Finite Group Databasebeta

← Group #310197

Character table — Group #310197

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488882
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-11111-1-1-1-1-1-1111-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-111111-1-111-1
χ911111111111111111-1-1-1-11111111111111-1-11111-1-111-1-1-1-11111111111-1-1-1-1-11-1-111-1-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1111-1-1111
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111-1-111-11111-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-11111-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-1-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-11111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-11111111-1-11-1-1-1-1-1-11
χ17222222222-2-22-2-222-200002222-2222200000022-2-2000000000000-2-2000000000-20000000
χ18222222222-2-22-2-222-200002222-2-2-2-2-2000000-2-2-2-20000000000002200000000020000000
χ19222222222-2-22-2-222-20000-2-2-2-2-22222000000-2-222000000000000-2-200000000020000000
χ20222222222-2-22-2-222-20000-2-2-2-2-2-2-2-2-2000000222200000000000022000000000-20000000
χ2122222222-222-222-2-2-222220000-200002222-2-2000022-2-200000000000000-2000000000000
χ2222222222-222-222-2-2-222220000-20000-2-2-2-2-2-20000-2-222000000000000002000000000000
χ2322222222-222-222-2-2-2-2-2-2-20000-200002222220000-2-2-2-2000000000000002000000000000
χ2422222222-222-222-2-2-2-2-2-2-20000-20000-2-2-2-2220000222200000000000000-2000000000000
χ2522-22-2-2-22-2002002-2000002i2i−2i−2i022-2-2i2i2−i2−i2002i−2i0000i2−i2000022−2−200i2i2−i2−i2000000002−2000
χ2622-22-2-2-22-2002002-2000002i2i−2i−2i022-2-2−i2−i2i2i2002i−2i0000−i2i20000−2−22200−i2−i2i2i200000000−22000
χ2722-22-2-2-22-2002002-2000002i2i−2i−2i0-2-222i2i2−i2−i200−2i2i0000i2−i2000022−2−200−i2−i2i2i200000000−22000
χ2822-22-2-2-22-2002002-2000002i2i−2i−2i0-2-222−i2−i2i2i200−2i2i0000−i2i20000−2−22200i2i2−i2−i2000000002−2000
χ2922-22-2-2-22-2002002-200000−2i−2i2i2i022-2-2i2i2−i2−i200−2i2i0000i2−i20000−2−22200i2i2−i2−i200000000−22000
χ3022-22-2-2-22-2002002-200000−2i−2i2i2i022-2-2−i2−i2i2i200−2i2i0000−i2i2000022−2−200−i2−i2i2i2000000002−2000
χ3122-22-2-2-22-2002002-200000−2i−2i2i2i0-2-222i2i2−i2−i2002i−2i0000i2−i20000−2−22200−i2−i2i2i2000000002−2000
χ3222-22-2-2-22-2002002-200000−2i−2i2i2i0-2-222−i2−i2i2i2002i−2i0000−i2i2000022−2−200i2i2−i2−i200000000−22000
χ332-22-2-22-22222-2-2-22-2-22i2i−2i−2i2i−2i2i−2i2000000002i−2i002i−2i00000000000000000002-20000000000
χ342-22-2-22-22222-2-2-22-2-22i2i−2i−2i−2i2i−2i2i2000000002i−2i00−2i2i0000000000000000000-220000000000
χ352-22-2-22-22222-2-2-22-2-2−2i−2i2i2i2i−2i2i−2i200000000−2i2i002i−2i0000000000000000000-220000000000
χ362-22-2-22-22222-2-2-22-2-2−2i−2i2i2i−2i2i−2i2i200000000−2i2i00−2i2i00000000000000000002-20000000000
χ372-22-2-22-222-2-2-2222-2200002i−2i2i−2i-2000000000000−2i2i000022-2-200000000000002i−2i00000000
χ382-22-2-22-222-2-2-2222-2200002i−2i2i−2i-2000000000000−2i2i0000-2-2220000000000000−2i2i00000000
χ392-22-2-22-222-2-2-2222-220000−2i2i−2i2i-20000000000002i−2i000022-2-20000000000000−2i2i00000000
