Finite Group Databasebeta

← Group #237199

Character table — Group #237199

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222244488888888888888881616161616161111222222224448888888888888888161616161616
order12222244444444422448888888888884444882222224444444442244888888888888444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1
χ31111111111111111111-1-1-1-111111111-1-1-1-1-1-11111111111111111111-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ5111111111111111-1-1-1-111111111-1-1-1-11-1-11-1-1111111111111111-1-1-1-111111111-1-1-1-11-1-11-1-1
χ6111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ7111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-111
χ8111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ922222222-2-222-2-2-222-2-200000000000000000022222222-2-222-2-2-222-2-2000000000000000000
χ1022222222-2-222-2-2-2-2-22200000000000000000022222222-2-222-2-2-2-2-222000000000000000000
χ11222222-2-222-2-22-2-2000000002i2i−2i−2i0000000000222222-2-222-2-22-2-2000000002i2i−2i−2i0000000000
χ12222222-2-222-2-22-2-200000000−2i−2i2i2i0000000000222222-2-222-2-22-2-200000000−2i−2i2i2i0000000000
χ13222222-2-2-2-2-2-2-22200000000000022-2-2000000222222-2-2-2-2-2-2-22200000000000022-2-2000000
χ14222222-2-2-2-2-2-2-222000000000000-2-222000000222222-2-2-2-2-2-2-222000000000000-2-222000000
χ152222-2-22-2222-2-22-20000000000000000200-2002222-2-22-2222-2-22-20000000000000000200-200
χ162222-2-22-2222-2-22-20000000000000000-2002002222-2-22-2222-2-22-20000000000000000-200200
χ172222-2-22-2-2-22-22-22000000000000000000002-22222-2-22-2-2-22-22-22000000000000000000002-2
χ182222-2-22-2-2-22-22-2200000000000000000000-222222-2-22-2-2-22-22-2200000000000000000000-22
χ192222-2-2-2222-22-2-22000022-2-2000000000000002222-2-2-2222-22-2-22000022-2-200000000000000
χ202222-2-2-2222-22-2-220000-2-222000000000000002222-2-2-2222-22-2-220000-2-22200000000000000
χ212222-2-2-22-2-2-2222-2000000000000000002-20002222-2-2-22-2-2-2222-2000000000000000002-2000
χ222222-2-2-22-2-2-2222-200000000000000000-220002222-2-2-22-2-2-2222-200000000000000000-22000
χ2322-2-22-22200-2-20002-20000002−22−22−22−200000022-2-22-22200-2-20002-20000002−22−22−22−2000000
χ2422-2-22-22200-2-20002-2000000−22−22−22−2200000022-2-22-22200-2-20002-2000000−22−22−22−22000000
χ2522-2-22-22200-2-2000-220000002−22−2−22−2200000022-2-22-22200-2-2000-220000002−22−2−22−22000000
χ2622-2-22-22200-2-2000-22000000−22−222−22−200000022-2-22-22200-2-2000-22000000−22−222−22−2000000
χ2722-2-22-2-2-20022000002i−2i0000i2−i2−i2i22−2−2200000022-2-22-2-2-20022000002i−2i0000i2−i2−i2i22−2−22000000
χ2822-2-22-2-2-20022000002i−2i0000−i2i2i2−i2−222−200000022-2-22-2-2-20022000002i−2i0000−i2i2i2−i2−222−2000000
χ2922-2-22-2-2-2002200000−2i2i0000i2−i2−i2i2−222−200000022-2-22-2-2-2002200000−2i2i0000i2−i2−i2i2−222−2000000
χ3022-2-22-2-2-2002200000−2i2i0000−i2i2i2−i22−2−2200000022-2-22-2-2-2002200000−2i2i0000−i2i2i2−i22−2−22000000
χ3144-4-4-444-400-44000000000000000000000000044-4-4-444-400-440000000000000000000000000
χ3244-4-4-44-44004-4000000000000000000000000044-4-4-44-44004-40000000000000000000000000
χ334-4-4400004-40000000000022−22000000000000004-4-4400004-40000000000022−2200000000000000
χ344-4-4400004-400000000000−2222000000000000004-4-4400004-400000000000−222200000000000000
χ354-4-440000-4400000000022−2200000000000000004-4-440000-4400000000022−220000000000000000
χ364-4-440000-44000000000−222200000000000000004-4-440000-44000000000−22220000000000000000
