Finite Group Databasebeta

← Group #308080

Character table — Group #308080

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-111-1-1-1-11111111111-1-11-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1111-1-111-1
χ911111111111111111-1-1-1-11111111111111-1-111-1-11111111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-11-1-1-1-1111
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-11111-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-111-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-1111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1111-1-11111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-11111-1-1-1-1-1-11
χ172222222222-22-2-2-22-200002222-222220000002200-2-2000000-2-20000000000000-20000000
χ182222222222-22-2-2-22-200002222-2-2-2-2-2000000-2-200-2-200000022000000000000020000000
χ192222222222-22-2-2-22-20000-2-2-2-2-22222000000-2-20022000000-2-2000000000000020000000
χ202222222222-22-2-2-22-20000-2-2-2-2-2-2-2-2-2000000220022000000220000000000000-20000000
χ2122222222-2-22-2222-2-222220000-200002222-2-2002200-2-20000000000000000-20000000000
χ2222222222-2-22-2222-2-222220000-20000-2-2-2-2-2-200-2-20022000000000000000020000000000
χ2322222222-2-22-2222-2-2-2-2-2-20000-2000022222200-2-200-2-2000000000000000020000000000
χ2422222222-2-22-2222-2-2-2-2-2-20000-20000-2-2-2-222002200220000000000000000-20000000000
χ252222-2-2-2-2222-2-22-2-2222-2-20000-2000000002-20000000022-2-200000000002-200000000000
χ262222-2-2-2-2222-2-22-2-2222-2-20000-2000000002-200000000-2-2220000000000-2200000000000
χ272222-2-2-2-2222-2-22-2-22-2-2220000-200000000-220000000022-2-20000000000-2200000000000
χ282222-2-2-2-2222-2-22-2-22-2-2220000-200000000-2200000000-2-22200000000002-200000000000
χ292222-2-2-2-2-2-222-22-22-222-2-22i2i−2i−2i200000000-2200002i−2i00000000000000000002i−2i00000000
χ302222-2-2-2-2-2-222-22-22-222-2-2−2i−2i2i2i200000000-220000−2i2i0000000000000000000−2i2i00000000
χ312222-2-2-2-2-2-222-22-22-2-2-2222i2i−2i−2i2000000002-200002i−2i0000000000000000000−2i2i00000000
χ322222-2-2-2-2-2-222-22-22-2-2-222−2i−2i2i2i2000000002-20000−2i2i00000000000000000002i−2i00000000
χ332222-2-2-2-2-2-2-222-222200002i2i−2i−2i-200000000000000−2i2i0000000022-2-200000000002i−2i00000
χ342222-2-2-2-2-2-2-222-222200002i2i−2i−2i-200000000000000−2i2i00000000-2-2220000000000−2i2i00000
χ352222-2-2-2-2-2-2-222-22220000−2i−2i2i2i-2000000000000002i−2i0000000022-2-20000000000−2i2i00000
χ362222-2-2-2-2-2-2-222-22220000−2i−2i2i2i-2000000000000002i−2i00000000-2-22200000000002i−2i00000
χ3722-2-2-2-2222-202000-2000002i−2i2i−2i022-2-222−2−2002i−2i00002−2i2−i2i2−i200000022−2−200000000i2−i2000
χ3822-2-2-2-2222-202000-2000002i−2i2i−2i022-2-2−2−222002i−2i0000−22−i2i2−i2i2000000−2−22200000000−i2i2000
χ3922-2-2-2-2222-202000-2000002i−2i2i−2i0-2-22222−2−200−2i2i00002−2i2−i2i2−i2000000−2−22200000000−i2i2000
χ4022-2-2-2-2222-202000-2000002i−2i2i−2i0-2-222−2−22200−2i2i0000−22−i2i2−i2i200000022−2−200000000i2−i2000
χ4122-2-2-2-2222-202000-200000−2i2i−2i2i022-2-222−2−200−2i2i00002−2−i2i2−i2i200000022−2−200000000−i2i2000
χ4222-2-2-2-2222-202000-200000−2i2i−2i2i022-2-2−2−22200−2i2i0000−22i2−i2i2−i2000000−2−22200000000i2−i2000
χ4322-2-2-2-2222-202000-200000−2i2i−2i2i0-2-22222−2−2002i−2i00002−2−i2i2−i2i2000000−2−22200000000i2−i2000
χ4422-2-2-2-2222-202000-200000−2i2i−2i2i0-2-222−2−222002i−2i0000−22i2−i2i2−i200000022−2−200000000−i2i2000
χ452-22-22-22-20020-2-22002i−2i2i−2i00000i2−i2i2−i22-22-200002i−2i00000000i2−i22−22−2i2−i2i2−i200000000002−20
χ462-22-22-22-20020-2-22002i−2i2i−2i00000i2−i2i2−i2-22-220000−2i2i00000000i2−i22−22−2−i2i2−i2i20000000000−220
χ472-22-22-22-20020-2-22002i−2i2i−2i00000−i2i2−i2i22-22-200002i−2i00000000−i2i2−22−22−i2i2−i2i20000000000−220
χ482-22-22-22-20020-2-22002i−2i2i−2i00000−i2i2−i2i2-22-220000−2i2i00000000−i2i2−22−22i2−i2i2−i200000000002−20
χ492-22-22-22-20020-2-2200−2i2i−2i2i00000i2−i2i2−i22-22-20000−2i2i00000000i2−i2−22−22i2−i2i2−i20000000000−220
χ502-22-22-22-20020-2-2200−2i2i−2i2i00000i2−i2i2−i2-22-2200002i−2i00000000i2−i2−22−22−i2i2−i2i200000000002−20
χ512-22-22-22-20020-2-2200−2i2i−2i2i00000−i2i2−i2i22-22-20000−2i2i00000000−i2i22−22−2−i2i2−i2i200000000002−20
χ522-22-22-22-20020-2-2200−2i2i−2i2i00000−i2i2−i2i2-22-2200002i−2i00000000−i2i22−22−2i2−i2i2−i20000000000−220
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ544444-4-4-4-444-4-44-44-4-4000000004000000000000000000000000000000000000000000000
χ5544-4-444-4-44-40-4000400000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ5644-4-444-4-44-40-400040000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ5744-4-444-4-4-4404000-4000004-4-440000000000000000000000000000000000000000000000
χ5844-4-444-4-4-4404000-400000-444-40000000000000000000000000000000000000000000000
χ5944-4-4-4-444-440-40004000000000000002222−22−2200000000−2222000000000000000000000000000
χ6044-4-4-4-444-440-4000400000000000000−22−2222220000000022−22000000000000000000000000000
χ614-44-44-44-400-4044-4000000000002i2−2i22i2−2i2000000000000000000−2i22i2000000000000000000000
χ624-44-44-44-400-4044-400000000000−2i22i2−2i22i20000000000000000002i2−2i2000000000000000000000
χ634-44-4-44-4400404-4-4004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ644-44-4-44-4400404-4-400−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ654-44-4-44-4400-40-4440000000000000000000000000000000000022−22−222200000000000000000
χ664-44-4-44-4400-40-44400000000000000000000000000000000000−222222−2200000000000000000
χ674-4-44-444-40000000000000000002i2−2i2−2i22i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ684-4-44-444-40000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ694-4-44-444-4000000000000000000−2i22i22i2−2i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ704-4-44-444-4000000000000000000−2i22i22i2−2i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ718-8-888-8-88000000000000000000000000000000000000000000000000000000000000000

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