χ402-22-2-22-222-2-2-2222-220000−2i2i−2i2i-20000000000002i−2i0000-2-22200000000000002i−2i00000000
χ412-22-2-22-22-2222-2-2-2222i2i−2i−2i0000-200000000−2i2i0000000000002i−2i2i−2i0000000000002-200000
χ422-22-2-22-22-2222-2-2-2222i2i−2i−2i0000-200000000−2i2i000000000000−2i2i−2i2i000000000000-2200000
χ432-22-2-22-22-2222-2-2-222−2i−2i2i2i0000-2000000002i−2i0000000000002i−2i2i−2i000000000000-2200000
χ442-22-2-22-22-2222-2-2-222−2i−2i2i2i0000-2000000002i−2i000000000000−2i2i−2i2i0000000000002-200000
χ452-2-2222-2-202-202-20002-22-200000i2−i2i2−i22i−2i2i−2i0000002i−2i00i2−i2i2−i20000i2−i22−22−200000000002−20
χ462-2-2222-2-202-202-20002-22-200000i2−i2i2−i2−2i2i−2i2i000000−2i2i00i2−i2i2−i20000i2−i2−22−220000000000−220
χ472-2-2222-2-202-202-20002-22-200000−i2i2−i2i22i−2i2i−2i0000002i−2i00−i2i2−i2i20000−i2i2−22−220000000000−220
χ482-2-2222-2-202-202-20002-22-200000−i2i2−i2i2−2i2i−2i2i000000−2i2i00−i2i2−i2i20000−i2i22−22−200000000002−20
χ492-2-2222-2-202-202-2000-22-2200000i2−i2i2−i22i−2i2i−2i000000−2i2i00−i2i2−i2i20000i2−i22−22−20000000000−220
χ502-2-2222-2-202-202-2000-22-2200000i2−i2i2−i2−2i2i−2i2i0000002i−2i00−i2i2−i2i20000i2−i2−22−2200000000002−20
χ512-2-2222-2-202-202-2000-22-2200000−i2i2−i2i22i−2i2i−2i000000−2i2i00i2−i2i2−i20000−i2i2−22−2200000000002−20
χ522-2-2222-2-202-202-2000-22-2200000−i2i2−i2i2−2i2i−2i2i0000002i−2i00i2−i2i2−i20000−i2i22−22−20000000000−220
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ5444-44-4-4-44400-400-44000000000000002i22i2−2i2−2i200000000−2i22i2000000000000000000000000000
χ5544-44-4-4-44400-400-4400000000000000−2i2−2i22i22i2000000002i2−2i2000000000000000000000000000
χ5644-4-4-444-404-40-440004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ5744-4-4-444-404-40-44000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ5844-4-4-444-40-4404-40000000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ5944-4-4-444-40-4404-4000000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ604-444-4-44-40000000000000000002i2−2i2−2i22i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ614-444-4-44-40000000000000000002i2−2i2−2i22i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ624-444-4-44-4000000000000000000−2i22i22i2−2i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ634-444-4-44-4000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ644-44-4-44-44-4-4-4444-44-4000000004000000000000000000000000000000000000000000000
χ654-4-4444-4-40-440-440000000000002i2−2i22i2−2i20000000000000000000000−2i22i200000000000000000
χ664-4-4444-4-40-440-44000000000000−2i22i2−2i22i200000000000000000000002i2−2i200000000000000000
χ674-4-4-44-444400400-4-4000000000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ684-4-4-44-444400400-4-400000000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ694-4-4-44-444-400-40044000004-4-440000000000000000000000000000000000000000000000
χ704-4-4-44-444-400-4004400000-444-40000000000000000000000000000000000000000000000
χ71888-88-8-8-8000000000000000000000000000000000000000000000000000000000000000

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