Finite Group Databasebeta

← Group #310092

Character table — Group #310092

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1111-1-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-1111111-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-11-1-11111-1-111-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111111111-1-1-1-11111-11-1-1-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1111111-1-1-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-111-1-1111111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111111-1-11111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11
χ17222222222-222-2-2-220000-22222-222220000002200-2-2-2-2000000000000000-200000000000
χ18222222222-222-2-2-220000-22222-2-2-2-2-2000000-2-200-2-222000000000000000200000000000
χ19222222222-222-2-2-220000-2-2-2-2-2-22222000000-2-20022-2-2000000000000000200000000000
χ20222222222-222-2-2-220000-2-2-2-2-2-2-2-2-2-200000022002222000000000000000-200000000000
χ2122222222-22-2-2222-22222-20000-2000022222200-2-20000-2-2000000000000-2000000000000
χ2222222222-22-2-2222-22222-20000-20000-2-2-2-2-2-200-2-20000220000000000002000000000000
χ2322222222-22-2-2222-2-2-2-2-2-20000-200002222-2-200220000-2-20000000000002000000000000
χ2422222222-22-2-2222-2-2-2-2-2-20000-20000-2-2-2-2220022000022000000000000-2000000000000
χ2522-22-2-2-220200-2-22022-2-2000000i2i2−i2−i222-2-22-2000000i2−i2000000i2i2−i2−i2i2i2−i2−i20000000000i2−i20
χ2622-22-2-2-220200-2-22022-2-2000000i2i2−i2−i2-2-222-22000000i2−i2000000i2i2−i2−i2−i2−i2i2i20000000000−i2i20
χ2722-22-2-2-220200-2-22022-2-2000000−i2−i2i2i222-2-22-2000000−i2i2000000−i2−i2i2i2−i2−i2i2i20000000000−i2i20
χ2822-22-2-2-220200-2-22022-2-2000000−i2−i2i2i2-2-222-22000000−i2i2000000−i2−i2i2i2i2i2−i2−i20000000000i2−i20
χ2922-22-2-2-220200-2-220-2-222000000i2i2−i2−i222-2-2-22000000i2−i2000000−i2−i2i2i2i2i2−i2−i20000000000−i2i20
χ3022-22-2-2-220200-2-220-2-222000000i2i2−i2−i2-2-2222-2000000i2−i2000000−i2−i2i2i2−i2−i2i2i20000000000i2−i20
χ3122-22-2-2-220200-2-220-2-222000000−i2−i2i2i222-2-2-22000000−i2i2000000i2i2−i2−i2−i2−i2i2i20000000000i2−i20
χ3222-22-2-2-220200-2-220-2-222000000−i2−i2i2i2-2-2222-2000000−i2i2000000i2i2−i2−i2i2i2−i2−i20000000000−i2i20
χ332-2222-2-2-2-202-20002000002i2i−2i−2i02-22-22−22−2002i−2i0000002−2i2i2−i2−i200002−22−200000000i2−i2000
χ342-2222-2-2-2-202-20002000002i2i−2i−2i02-22-2−22−22002i−2i000000−22−i2−i2i2i20000−22−2200000000−i2i2000
χ352-2222-2-2-2-202-20002000002i2i−2i−2i0-22-222−22−200−2i2i0000002−2i2i2−i2−i20000−22−2200000000−i2i2000
χ362-2222-2-2-2-202-20002000002i2i−2i−2i0-22-22−22−2200−2i2i000000−22−i2−i2i2i200002−22−200000000i2−i2000
χ372-2222-2-2-2-202-2000200000−2i−2i2i2i02-22-22−22−200−2i2i0000002−2−i2−i2i2i200002−22−200000000−i2i2000
χ382-2222-2-2-2-202-2000200000−2i−2i2i2i02-22-2−22−2200−2i2i000000−22i2i2−i2−i20000−22−2200000000i2−i2000
χ392-2222-2-2-2-202-2000200000−2i−2i2i2i0-22-222−22−2002i−2i0000002−2−i2−i2i2i20000−22−2200000000i2−i2000
χ402-2222-2-2-2-202-2000200000−2i−2i2i2i0-22-22−22−22002i−2i000000−22i2i2−i2−i200002−22−200000000−i2i2000
χ412-22-2-22-2222-2-2-22-222i−2i2i−2i20000-20000000000002i−2i0000002-22-20000000000002i−2i0000000
χ422-22-2-22-2222-2-2-22-222i−2i2i−2i20000-20000000000002i−2i000000-22-22000000000000−2i2i0000000
χ432-22-2-22-2222-2-2-22-22−2i2i−2i2i20000-2000000000000−2i2i0000002-22-2000000000000−2i2i0000000
χ442-22-2-22-2222-2-2-22-22−2i2i−2i2i20000-2000000000000−2i2i000000-22-220000000000002i−2i0000000
χ452-22-2-22-22-2222-22-2-22i−2i2i−2i-22i−2i2i−2i2000000000000−2i2i2i−2i0000000000000000002-2000000000
χ462-22-2-22-22-2222-22-2-22i−2i2i−2i-2−2i2i−2i2i2000000000000−2i2i−2i2i000000000000000000-22000000000
χ472-22-2-22-22-2222-22-2-2−2i2i−2i2i-22i−2i2i−2i20000000000002i−2i2i−2i000000000000000000-22000000000
χ482-22-2-22-22-2222-22-2-2−2i2i−2i2i-2−2i2i−2i2i20000000000002i−2i−2i2i0000000000000000002-2000000000
χ492-22-2-22-22-2-2222-22-2000022i−2i2i−2i-200000000000000−2i2i000000002i−2i2i−2i00000000002-200000
χ502-22-2-22-22-2-2222-22-2000022i−2i2i−2i-200000000000000−2i2i00000000−2i2i−2i2i0000000000-2200000
χ512-22-2-22-22-2-2222-22-200002−2i2i−2i2i-2000000000000002i−2i000000002i−2i2i−2i0000000000-2200000
χ522-22-2-22-22-2-2222-22-200002−2i2i−2i2i-2000000000000002i−2i00000000−2i2i−2i2i00000000002-200000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-4-4-44-4404-4000-4000004-4-440000000000000000000000000000000000000000000000
χ55444-4-4-44-4404-4000-400000-444-40000000000000000000000000000000000000000000000
χ56444-4-4-44-4-40-4400040000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ57444-4-4-44-4-40-440004000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ5844-44-4-4-440-40044-4000000000002i22i2−2i2−2i2000000000000−2i22i2000000000000000000000000000
χ5944-44-4-4-440-40044-400000000000−2i2−2i22i22i20000000000002i2−2i2000000000000000000000000000
χ604-4444-4-4-440-44000-40000000000000022−2222−220000000000−22220000000000000000000000000
χ614-4444-4-4-440-44000-400000000000000−2222−2222000000000022−220000000000000000000000000
χ624-44-4-44-444-4-4-44-4440000-400004000000000000000000000000000000000000000000000
χ634-4-44-444-40000000000000000002i2−2i2−2i22i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ644-4-44-444-40000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ654-4-44-444-4000000000000000000−2i22i22i2−2i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ664-4-44-444-4000000000000000000−2i22i22i2−2i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ674-4-4-44-44404004-4-404i−4i−4i4i000000000000000000000000000000000000000000000000000
χ684-4-4-44-44404004-4-40−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ694-4-4-44-4440-400-4440000000000000000000000000000000000022−22−222200000000000000000
χ704-4-4-44-4440-400-44400000000000000000000000000000000000−222222−2200000000000000000
χ7188-8-888-8-8000000000000000000000000000000000000000000000000000000000000000

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