Finite Group Databasebeta

← Group #237379

Character table — Group #237379

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222244488888888888888881616161616161111222222224448888888888888888161616161616
order12222244444444444448888888888882444442222224444444444444888888888888244444
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
χ31111111111111111111-1-1-1-11111-1-1-1-1-1-1-111-11111111111111111111-1-1-1-11111-1-1-1-1-1-1-111-1
χ41111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11
χ5111111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111111111111-1-1-1-1111111111111-1-1-1-1-1-1
χ6111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1111
χ7111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-11
χ8111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1
χ92222222-2-2-2-222-2-20000000022-2-200000000002222222-2-2-2-222-2-20000000022-2-20000000000
χ102222222-2-2-2-222-2-200000000-2-22200000000002222222-2-2-2-222-2-200000000-2-2220000000000
χ11222222-22222-2-2-2-2000022-2-200000000000000222222-22222-2-2-2-2000022-2-200000000000000
χ12222222-22222-2-2-2-20000-2-22200000000000000222222-22222-2-2-2-20000-2-22200000000000000
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
χ152222-2-2222-2-22-2-22000000000000000002-20002222-2-2222-2-22-2-22000000000000000002-2000
χ162222-2-2222-2-22-2-2200000000000000000-220002222-2-2222-2-22-2-2200000000000000000-22000
χ172222-2-22-2-2222-22-2000000000000000020000-22222-2-22-2-2222-22-2000000000000000020000-2
χ182222-2-22-2-2222-22-20000000000000000-2000022222-2-22-2-2222-22-20000000000000000-200002
χ192222-2-2-222-2-2-222-22i2i−2i−2i0000000000000000002222-2-2-222-2-2-222-22i2i−2i−2i000000000000000000
χ202222-2-2-222-2-2-222-2−2i−2i2i2i0000000000000000002222-2-2-222-2-2-222-2−2i−2i2i2i000000000000000000
χ212222-2-2-2-2-222-22-2200000000000000000002-202222-2-2-2-2-222-22-2200000000000000000002-20
χ222222-2-2-2-2-222-22-220000000000000000000-2202222-2-2-2-2-222-22-220000000000000000000-220
χ232-2-222-202-22-200000000002-2i2−i2i2−i2i2−i2i2−i20000002-2-222-202-22-200000000002-2i2−i2i2−i2i2−i2i2−i2000000
χ242-2-222-202-22-200000000002-2−i2i2−i2i2−i2i2−i2i20000002-2-222-202-22-200000000002-2−i2i2−i2i2−i2i2−i2i2000000
χ252-2-222-202-22-20000000000-22i2−i2i2−i2−i2i2−i2i20000002-2-222-202-22-20000000000-22i2−i2i2−i2−i2i2−i2i2000000
χ262-2-222-202-22-20000000000-22−i2i2−i2i2i2−i2i2−i20000002-2-222-202-22-20000000000-22−i2i2−i2i2i2−i2i2−i2000000
χ272-2-222-20-22-22000000002-200i2−i2−i2i2i2−i2−i2i20000002-2-222-20-22-22000000002-200i2−i2−i2i2i2−i2−i2i2000000
χ282-2-222-20-22-22000000002-200−i2i2i2−i2−i2i2i2−i20000002-2-222-20-22-22000000002-200−i2i2i2−i2−i2i2i2−i2000000
χ292-2-222-20-22-2200000000-2200i2−i2−i2i2−i2i2i2−i20000002-2-222-20-22-2200000000-2200i2−i2−i2i2−i2i2i2−i2000000
χ302-2-222-20-22-2200000000-2200−i2i2i2−i2i2−i2−i2i20000002-2-222-20-22-2200000000-2200−i2i2i2−i2i2−i2−i2i2000000
χ3144-4-40040000-40002-22-200000000000000000044-4-40040000-40002-22-2000000000000000000
χ3244-4-40040000-4000-22-2200000000000000000044-4-40040000-4000-22-22000000000000000000
χ3344-4-400-4000040002i−2i−2i2i00000000000000000044-4-400-4000040002i−2i−2i2i000000000000000000
χ3444-4-400-400004000−2i2i2i−2i00000000000000000044-4-400-400004000−2i2i2i−2i000000000000000000
χ354-4-44-4404-4-44000000000000000000000000004-4-44-4404-4-4400000000000000000000000000
