Finite Group Databasebeta

← Group #314690

Character table — Group #314690

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444888888882244444488888888888822444444888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ91111111111-1-1-1-111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1
χ101111111111-1-1-1-111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111
χ111111111111-1-1-1-111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-111-1-111-1-111
χ121111111111-1-1-1-111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-111-1-111-1-1
χ131111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111
χ141111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ151111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ161111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ1722222222222222-2-2-222-20000000022-2-2-2-2-2-20000000000002222-2-2-2-2000000000000000000000000
χ1822222222222222-2-2-222-20000000022-2-2-2-2-2-2000000000000-2-2-2-22222000000000000000000000000
χ192222222222-2-2-2-2-2-2-222-200000000-2-2-2-2222200000000000022-2-2-2-222000000000000000000000000
χ202222222222-2-2-2-2-2-2-222-200000000-2-2-2-22222000000000000-2-22222-2-2000000000000000000000000
χ2122222222-2-22222222-2-2222222222-2-2-2-222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2222222222-2-22222222-2-22-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-2222200000000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-200000000-2-222-2-222000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2422222222-2-22222-2-2-2-2-2-200000000-2-222-2-22200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2522222222-2-2-2-2-2-2222-2-222222222222-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2622222222-2-2-2-2-2-2222-2-22-2-2-2-2-2-2-2-222-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-2000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ292222-2-2-2-22222-2-2000-2-202222−2−2−2−22-200000022−2−222−2−222−2−22-22-200002−22−22−22−20000000000000000
χ302222-2-2-2-22222-2-2000-2-202222−2−2−2−22-200000022−2−222−2−222−2−2-22-220000−22−22−22−220000000000000000
χ312222-2-2-2-22222-2-2000-2-20−2−2−2−222222-2000000−2−222−2−222−2−2222-22-20000−22−22−22−220000000000000000
χ322222-2-2-2-22222-2-2000-2-20−2−2−2−222222-2000000−2−222−2−222−2−222-22-2200002−22−22−22−20000000000000000
χ332222-2-2-2-222-2-222000-2-202222−2−2−2−2-2200000022−2−2−2−222−2−2222-2-220000−22−222−22−20000000000000000
χ342222-2-2-2-222-2-222000-2-202222−2−2−2−2-2200000022−2−2−2−222−2−222-222-200002−22−2−22−220000000000000000
χ352222-2-2-2-222-2-222000-2-20−2−2−2−22222-22000000−2−22222−2−222−2−22-2-2200002−22−2−22−220000000000000000
χ362222-2-2-2-222-2-222000-2-20−2−2−2−22222-22000000−2−22222−2−222−2−2-222-20000−22−222−22−20000000000000000
χ372222-2-2-2-2-2-222-2-20002202222−2−2−2−2-22000000−2−22222−2−2−2−22200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i20000000000000000
χ382222-2-2-2-2-2-222-2-20002202222−2−2−2−2-22000000−2−22222−2−2−2−2220000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i20000000000000000
χ392222-2-2-2-2-2-222-2-2000220−2−2−2−22222-2200000022−2−2−2−22222−2−200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i20000000000000000
χ402222-2-2-2-2-2-222-2-2000220−2−2−2−22222-2200000022−2−2−2−22222−2−20000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i20000000000000000
χ412222-2-2-2-2-2-2-2-2220002202222−2−2−2−22-2000000−2−222−2−22222−2−200002i−2i−2i2i−i2i2i2−i2i2−i2−i2i20000000000000000
χ422222-2-2-2-2-2-2-2-2220002202222−2−2−2−22-2000000−2−222−2−22222−2−20000−2i2i2i−2ii2−i2−i2i2−i2i2i2−i20000000000000000
χ432222-2-2-2-2-2-2-2-222000220−2−2−2−222222-200000022−2−222−2−2−2−22200002i−2i−2i2ii2−i2−i2i2−i2i2i2−i20000000000000000
χ442222-2-2-2-2-2-2-2-222000220−2−2−2−222222-200000022−2−222−2−2−2−2220000−2i2i2i−2i−i2i2i2−i2i2−i2−i2i20000000000000000
χ4522-2-2-222-2002i−2i2i−2i-22200-22i2i−2i−2i2i2i−2i−2i00002i−2i0000002-22-200000000000000000000000000002−2i2−i2i2−i22−2
