Finite Group Databasebeta

← Group #237191

Character table — Group #237191

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222244488888888888888881616161616161111222222224448888888888888888161616161616
order12222244444444444448888888888882224882222224444444444444888888888888222488
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111-1-1-1-111111111-1-1-1-1-1-11111111111111111111-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1
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
χ7111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
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
χ922222222-2-2-2-22-2-2000000002i2i−2i−2i000000000022222222-2-2-2-22-2-2000000002i2i−2i−2i0000000000
χ1022222222-2-2-2-22-2-200000000−2i−2i2i2i000000000022222222-2-2-2-22-2-200000000−2i−2i2i2i0000000000
χ11222222-2-22222-2-2-222-2-2000000000000000000222222-2-22222-2-2-222-2-2000000000000000000
χ12222222-2-22222-2-2-2-2-222000000000000000000222222-2-22222-2-2-2-2-222000000000000000000
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
χ152222-2-2222-22-2-22-20000000000000000002-2002222-2-2222-22-2-22-20000000000000000002-200
χ162222-2-2222-22-2-22-2000000000000000000-22002222-2-2222-22-2-22-2000000000000000000-2200
χ172222-2-222-22-22-2-22000022-2-2000000000000002222-2-222-22-22-2-22000022-2-200000000000000
χ182222-2-222-22-22-2-220000-2-222000000000000002222-2-222-22-22-2-220000-2-22200000000000000
χ192222-2-2-2-22-22-22-22000000000000000000002-22222-2-2-2-22-22-22-22000000000000000000002-2
χ202222-2-2-2-22-22-22-2200000000000000000000-222222-2-2-2-22-22-22-2200000000000000000000-22
χ212222-2-2-2-2-22-2222-200000000000000002-200002222-2-2-2-2-22-2222-200000000000000002-20000
χ222222-2-2-2-2-22-2222-20000000000000000-2200002222-2-2-2-2-22-2222-20000000000000000-220000
χ232-2-222-20022-2-20002i−2i000000i2−i2i2−i22−22−20000002-2-222-20022-2-20002i−2i000000i2−i2i2−i22−22−2000000
χ242-2-222-20022-2-20002i−2i000000−i2i2−i2i2−22−220000002-2-222-20022-2-20002i−2i000000−i2i2−i2i2−22−22000000
χ252-2-222-20022-2-2000−2i2i000000i2−i2i2−i2−22−220000002-2-222-20022-2-2000−2i2i000000i2−i2i2−i2−22−22000000
χ262-2-222-20022-2-2000−2i2i000000−i2i2−i2i22−22−20000002-2-222-20022-2-2000−2i2i000000−i2i2−i2i22−22−2000000
χ272-2-222-200-2-222000002-200002−2−222−2−220000002-2-222-200-2-222000002-200002−2−222−2−22000000
χ282-2-222-200-2-222000002-20000−222−2−222−20000002-2-222-200-2-222000002-20000−222−2−222−2000000
χ292-2-222-200-2-22200000-2200002−2−22−222−20000002-2-222-200-2-22200000-2200002−2−22−222−2000000
χ302-2-222-200-2-22200000-220000−222−22−2−220000002-2-222-200-2-22200000-220000−222−22−2−22000000
χ3144-4-4004-400000000000002i2−2i20000000000000044-4-4004-400000000000002i2−2i200000000000000
χ3244-4-4004-40000000000000−2i22i20000000000000044-4-4004-40000000000000−2i22i200000000000000
χ3344-4-400-44000000000002i2−2i2000000000000000044-4-400-44000000000002i2−2i20000000000000000
χ3444-4-400-4400000000000−2i22i2000000000000000044-4-400-4400000000000−2i22i20000000000000000
χ354-4-44-44004-4-4400000000000000000000000004-4-44-44004-4-440000000000000000000000000
χ364-4-44-4400-444-400000000000000000000000004-4-44-4400-444-40000000000000000000000000
