Finite Group Databasebeta

← Group #306559

Character table — Group #306559

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111
χ5111111111111111111111-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-11111-1-1-11-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111-1-1-111-1-111-1
χ911111111111111111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-111-1-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1111
χ1111111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-1-1-1111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1111-1-11111-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-111111-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-111111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111111-1-1111-1-1-1-1-1-11
χ17222222222-22-22-22-2-200002222-222220000-2-2220000-2-200000000000000-2000000000000
χ18222222222-22-22-22-2-200002222-2-2-2-2-20000-2-2-2-2000022000000000000002000000000000
χ19222222222-22-22-22-2-20000-2-2-2-2-22222000022-2-20000-2-2000000000000002000000000000
χ20222222222-22-22-22-2-20000-2-2-2-2-2-2-2-2-20000222200002200000000000000-2000000000000
χ2122222222-22-22-22-22-222220000-2000022220000-2-22200-2-2000000000000000-2000000000
χ2222222222-22-22-22-22-222220000-20000-2-2-2-20000-2-2-2-200220000000000000002000000000
χ2322222222-22-22-22-22-2-2-2-2-20000-200002222000022-2-200-2-20000000000000002000000000
χ2422222222-22-22-22-22-2-2-2-2-20000-20000-2-2-2-2000022220022000000000000000-2000000000
χ25222-2-2-22-22-2-222-2-22-22i2i−2i−2i000020000000000002i−2i000000000022-2-200000000002i−2i00000
χ26222-2-2-22-22-2-222-2-22-22i2i−2i−2i000020000000000002i−2i0000000000-2-2220000000000−2i2i00000
χ27222-2-2-22-22-2-222-2-22-2−2i−2i2i2i00002000000000000−2i2i000000000022-2-20000000000−2i2i00000
χ28222-2-2-22-22-2-222-2-22-2−2i−2i2i2i00002000000000000−2i2i0000000000-2-22200000000002i−2i00000
χ29222-2-2-22-2-222-2-222-2-2000022-2-22000000002-200000000002i2i−2i−2i0000000002i−2i0000000000
χ30222-2-2-22-2-222-2-222-2-2000022-2-22000000002-20000000000−2i−2i2i2i000000000−2i2i0000000000
χ31222-2-2-22-2-222-2-222-2-20000-2-222200000000-2200000000002i2i−2i−2i000000000−2i2i0000000000
χ32222-2-2-22-2-222-2-222-2-20000-2-222200000000-220000000000−2i−2i2i2i0000000002i−2i0000000000
χ33222-2-2-22-2-2-222-2-22222i2i−2i−2i22-2-2-200000000-2200−2i2i00000000000000000000002i−2i0000000
χ34222-2-2-22-2-2-222-2-22222i2i−2i−2i-2-222-2000000002-200−2i2i0000000000000000000000−2i2i0000000
χ35222-2-2-22-2-2-222-2-2222−2i−2i2i2i22-2-2-200000000-22002i−2i0000000000000000000000−2i2i0000000
χ36222-2-2-22-2-2-222-2-2222−2i−2i2i2i-2-222-2000000002-2002i−2i00000000000000000000002i−2i0000000
χ3722-222-2-2-2-20-202020000002i−2i2i−2i022-2-222−2−2002i−2i0000002−20000i2−i2i2−i222−2−200000000i2−i2000
χ3822-222-2-2-2-20-202020000002i−2i2i−2i022-2-2−2−222002i−2i000000−220000−i2i2−i2i2−2−22200000000−i2i2000
χ3922-222-2-2-2-20-202020000002i−2i2i−2i0-2-22222−2−200−2i2i0000002−20000i2−i2i2−i2−2−22200000000−i2i2000
χ4022-222-2-2-2-20-202020000002i−2i2i−2i0-2-222−2−22200−2i2i000000−220000−i2i2−i2i222−2−200000000i2−i2000
χ4122-222-2-2-2-20-20202000000−2i2i−2i2i022-2-222−2−200−2i2i0000002−20000−i2i2−i2i222−2−200000000−i2i2000
χ4222-222-2-2-2-20-20202000000−2i2i−2i2i022-2-2−2−22200−2i2i000000−220000i2−i2i2−i2−2−22200000000i2−i2000
χ4322-222-2-2-2-20-20202000000−2i2i−2i2i0-2-22222−2−2002i−2i0000002−20000−i2i2−i2i2−2−22200000000i2−i2000
χ4422-222-2-2-2-20-20202000000−2i2i−2i2i0-2-222−2−222002i−2i000000−220000i2−i2i2−i222−2−200000000−i2i2000
χ452-2-22-222-2020-20-20202i−2i2i−2i00000i2−i2i2−i22-22-20000002i−2ii2−i2002−22−20000i2−i2i2−i200000000002−20
χ462-2-22-222-2020-20-20202i−2i2i−2i00000i2−i2i2−i2-22-22000000−2i2ii2−i2002−22−20000−i2i2−i2i20000000000−220
χ472-2-22-222-2020-20-20202i−2i2i−2i00000−i2i2−i2i22-22-20000002i−2i−i2i200−22−220000−i2i2−i2i20000000000−220
χ482-2-22-222-2020-20-20202i−2i2i−2i00000−i2i2−i2i2-22-22000000−2i2i−i2i200−22−220000i2−i2i2−i200000000002−20
χ492-2-22-222-2020-20-2020−2i2i−2i2i00000i2−i2i2−i22-22-2000000−2i2ii2−i200−22−220000i2−i2i2−i20000000000−220
χ502-2-22-222-2020-20-2020−2i2i−2i2i00000i2−i2i2−i2-22-220000002i−2ii2−i200−22−220000−i2i2−i2i200000000002−20
χ512-2-22-222-2020-20-2020−2i2i−2i2i00000−i2i2−i2i22-22-2000000−2i2i−i2i2002−22−20000−i2i2−i2i200000000002−20
χ522-2-22-222-2020-20-2020−2i2i−2i2i00000−i2i2−i2i2-22-220000002i−2i−i2i2002−22−20000i2−i2i2−i20000000000−220
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-4-44-444-4-444-4-4400000000-4000000000000000000000000000000000000000000000
χ5544-444-4-4-44040-40-40000000000000002222−22−220000000000−22220000000000000000000000000
χ5644-444-4-4-44040-40-4000000000000000−22−222222000000000022−220000000000000000000000000
χ5744-4-4-44-4440-40-4040000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ5844-4-4-44-4440-40-404000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ5944-4-4-44-44-404040-4000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ6044-4-4-44-44-404040-400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ614-444-4-4-440000000000000000002i2−2i2−2i22i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ624-444-4-4-440000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ634-444-4-4-44000000000000000000−2i22i22i2−2i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ644-444-4-4-44000000000000000000−2i22i22i2−2i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ654-4-44-444-40-404040-400000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ664-4-44-444-40-404040-40000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ674-4-4-44-44404040-40-40000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ684-4-4-44-44404040-40-4000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ694-4-4-44-4440-40-4040404-4-4400000000000000000000000000000000000000000000000000
χ704-4-4-44-4440-40-404040-444-400000000000000000000000000000000000000000000000000
χ718-88-888-8-8000000000000000000000000000000000000000000000000000000000000000

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