Finite Group Databasebeta

← Group #308114

Character table — Group #308114

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-111-1-1-1-1111111111111-1-11-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-1-1-111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1111-1-111-1
χ911111111111111111-1-1-1-11111111111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1
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
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111111-1-1-11111-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-111-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1111-1111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-111-1111-1-11111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11111-1-1-1-1-1-11
χ172222222222-22-2-2-22-200002222-22222000000-2-22200000000-2-20000000000000-20000000
χ182222222222-22-2-2-22-200002222-2-2-2-2-2000000-2-2-2-20000000022000000000000020000000
χ192222222222-22-2-2-22-20000-2-2-2-2-2222200000022-2-200000000-2-2000000000000020000000
χ202222222222-22-2-2-22-20000-2-2-2-2-2-2-2-2-2000000222200000000220000000000000-20000000
χ2122222222-2-22-2222-2-222220000-200002222-2-20000220000-2-2000000000000-20000000000
χ2222222222-2-22-2222-2-222220000-20000-2-2-2-2-2-20000-2-200002200000000000020000000000
χ2322222222-2-22-2222-2-2-2-2-2-20000-200002222220000-2-20000-2-200000000000020000000000
χ2422222222-2-22-2222-2-2-2-2-2-20000-20000-2-2-2-222000022000022000000000000-20000000000
χ25222-2-2-22-22-20-20002000002i2i−2i−2i02i2i−2i−2i22−2−200002-200i2i2−i2−i22−2000000i2i2−i2−i2000000002−2000
χ26222-2-2-22-22-20-20002000002i2i−2i−2i02i2i−2i−2i−2−22200002-200−i2−i2i2i2−22000000−i2−i2i2i200000000−22000
χ27222-2-2-22-22-20-20002000002i2i−2i−2i0−2i−2i2i2i22−2−20000-2200i2i2−i2−i22−2000000−i2−i2i2i200000000−22000
χ28222-2-2-22-22-20-20002000002i2i−2i−2i0−2i−2i2i2i−2−2220000-2200−i2−i2i2i2−22000000i2i2−i2−i2000000002−2000
χ29222-2-2-22-22-20-2000200000−2i−2i2i2i02i2i−2i−2i22−2−20000-2200−i2−i2i2i22−2000000i2i2−i2−i200000000−22000
χ30222-2-2-22-22-20-2000200000−2i−2i2i2i02i2i−2i−2i−2−2220000-2200i2i2−i2−i2−22000000−i2−i2i2i2000000002−2000
χ31222-2-2-22-22-20-2000200000−2i−2i2i2i0−2i−2i2i2i22−2−200002-200−i2−i2i2i22−2000000−i2−i2i2i2000000002−2000
χ32222-2-2-22-22-20-2000200000−2i−2i2i2i0−2i−2i2i2i−2−22200002-200i2i2−i2−i2−22000000i2i2−i2−i200000000−22000
χ3322-22-22-2-200-20-2220022-2-2000002−22−22i−2i2i−2i0000002i−2i0000002−222−2−2i2−i2i2−i20000000000i2−i20
χ3422-22-22-2-200-20-2220022-2-2000002−22−2−2i2i−2i2i000000−2i2i0000002−222−2−2−i2i2−i2i20000000000−i2i20
χ3522-22-22-2-200-20-2220022-2-200000−22−222i−2i2i−2i0000002i−2i000000−22−2−222−i2i2−i2i20000000000−i2i20
χ3622-22-22-2-200-20-2220022-2-200000−22−22−2i2i−2i2i000000−2i2i000000−22−2−222i2−i2i2−i20000000000i2−i20
χ3722-22-22-2-200-20-22200-2-222000002−22−22i−2i2i−2i000000−2i2i0000002−2−2−222i2−i2i2−i20000000000−i2i20
χ3822-22-22-2-200-20-22200-2-222000002−22−2−2i2i−2i2i0000002i−2i0000002−2−2−222−i2i2−i2i20000000000i2−i20
χ3922-22-22-2-200-20-22200-2-22200000−22−222i−2i2i−2i000000−2i2i000000−2222−2−2−i2i2−i2i20000000000i2−i20
χ4022-22-22-2-200-20-22200-2-22200000−22−22−2i2i−2i2i0000002i−2i000000−2222−2−2i2−i2i2−i20000000000−i2i20
χ412-2222-2-2-2222-2-22-2-222-22-20000-2000000002-20000002-22-20000000000002-200000000000
χ422-2222-2-2-2222-2-22-2-222-22-20000-2000000002-2000000-22-22000000000000-2200000000000
χ432-2222-2-2-2222-2-22-2-22-22-220000-200000000-220000002-22-2000000000000-2200000000000
χ442-2222-2-2-2222-2-22-2-22-22-220000-200000000-22000000-22-220000000000002-200000000000
χ452-2222-2-2-2-2-222-22-22-22-22-22i−2i2i−2i200000000-222i−2i000000000000000000000002i−2i00000000
χ462-2222-2-2-2-2-222-22-22-22-22-2−2i2i−2i2i200000000-22−2i2i00000000000000000000000−2i2i00000000
χ472-2222-2-2-2-2-222-22-22-2-22-222i−2i2i−2i2000000002-22i−2i00000000000000000000000−2i2i00000000
χ482-2222-2-2-2-2-222-22-22-2-22-22−2i2i−2i2i2000000002-2−2i2i000000000000000000000002i−2i00000000
χ492-2222-2-2-2-2-2-222-222200002i−2i2i−2i-20000000000−2i2i0000000000002-22-200000000002i−2i00000
χ502-2222-2-2-2-2-2-222-222200002i−2i2i−2i-20000000000−2i2i000000000000-22-220000000000−2i2i00000
χ512-2222-2-2-2-2-2-222-22220000−2i2i−2i2i-200000000002i−2i0000000000002-22-20000000000−2i2i00000
χ522-2222-2-2-2-2-2-222-22220000−2i2i−2i2i-200000000002i−2i000000000000-22-2200000000002i−2i00000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-4-44-4-4404000-4000000000000002222−22−22000000000000−222200000000000000000000000
χ55444-4-4-44-4-4404000-400000000000000−22−22222200000000000022−2200000000000000000000000
χ5644-44-44-4-400404-4-40000000000022−2222−22000000000000000000−2222000000000000000000000
χ5744-44-44-4-400404-4-400000000000−2222−222200000000000000000022−22000000000000000000000
χ5844-4-44-4-440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ5944-4-44-4-440000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ6044-4-44-4-44000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ6144-4-44-4-44000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ624-4444-4-4-444-4-44-44-4-4000000004000000000000000000000000000000000000000000000
χ634-44-4-44-444-404000-4000000000000000000000000002i2−2i2−2i22i20000000000000000000000000
χ644-44-4-44-444-404000-400000000000000000000000000−2i22i22i2−2i20000000000000000000000000
χ654-44-4-44-44-440-40004000004-4-440000000000000000000000000000000000000000000000
χ664-44-4-44-44-440-4000400000-444-40000000000000000000000000000000000000000000000
χ674-4-44-4-4440040-4-440000000000000000000000000000000000022−22−222200000000000000000
χ684-4-44-4-4440040-4-4400000000000000000000000000000000000−222222−2200000000000000000
χ694-4-44-4-44400-4044-4004-4-4400000000000000000000000000000000000000000000000000
χ704-4-44-4-44400-4044-400-444-400000000000000000000000000000000000000000000000000
χ718-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000

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