χ378-88-80000000000000000000000000000000008-88-8000000000000000000000000000000000
χ381111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3911111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111
χ401111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-111-1-1-1
χ42111111111111111-1-1-1-111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-111
χ43111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ44111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-11-1-1
χ45111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ4622222222-2-222-2-2-222-2-2000000000000000000-2-2-2-2-2-2-2-222-2-2222-2-222000000000000000000
χ4722222222-2-222-2-2-2-2-222000000000000000000-2-2-2-2-2-2-2-222-2-222222-2-2000000000000000000
χ48222222-2-222-2-22-2-2000000002i2i−2i−2i0000000000-2-2-2-2-2-222-2-222-22200000000−2i−2i2i2i0000000000
χ49222222-2-222-2-22-2-200000000−2i−2i2i2i0000000000-2-2-2-2-2-222-2-222-222000000002i2i−2i−2i0000000000
χ50222222-2-2-2-2-2-2-22200000000000022-2-2000000-2-2-2-2-2-22222222-2-2000000000000-2-222000000
χ51222222-2-2-2-2-2-2-222000000000000-2-222000000-2-2-2-2-2-22222222-2-200000000000022-2-2000000
χ522222-2-22-2222-2-22-20000000000000000200-200-2-2-2-222-22-2-2-222-220000000000000000-200200
χ532222-2-22-2222-2-22-20000000000000000-200200-2-2-2-222-22-2-2-222-220000000000000000200-200
χ542222-2-22-2-2-22-22-22000000000000000000002-2-2-2-2-222-2222-22-22-200000000000000000000-22
χ552222-2-22-2-2-22-22-2200000000000000000000-22-2-2-2-222-2222-22-22-2000000000000000000002-2
χ562222-2-2-2222-22-2-22000022-2-200000000000000-2-2-2-2222-2-2-22-222-20000-2-22200000000000000
χ572222-2-2-2222-22-2-220000-2-22200000000000000-2-2-2-2222-2-2-22-222-2000022-2-200000000000000
χ582222-2-2-22-2-2-2222-2000000000000000002-2000-2-2-2-2222-2222-2-2-2200000000000000000-22000
χ592222-2-2-22-2-2-2222-200000000000000000-22000-2-2-2-2222-2222-2-2-22000000000000000002-2000
χ6022-2-22-22200-2-20002-20000002−22−22−22−2000000-2-222-22-2-20022000-22000000−22−22−22−22000000
χ6122-2-22-22200-2-20002-2000000−22−22−22−22000000-2-222-22-2-20022000-220000002−22−22−22−2000000
χ6222-2-22-22200-2-2000-220000002−22−2−22−22000000-2-222-22-2-200220002-2000000−22−222−22−2000000
χ6322-2-22-22200-2-2000-22000000−22−222−22−2000000-2-222-22-2-200220002-20000002−22−2−22−22000000
χ6422-2-22-2-2-20022000002i−2i0000i2−i2−i2i22−2−22000000-2-222-222200-2-200000−2i2i0000−i2i2i2−i2−222−2000000
χ6522-2-22-2-2-20022000002i−2i0000−i2i2i2−i2−222−2000000-2-222-222200-2-200000−2i2i0000i2−i2−i2i22−2−22000000
χ6622-2-22-2-2-2002200000−2i2i0000i2−i2−i2i2−222−2000000-2-222-222200-2-2000002i−2i0000−i2i2i2−i22−2−22000000
χ6722-2-22-2-2-2002200000−2i2i0000−i2i2i2−i22−2−22000000-2-222-222200-2-2000002i−2i0000i2−i2−i2i2−222−2000000
χ6844-4-4-444-400-440000000000000000000000000-4-4444-4-44004-40000000000000000000000000
χ6944-4-4-44-44004-40000000000000000000000000-4-4444-44-400-440000000000000000000000000
χ704-4-4400004-40000000000022−2200000000000000-444-40000-4400000000000−222200000000000000
χ714-4-4400004-400000000000−222200000000000000-444-40000-440000000000022−2200000000000000
χ724-4-440000-4400000000022−220000000000000000-444-400004-4000000000−22220000000000000000
χ734-4-440000-44000000000−22220000000000000000-444-400004-400000000022−220000000000000000
χ748-88-8000000000000000000000000000000000-88-88000000000000000000000000000000000

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