22i2i−2i−2i000000−2i2i−i2i2000000i2i2−i2−i2−2−22200000000002−20
χ3222-2-22-2-22-202002-2000000-2-2220−i2−i2i2i2−2i−2i2i2i0000002i−2i−i2i2000000i2i2−i2−i222−2−20000000000−220
χ332-2-22-2-2220202-200-222-2-20000002i−2i2i−2i2−22−2002i−2i0000002−222−2−20000i2−i2i2−i200000000i2−i2000
χ342-2-22-2-2220202-200-222-2-20000002i−2i2i−2i−22−22002i−2i000000−22−2−2220000−i2i2−i2i200000000−i2i2000
χ352-2-22-2-2220202-200-222-2-2000000−2i2i−2i2i2−22−200−2i2i0000002−222−2−20000−i2i2−i2i200000000−i2i2000
χ362-2-22-2-2220202-200-222-2-2000000−2i2i−2i2i−22−2200−2i2i000000−22−2−2220000i2−i2i2−i200000000i2−i2000
χ372-2-22-2-2220202-200-2-2-2220000002i−2i2i−2i2−22−200−2i2i0000002−2−2−2220000i2−i2i2−i200000000−i2i2000
χ382-2-22-2-2220202-200-2-2-2220000002i−2i2i−2i−22−2200−2i2i000000−2222−2−20000−i2i2−i2i200000000i2−i2000
χ392-2-22-2-2220202-200-2-2-222000000−2i2i−2i2i2−22−2002i−2i0000002−2−2−2220000−i2i2−i2i200000000i2−i2000
χ402-2-22-2-2220202-200-2-2-222000000−2i2i−2i2i−22−22002i−2i000000−2222−2−20000i2−i2i2−i200000000−i2i2000
χ412-2-2-2222-222-2-2-22-22000022i−2i2i−2i-20000000000002i−2i0000002-22-2000000000000002i−2i00000
χ422-2-2-2222-222-2-2-22-22000022i−2i2i−2i-20000000000002i−2i000000-22-2200000000000000−2i2i00000
χ432-2-2-2222-222-2-2-22-2200002−2i2i−2i2i-2000000000000−2i2i0000002-22-200000000000000−2i2i00000
χ442-2-2-2222-222-2-2-22-2200002−2i2i−2i2i-2000000000000−2i2i000000-22-22000000000000002i−2i00000
χ452-2-2-2222-22-2-2222-2-22i−2i2i−2i-22i−2i2i−2i2000000002i−2i00−2i2i0000000000000000000002-200000000
χ462-2-2-2222-22-2-2222-2-22i−2i2i−2i-2−2i2i−2i2i2000000002i−2i002i−2i000000000000000000000-2200000000
χ472-2-2-2222-22-2-2222-2-2−2i2i−2i2i-22i−2i2i−2i200000000−2i2i00−2i2i000000000000000000000-2200000000
χ482-2-2-2222-22-2-2222-2-2−2i2i−2i2i-2−2i2i−2i2i200000000−2i2i002i−2i0000000000000000000002-200000000
χ492-2-2-2222-2-2-2222-22-22i−2i2i−2i20000-200000000−2i2i000000000000002i−2i2i−2i000002-20000000000
χ502-2-2-2222-2-2-2222-22-22i−2i2i−2i20000-200000000−2i2i00000000000000−2i2i−2i2i00000-220000000000
χ512-2-2-2222-2-2-2222-22-2−2i2i−2i2i20000-2000000002i−2i000000000000002i−2i2i−2i00000-220000000000
χ522-2-2-2222-2-2-2222-22-2−2i2i−2i2i20000-2000000002i−2i00000000000000−2i2i−2i2i000002-20000000000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-4-44-4040-4400-400000000000000000000000000000022−22−2222000000000000000000000
χ55444-4-4-44-4040-4400-4000000000000000000000000000000−222222−22000000000000000000000
χ56444-4-4-44-40-404-40044i−4i−4i4i000000000000000000000000000000000000000000000000000
χ57444-4-4-44-40-404-4004−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ5844-4-44-4-4440-400-44000000000002i22i2−2i2−2i2000000000000−2i22i2000000000000000000000000000
χ5944-4-44-4-4440-400-4400000000000−2i2−2i22i22i20000000000002i2−2i2000000000000000000000000000
χ604-4444-4-4-440400-4-40000000000000000000000000000000000022−22−222200000000000000000
χ614-4444-4-4-440400-4-400000000000000000000000000000000000−222222−2200000000000000000
χ624-4444-4-4-4-40-400440000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ634-4444-4-4-4-40-40044000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ644-44-4-44-4400000000000000000022−22−22222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ654-44-4-44-4400000000000000000022−22−2222−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ664-44-4-44-44000000000000000000−222222−222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ674-44-4-44-44000000000000000000−222222−22−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ684-4-44-4-4440-40-440040000000000000022−2222−220000000000−22220000000000000000000000000
χ694-4-44-4-4440-40-4400400000000000000−2222−2222000000000022−220000000000000000000000000
χ704-4-4-4444-4-444-4-4-4440000-400004000000000000000000000000000000000000000000000
χ7188-88-88-8-8000000000000000000000000000000000000000000000000000000000000000

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