Finite Group Databasebeta

← Group #305343

Character table — Group #305343

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1111111-1-1-1-111-1-111-11-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-11-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-11111-1111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-11-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111111-1-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1111-11111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111111111-1-1-1-111-1-1-1-11
χ172222222222-2-22-22-2-200002222-20000222200-2-20022000000-2-2000000000000000-200000
χ182222222222-2-22-22-2-200002222-20000-2-2-2-200-2-200-2-200000022000000000000000200000
χ192222222222-2-22-22-2-20000-2-2-2-2-200002222002200-2-2000000-2-2000000000000000200000
χ202222222222-2-22-22-2-20000-2-2-2-2-20000-2-2-2-20022002200000022000000000000000-200000
χ2122222222-2-222-22-22-222220000-222220000-2-2002200-2-200000000000000000000-2000000
χ2222222222-2-222-22-22-222220000-2-2-2-2-20000-2-200-2-20022000000000000000000002000000
χ2322222222-2-222-22-22-2-2-2-2-20000-2222200002200-2-200-2-2000000000000000000002000000
χ2422222222-2-222-22-22-2-2-2-2-20000-2-2-2-2-20000220022002200000000000000000000-2000000
χ25222-2-22-2-2002-20-20202i2i−2i−2i000002i2i−2i−2i22−2−200002-2000000002−2i2i2−i2−i2i2i2−i2−i2000000002−2000
χ26222-2-22-2-2002-20-20202i2i−2i−2i000002i2i−2i−2i−2−22200002-200000000−22−i2−i2i2i2−i2−i2i2i200000000−22000
χ27222-2-22-2-2002-20-20202i2i−2i−2i00000−2i−2i2i2i22−2−20000-22000000002−2i2i2−i2−i2−i2−i2i2i200000000−22000
χ28222-2-22-2-2002-20-20202i2i−2i−2i00000−2i−2i2i2i−2−2220000-2200000000−22−i2−i2i2i2i2i2−i2−i2000000002−2000
χ29222-2-22-2-2002-20-2020−2i−2i2i2i000002i2i−2i−2i22−2−20000-22000000002−2−i2−i2i2i2i2i2−i2−i200000000−22000
χ30222-2-22-2-2002-20-2020−2i−2i2i2i000002i2i−2i−2i−2−2220000-2200000000−22i2i2−i2−i2−i2−i2i2i2000000002−2000
χ31222-2-22-2-2002-20-2020−2i−2i2i2i00000−2i−2i2i2i22−2−200002-2000000002−2−i2−i2i2i2−i2−i2i2i2000000002−2000
χ32222-2-22-2-2002-20-2020−2i−2i2i2i00000−2i−2i2i2i−2−22200002-200000000−22i2i2−i2−i2i2i2−i2−i200000000−22000
χ3322-22-2-22-22-200-2020000002i2i−2i−2i02−22−22i−2i2i−2i0000002-22−2i2i2−i2−i2000000i2−i2i2−i200000000002−20
χ3422-22-2-22-22-200-2020000002i2i−2i−2i02−22−2−2i2i−2i2i000000-222−2i2i2−i2−i2000000−i2i2−i2i20000000000−220
χ3522-22-2-22-22-200-2020000002i2i−2i−2i0−22−222i−2i2i−2i0000002-2−22−i2−i2i2i2000000−i2i2−i2i20000000000−220
χ3622-22-2-22-22-200-2020000002i2i−2i−2i0−22−22−2i2i−2i2i000000-22−22−i2−i2i2i2000000i2−i2i2−i200000000002−20
χ3722-22-2-22-22-200-202000000−2i−2i2i2i02−22−22i−2i2i−2i000000-222−2−i2−i2i2i2000000i2−i2i2−i20000000000−220
χ3822-22-2-22-22-200-202000000−2i−2i2i2i02−22−2−2i2i−2i2i0000002-22−2−i2−i2i2i2000000−i2i2−i2i200000000002−20
χ3922-22-2-22-22-200-202000000−2i−2i2i2i0−22−222i−2i2i−2i000000-22−22i2i2−i2−i2000000−i2i2−i2i200000000002−20
χ4022-22-2-22-22-200-202000000−2i−2i2i2i0−22−22−2i2i−2i2i0000002-2−22i2i2−i2−i2000000i2−i2i2−i20000000000−220
χ412-2222-2-2-22222-2-2-2-222-22-22-22-2-2000000002-22-2000000000000000000002-200000000000
χ422-2222-2-2-22222-2-2-2-222-22-2-22-22-2000000002-2-2200000000000000000000-2200000000000
χ432-2222-2-2-22222-2-2-2-22-22-222-22-2-200000000-222-200000000000000000000-2200000000000
χ442-2222-2-2-22222-2-2-2-22-22-22-22-22-200000000-22-22000000000000000000002-200000000000
χ452-2222-2-2-222-2-2-22-22-200002-22-220000000000-220000000000002i−2i2i−2i000000002i−2i0000000
χ462-2222-2-2-222-2-2-22-22-200002-22-220000000000-22000000000000−2i2i−2i2i00000000−2i2i0000000
χ472-2222-2-2-222-2-2-22-22-20000-22-22200000000002-20000000000002i−2i2i−2i00000000−2i2i0000000
χ482-2222-2-2-222-2-2-22-22-20000-22-22200000000002-2000000000000−2i2i−2i2i000000002i−2i0000000
χ492-2222-2-2-2-2-2222-22-2-22-22-20000200000000-22000000002i−2i2i−2i0000000000002i−2i000000000
χ502-2222-2-2-2-2-2222-22-2-22-22-20000200000000-2200000000−2i2i−2i2i000000000000−2i2i000000000
χ512-2222-2-2-2-2-2222-22-2-2-22-2200002000000002-2000000002i−2i2i−2i000000000000−2i2i000000000
χ522-2222-2-2-2-2-2222-22-2-2-22-2200002000000002-200000000−2i2i−2i2i0000000000002i−2i000000000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-44-4-400-44040-4000000000000002222−22−2200000000000000−2222000000000000000000000
χ55444-4-44-4-400-44040-400000000000000−22−2222220000000000000022−22000000000000000000000
χ5644-44-4-44-4-440040-40000000000022−2222−22000000000000−2222000000000000000000000000000
χ5744-44-4-44-4-440040-400000000000−2222−222200000000000022−22000000000000000000000000000
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
χ624-4444-4-4-4-4-4-4-44444400000000-4000000000000000000000000000000000000000000000
χ634-44-4-4-444004-4040-404i−4i−4i4i00000000000000000000000000000000000000000000000000
χ644-44-4-4-444004-4040-40−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ654-44-4-4-44400-440-404000000000000000000000000000000000022−22−222200000000000000000
χ664-44-4-4-44400-440-4040000000000000000000000000000000000−222222−2200000000000000000
χ674-4-44-44-444-40040-40000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ684-4-44-44-444-40040-4000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ694-4-44-44-44-4400-4040000000000000000000000000000022−22−222200000000000000000000000
χ704-4-44-44-44-4400-40400000000000000000000000000000−222222−2200000000000000000000000
χ718-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000

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