χ4622-2-2-222-2002i−2i2i−2i-22200-22i2i−2i−2i2i2i−2i−2i00002i−2i0000002-22-20000000000000000000000000000−22−i2i2−i2i2−22
χ4722-2-2-222-2002i−2i2i−2i-22200-2−2i−2i2i2i−2i−2i2i2i00002i−2i000000-22-2200000000000000000000000000002−2i2−i2−i2i2−22
χ4822-2-2-222-2002i−2i2i−2i-22200-2−2i−2i2i2i−2i−2i2i2i00002i−2i000000-22-220000000000000000000000000000−22−i2i2i2−i22−2
χ4922-2-2-222-200−2i2i−2i2i-22200-22i2i−2i−2i2i2i−2i−2i0000−2i2i000000-22-2200000000000000000000000000002−2−i2i2i2−i2−22
χ5022-2-2-222-200−2i2i−2i2i-22200-22i2i−2i−2i2i2i−2i−2i0000−2i2i000000-22-220000000000000000000000000000−22i2−i2−i2i22−2
χ5122-2-2-222-200−2i2i−2i2i-22200-2−2i−2i2i2i−2i−2i2i2i0000−2i2i0000002-22-200000000000000000000000000002−2−i2i2−i2i22−2
χ5222-2-2-222-200−2i2i−2i2i-22200-2−2i−2i2i2i−2i−2i2i2i0000−2i2i0000002-22-20000000000000000000000000000−22i2−i2i2−i2−22
χ532-22-222-2-22-20000-22-22-222-22-22-22-2002-200002-22-2000000000000000000000000002i−2i2i−2i0000000000
χ542-22-222-2-22-20000-22-22-222-22-22-22-2002-200002-22-200000000000000000000000000−2i2i−2i2i0000000000
χ552-22-222-2-22-20000-22-22-22-22-22-22-22002-20000-22-22000000000000000000000000002i−2i−2i2i0000000000
χ562-22-222-2-22-20000-22-22-22-22-22-22-22002-20000-22-2200000000000000000000000000−2i2i2i−2i0000000000
χ572-22-222-2-2-220000-22-2-2222-22-22-22-200-220000-22-220000000000000000000000002i−2i00002i−2i00000000
χ582-22-222-2-2-220000-22-2-2222-22-22-22-200-220000-22-22000000000000000000000000−2i2i0000−2i2i00000000
χ592-22-222-2-2-220000-22-2-222-22-22-22-2200-2200002-22-20000000000000000000000002i−2i0000−2i2i00000000
χ602-22-222-2-2-220000-22-2-222-22-22-22-2200-2200002-22-2000000000000000000000000−2i2i00002i−2i00000000
χ6144-4-44-4-44004i−4i−4i4i0000002i22i2−2i2−2i2−2i2−2i22i22i200000000000022−22−2222000000000000000000000000000000000000
χ6244-4-44-4-44004i−4i−4i4i000000−2i2−2i22i22i22i22i2−2i2−2i2000000000000−222222−22000000000000000000000000000000000000
χ6344-4-44-4-4400−4i4i4i−4i0000002i22i2−2i2−2i2−2i2−2i22i22i2000000000000−222222−22000000000000000000000000000000000000
χ6444-4-44-4-4400−4i4i4i−4i000000−2i2−2i22i22i22i22i2−2i2−2i200000000000022−22−2222000000000000000000000000000000000000
χ6544-4-4-444-4004i−4i4i−4i4-4-4004000000000000−4i4i0000000000000000000000000000000000000000000000
χ6644-4-4-444-400−4i4i−4i4i4-4-40040000000000004i−4i0000000000000000000000000000000000000000000000
χ674-44-444-4-44-400004-444-4-40000000000-44000000000000000000000000000000000000000000000000
χ684-44-444-4-4-4400004-44-44-400000000004-4000000000000000000000000000000000000000000000000
χ694-44-4-4-4444-40000000-44022−2222−22−2222−22220000000022−22−22220000000000000000000000000000000000000000
χ704-44-4-4-4444-40000000-440−2222−222222−2222−2200000000−222222−220000000000000000000000000000000000000000
χ714-44-4-4-444-4400000004-4022−2222−22−2222−222200000000−222222−220000000000000000000000000000000000000000
χ724-44-4-4-444-4400000004-40−2222−222222−2222−220000000022−22−22220000000000000000000000000000000000000000
χ734-4-444-44-40000000000002i2−2i2−2i22i2−2i22i22i2−2i20000004i−4i0000000022−2222−2200000000000000000000000000000000
χ744-4-444-44-40000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000−4i4i00000000−2222−222200000000000000000000000000000000
χ754-4-444-44-4000000000000−2i22i22i2−2i22i2−2i2−2i22i20000004i−4i00000000−2222−222200000000000000000000000000000000
χ764-4-444-44-4000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000−4i4i0000000022−2222−2200000000000000000000000000000000
χ774-4-44-44-4400000044-400-44i−4i−4i4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ784-4-44-44-4400000044-400-4−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ794-4-44-44-44000000-4-440040000000000000000000000004-4-4400000000000000000000000000000000
χ804-4-44-44-44000000-4-44004000000000000000000000000-444-400000000000000000000000000000000

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