Finite Group Databasebeta

← Group #310121

Character table — Group #310121

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-11-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-11-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1111-1-111-1
χ91111111111111111-1-1-1-111111111111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-11111-1-1-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-1-1-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-11111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-11
χ17222222222-22-2-222-22222-20000-200002222220000-2-200-2-20000000000000000-200000000
χ18222222222-22-2-222-22222-20000-20000-2-2-2-2-2-20000-2-200220000000000000000200000000
χ19222222222-22-2-222-2-2-2-2-2-20000-200002222-2-200002200-2-20000000000000000200000000
χ20222222222-22-2-222-2-2-2-2-2-20000-20000-2-2-2-22200002200220000000000000000-200000000
χ2122222222-22-222-2-220000-22222-22222000000-2-22200-2-20000000000000000000-20000000
χ2222222222-22-222-2-220000-22222-2-2-2-2-2000000-2-2-2-20022000000000000000000020000000
χ2322222222-22-222-2-220000-2-2-2-2-2-2222200000022-2-200-2-2000000000000000000020000000
χ2422222222-22-222-2-220000-2-2-2-2-2-2-2-2-2-2000000222200220000000000000000000-20000000
χ252-22-2-2-2220202-200-20000022-2-202i2i−2i−2i22−2−200002i−2i00002−222−2−20000i2i2−i2−i200000000i2−i2000
χ262-22-2-2-2220202-200-20000022-2-202i2i−2i−2i−2−22200002i−2i0000−22−2−2220000−i2−i2i2i200000000−i2i2000
χ272-22-2-2-2220202-200-20000022-2-20−2i−2i2i2i22−2−20000−2i2i00002−222−2−20000−i2−i2i2i200000000−i2i2000
χ282-22-2-2-2220202-200-20000022-2-20−2i−2i2i2i−2−2220000−2i2i0000−22−2−2220000i2i2−i2−i200000000i2−i2000
χ292-22-2-2-2220202-200-200000-2-22202i2i−2i−2i22−2−20000−2i2i00002−2−2−2220000i2i2−i2−i200000000−i2i2000
χ302-22-2-2-2220202-200-200000-2-22202i2i−2i−2i−2−2220000−2i2i0000−2222−2−20000−i2−i2i2i200000000i2−i2000
χ312-22-2-2-2220202-200-200000-2-2220−2i−2i2i2i22−2−200002i−2i00002−2−2−2220000−i2−i2i2i200000000i2−i2000
χ322-22-2-2-2220202-200-200000-2-2220−2i−2i2i2i−2−22200002i−2i0000−2222−2−20000i2i2−i2−i200000000−i2i2000
χ332-2-222-2-2220200-2-202i2i−2i−2i0000002−22−22i−2i2i−2i2-20000002−2000000i2i2−i2−i2i2−i2i2−i200000000002−20
χ342-2-222-2-2220200-2-202i2i−2i−2i0000002−22−2−2i2i−2i2i-220000002−2000000i2i2−i2−i2−i2i2−i2i20000000000−220
χ352-2-222-2-2220200-2-202i2i−2i−2i000000−22−222i−2i2i−2i2-2000000−22000000−i2−i2i2i2−i2i2−i2i20000000000−220
χ362-2-222-2-2220200-2-202i2i−2i−2i000000−22−22−2i2i−2i2i-22000000−22000000−i2−i2i2i2i2−i2i2−i200000000002−20
χ372-2-222-2-2220200-2-20−2i−2i2i2i0000002−22−22i−2i2i−2i-220000002−2000000−i2−i2i2i2i2−i2i2−i20000000000−220
χ382-2-222-2-2220200-2-20−2i−2i2i2i0000002−22−2−2i2i−2i2i2-20000002−2000000−i2−i2i2i2−i2i2−i2i200000000002−20
χ392-2-222-2-2220200-2-20−2i−2i2i2i000000−22−222i−2i2i−2i-22000000−22000000i2i2−i2−i2−i2i2−i2i200000000002−20
χ402-2-222-2-2220200-2-20−2i−2i2i2i000000−22−22−2i2i−2i2i2-2000000−22000000i2i2−i2−i2i2−i2i2−i20000000000−220
χ412-2-2-2222-222-2-2-22-222i−2i2i−2i20000-2000000000000002i−2i00002-22-2000000000000002i−2i00000
χ422-2-2-2222-222-2-2-22-222i−2i2i−2i20000-2000000000000002i−2i0000-22-2200000000000000−2i2i00000
χ432-2-2-2222-222-2-2-22-22−2i2i−2i2i20000-200000000000000−2i2i00002-22-200000000000000−2i2i00000
χ442-2-2-2222-222-2-2-22-22−2i2i−2i2i20000-200000000000000−2i2i0000-22-22000000000000002i−2i00000
χ452-2-2-2222-22-2-2222-2-22i−2i2i−2i-22i−2i2i−2i200000000002i−2i00−2i2i0000000000000000002-2000000000
χ462-2-2-2222-22-2-2222-2-22i−2i2i−2i-2−2i2i−2i2i20000000000−2i2i00−2i2i000000000000000000-22000000000
χ472-2-2-2222-22-2-2222-2-2−2i2i−2i2i-22i−2i2i−2i200000000002i−2i002i−2i000000000000000000-22000000000
χ482-2-2-2222-22-2-2222-2-2−2i2i−2i2i-2−2i2i−2i2i20000000000−2i2i002i−2i0000000000000000002-2000000000
χ492-2-2-2222-2-2-2222-22-2000022i−2i2i−2i-20000000000−2i2i0000000000002i−2i2i−2i00002-200000000000
χ502-2-2-2222-2-2-2222-22-2000022i−2i2i−2i-20000000000−2i2i000000000000−2i2i−2i2i0000-2200000000000
χ512-2-2-2222-2-2-2222-22-200002−2i2i−2i2i-200000000002i−2i0000000000002i−2i2i−2i0000-2200000000000
χ522-2-2-2222-2-2-2222-22-200002−2i2i−2i2i-200000000002i−2i000000000000−2i2i−2i2i00002-200000000000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-44-4-4-440-400-4404-4-44000000000000000000000000000000000000000000000000000
χ55444-44-4-4-440-400-440-444-4000000000000000000000000000000000000000000000000000
χ56444-44-4-4-4-404004-40000000000000000000000000000000000022−22−222200000000000000000
χ57444-44-4-4-4-404004-400000000000000000000000000000000000−222222−2200000000000000000
χ5844-44-4-44-4040-4400-400000000000000000000000000000022−22−2222000000000000000000000
χ5944-44-4-44-4040-4400-4000000000000000000000000000000−222222−22000000000000000000000
χ6044-44-4-44-40-404-4004000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ6144-44-4-44-40-404-400400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ6244-4-4-44-440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ6344-4-4-44-440000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ6444-4-4-44-44000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ6544-4-4-44-44000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ664-44-4-4-4440-40-44004000000000000002222−22−220000000000−22220000000000000000000000000
χ674-44-4-4-4440-40-4400400000000000000−22−222222000000000022−220000000000000000000000000
χ684-4-444-4-44-40-400440000000000022−2222−22000000000000−2222000000000000000000000000000
χ694-4-444-4-44-40-4004400000000000−2222−222200000000000022−22000000000000000000000000000
χ704-4-4-4444-4-444-4-4-4440000-400004000000000000000000000000000000000000000000000
χ718-888-88-8-8000000000000000000000000000000000000000000000000000000000000000

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