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
χ3911111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111
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
χ411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ42111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111
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
χ44111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1
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
χ4622222222-2-2-2-22-2-2000000002i2i−2i−2i0000000000-2-2-2-2-2-2-2-22222-22200000000−2i−2i2i2i0000000000
χ4722222222-2-2-2-22-2-200000000−2i−2i2i2i0000000000-2-2-2-2-2-2-2-22222-222000000002i2i−2i−2i0000000000
χ48222222-2-22222-2-2-222-2-2000000000000000000-2-2-2-2-2-222-2-2-2-2222-2-222000000000000000000
χ49222222-2-22222-2-2-2-2-222000000000000000000-2-2-2-2-2-222-2-2-2-222222-2-2000000000000000000
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
χ522222-2-2222-22-2-22-20000000000000000002-200-2-2-2-222-2-2-22-222-22000000000000000000-2200
χ532222-2-2222-22-2-22-2000000000000000000-2200-2-2-2-222-2-2-22-222-220000000000000000002-200
χ542222-2-222-22-22-2-22000022-2-200000000000000-2-2-2-222-2-22-22-222-20000-2-22200000000000000
χ552222-2-222-22-22-2-220000-2-22200000000000000-2-2-2-222-2-22-22-222-2000022-2-200000000000000
χ562222-2-2-2-22-22-22-22000000000000000000002-2-2-2-2-22222-22-22-22-200000000000000000000-22
χ572222-2-2-2-22-22-22-2200000000000000000000-22-2-2-2-22222-22-22-22-2000000000000000000002-2
χ582222-2-2-2-2-22-2222-200000000000000002-20000-2-2-2-222222-22-2-2-220000000000000000-220000
χ592222-2-2-2-2-22-2222-20000000000000000-220000-2-2-2-222222-22-2-2-2200000000000000002-20000
χ602-2-222-20022-2-20002i−2i000000i2−i2i2−i22−22−2000000-222-2-2200-2-222000−2i2i000000−i2i2−i2i2−22−22000000
χ612-2-222-20022-2-20002i−2i000000−i2i2−i2i2−22−22000000-222-2-2200-2-222000−2i2i000000i2−i2i2−i22−22−2000000
χ622-2-222-20022-2-2000−2i2i000000i2−i2i2−i2−22−22000000-222-2-2200-2-2220002i−2i000000−i2i2−i2i22−22−2000000
χ632-2-222-20022-2-2000−2i2i000000−i2i2−i2i22−22−2000000-222-2-2200-2-2220002i−2i000000i2−i2i2−i2−22−22000000
χ642-2-222-200-2-222000002-200002−2−222−2−22000000-222-2-220022-2-200000-220000−222−2−222−2000000
χ652-2-222-200-2-222000002-20000−222−2−222−2000000-222-2-220022-2-200000-2200002−2−222−2−22000000
χ662-2-222-200-2-22200000-2200002−2−22−222−2000000-222-2-220022-2-2000002-20000−222−22−2−22000000
χ672-2-222-200-2-22200000-220000−222−22−2−22000000-222-2-220022-2-2000002-200002−2−22−222−2000000
χ6844-4-4004-400000000000002i2−2i200000000000000-4-44400-440000000000000−2i22i200000000000000
χ6944-4-4004-40000000000000−2i22i200000000000000-4-44400-4400000000000002i2−2i200000000000000
χ7044-4-400-44000000000002i2−2i20000000000000000-4-444004-400000000000−2i22i20000000000000000
χ7144-4-400-4400000000000−2i22i20000000000000000-4-444004-4000000000002i2−2i20000000000000000
χ724-4-44-44004-4-440000000000000000000000000-444-44-400-444-40000000000000000000000000
χ734-4-44-4400-444-40000000000000000000000000-444-44-4004-4-440000000000000000000000000
χ748-88-8000000000000000000000000000000000-88-88000000000000000000000000000000000

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