χ364-4-44-440-444-4000000000000000000000000004-4-44-440-444-400000000000000000000000000
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
χ401111111111111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-11
χ411111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11111-1
χ42111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ43111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-111-1-1-1
χ44111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-111-1
χ45111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1-1-11
χ462222222-2-2-2-222-2-20000000022-2-20000000000-2-2-2-2-2-2-22222-2-22200000000-2-2220000000000
χ472222222-2-2-2-222-2-200000000-2-2220000000000-2-2-2-2-2-2-22222-2-2220000000022-2-20000000000
χ48222222-22222-2-2-2-2000022-2-200000000000000-2-2-2-2-2-22-2-2-2-222220000-2-22200000000000000
χ49222222-22222-2-2-2-20000-2-22200000000000000-2-2-2-2-2-22-2-2-2-22222000022-2-200000000000000
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
χ522222-2-2222-2-22-2-22000000000000000002-2000-2-2-2-222-2-2-222-222-200000000000000000-22000
χ532222-2-2222-2-22-2-2200000000000000000-22000-2-2-2-222-2-2-222-222-2000000000000000002-2000
χ542222-2-22-2-2222-22-2000000000000000020000-2-2-2-2-222-222-2-2-22-220000000000000000-200002
χ552222-2-22-2-2222-22-20000000000000000-200002-2-2-2-222-222-2-2-22-22000000000000000020000-2
χ562222-2-2-222-2-2-222-22i2i−2i−2i000000000000000000-2-2-2-2222-2-2222-2-22−2i−2i2i2i000000000000000000
χ572222-2-2-222-2-2-222-2−2i−2i2i2i000000000000000000-2-2-2-2222-2-2222-2-222i2i−2i−2i000000000000000000
χ582222-2-2-2-2-222-22-2200000000000000000002-20-2-2-2-222222-2-22-22-20000000000000000000-220
χ592222-2-2-2-2-222-22-220000000000000000000-220-2-2-2-222222-2-22-22-200000000000000000002-20
χ602-2-222-202-22-200000000002-2i2−i2i2−i2i2−i2i2−i2000000-222-2-220-22-220000000000-22−i2i2−i2i2−i2i2−i2i2000000
χ612-2-222-202-22-200000000002-2−i2i2−i2i2−i2i2−i2i2000000-222-2-220-22-220000000000-22i2−i2i2−i2i2−i2i2−i2000000
χ622-2-222-202-22-20000000000-22i2−i2i2−i2−i2i2−i2i2000000-222-2-220-22-2200000000002-2−i2i2−i2i2i2−i2i2−i2000000
χ632-2-222-202-22-20000000000-22−i2i2−i2i2i2−i2i2−i2000000-222-2-220-22-2200000000002-2i2−i2i2−i2−i2i2−i2i2000000
χ642-2-222-20-22-22000000002-200i2−i2−i2i2i2−i2−i2i2000000-222-2-2202-22-200000000-2200−i2i2i2−i2−i2i2i2−i2000000
χ652-2-222-20-22-22000000002-200−i2i2i2−i2−i2i2i2−i2000000-222-2-2202-22-200000000-2200i2−i2−i2i2i2−i2−i2i2000000
χ662-2-222-20-22-2200000000-2200i2−i2−i2i2−i2i2i2−i2000000-222-2-2202-22-2000000002-200−i2i2i2−i2i2−i2−i2i2000000
χ672-2-222-20-22-2200000000-2200−i2i2i2−i2i2−i2−i2i2000000-222-2-2202-22-2000000002-200i2−i2−i2i2−i2i2i2−i2000000
χ6844-4-40040000-40002-22-2000000000000000000-4-44400-400004000-22-22000000000000000000
χ6944-4-40040000-4000-22-22000000000000000000-4-44400-4000040002-22-2000000000000000000
χ7044-4-400-4000040002i−2i−2i2i000000000000000000-4-4440040000-4000−2i2i2i−2i000000000000000000
χ7144-4-400-400004000−2i2i2i−2i000000000000000000-4-4440040000-40002i−2i−2i2i000000000000000000
χ724-4-44-4404-4-4400000000000000000000000000-444-44-40-444-400000000000000000000000000
χ734-4-44-440-444-400000000000000000000000000-444-44-404-4-4400000000000000000000000000
χ748-88-8000000000000000000000000000000000-88-88000000000000000000000000000000000

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