Finite Group Databasebeta

← Group #350139

Character table — Group #350139

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444224444444444444444444444444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ9111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ10111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ11111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ12111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ13111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ14111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ172222222222-2-2222222-2-2222222-2-2222200000000-2-2-2-2-2-2-2000000000000000000000000000000
χ182222222222-2-2222222-2-222-2-2-2-2-2-2-2-2-2-200000000-2-2-22222000000000000000000000000000000
χ192222222222-2-2-2-2-2-222-2-2-2-2222222-2-2-2-200000000-2-22-2-222000000000000000000000000000000
χ202222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-222222200000000-2-2222-2-2000000000000000000000000000000
χ2122222222-2-2222222-2-222-2-2000022000022222222-2-2-20000-2-2-2-200000000000000000000000000
χ2222222222-2-2222222-2-222-2-20000220000-2-2-2-2-2-2-2-2-2-2-20000222200000000000000000000000000
χ2322222222-2-222-2-2-2-2-2-222220000-2-200002222-2-2-2-2-2-220000-2-22200000000000000000000000000
χ2422222222-2-222-2-2-2-2-2-222220000-2-20000-2-2-2-22222-2-22000022-2-200000000000000000000000000
χ2522222222-2-2-2-22222-2-2-2-2-2-20000-2-20000000000002220000000022-2-222-2-2000000000000000000
χ2622222222-2-2-2-22222-2-2-2-2-2-20000-2-200000000000022200000000-2-222-2-222000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22200002200000000000022-20000000022-2-2-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22200002200000000000022-200000000-2-22222-2-2000000000000000000
χ292222-2-2-2-2-2-20022-2-222002-222-2-20022-2-2000000000000000000000000000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2000000
χ302222-2-2-2-2-2-20022-2-222002-222-2-20022-2-2000000000000000000000000000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2000000
χ312222-2-2-2-2-2-20022-2-222002-2-2-22200-2-222000000000000000000000000000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2000000
χ322222-2-2-2-2-2-20022-2-222002-2-2-22200-2-222000000000000000000000000000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2000000
χ332222-2-2-2-2-2-200-2-2222200-2222-2-200-2-222000000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2−i2−i2i2000000
χ342222-2-2-2-2-2-200-2-2222200-2222-2-200-2-222000000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2i2i2−i2000000
χ352222-2-2-2-2-2-200-2-2222200-22-2-2220022-2-2000000000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2000000
χ362222-2-2-2-2-2-200-2-2222200-22-2-2220022-2-2000000000000000000000000000−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2000000
χ372-22-222-2-2002-22i−2i2i−2i002-20000002i−2i000022-2-22i2i−2i−2i0000000000000000000i2−i2i2−i22−22−20000i2−i22−200
χ382-22-222-2-2002-22i−2i2i−2i002-20000002i−2i000022-2-22i2i−2i−2i0000000000000000000−i2i2−i2i2−22−220000−i2i2−2200
χ392-22-222-2-2002-22i−2i2i−2i002-20000002i−2i0000-2-222−2i−2i2i2i0000000000000000000i2−i2i2−i22−22−20000−i2i2−2200
χ402-22-222-2-2002-22i−2i2i−2i002-20000002i−2i0000-2-222−2i−2i2i2i0000000000000000000−i2i2−i2i2−22−220000i2−i22−200
χ412-22-222-2-2002-2−2i2i−2i2i002-2000000−2i2i000022-2-2−2i−2i2i2i0000000000000000000i2−i2i2−i2−22−220000i2−i2−2200
χ422-22-222-2-2002-2−2i2i−2i2i002-2000000−2i2i000022-2-2−2i−2i2i2i0000000000000000000−i2i2−i2i22−22−20000−i2i22−200
χ432-22-222-2-2002-2−2i2i−2i2i002-2000000−2i2i0000-2-2222i2i−2i−2i0000000000000000000i2−i2i2−i2−22−220000−i2i22−200
χ442-22-222-2-2002-2−2i2i−2i2i002-2000000−2i2i0000-2-2222i2i−2i−2i0000000000000000000−i2i2−i2i22−22−20000i2−i2−2200
χ452-2-222-22-22-22-200002-2-22000000002i−2i2i−2i00002i−2i2i−2i2-20002i−2i002i−2i2-22-20000000000000000000000
χ462-2-222-22-22-22-200002-2-22000000002i−2i2i−2i0000−2i2i−2i2i2-20002i−2i00−2i2i-22-220000000000000000000000
χ472-2-222-22-22-22-200002-2-2200000000−2i2i−2i2i00002i−2i2i−2i2-2000−2i2i002i−2i-22-220000000000000000000000
χ482-2-222-22-22-22-200002-2-2200000000−2i2i−2i2i0000−2i2i−2i2i2-2000−2i2i00−2i2i2-22-20000000000000000000000
χ492-2-222-22-22-2-2200002-22-2000000002i−2i2i−2i2i−2i2i−2i0000-22000−2i2i2i−2i0000002-22-2000000000000000000
χ502-2-222-22-22-2-2200002-22-2000000002i−2i2i−2i−2i2i−2i2i0000-22000−2i2i−2i2i000000-22-22000000000000000000
χ512-2-222-22-22-2-2200002-22-200000000−2i2i−2i2i2i−2i2i−2i0000-220002i−2i2i−2i000000-22-22000000000000000000
χ522-2-222-22-22-2-2200002-22-200000000−2i2i−2i2i−2i2i−2i2i0000-220002i−2i−2i2i0000002-22-2000000000000000000
χ532-2-222-22-2-222-20000-22-22002i−2i2i−2i00000000002i−2i2i−2i-2202i−2i0000−2i2i00002-2-22000000000000000000
χ542-2-222-22-2-222-20000-22-22002i−2i2i−2i0000000000−2i2i−2i2i-2202i−2i00002i−2i0000-222-2000000000000000000
χ552-2-222-22-2-222-20000-22-2200−2i2i−2i2i00000000002i−2i2i−2i-220−2i2i0000−2i2i0000-222-2000000000000000000
χ562-2-222-22-2-222-20000-22-2200−2i2i−2i2i0000000000−2i2i−2i2i-220−2i2i00002i−2i00002-2-22000000000000000000
χ572-2-222-22-2-22-220000-222-2002i−2i2i−2i0000002i−2i2i−2i00002-20−2i2i00−2i2i002-2-220000000000000000000000
χ582-2-222-22-2-22-220000-222-2002i−2i2i−2i000000−2i2i−2i2i00002-20−2i2i002i−2i00-222-20000000000000000000000
χ592-2-222-22-2-22-220000-222-200−2i2i−2i2i0000002i−2i2i−2i00002-202i−2i00−2i2i00-222-20000000000000000000000
χ602-2-222-22-2-22-220000-222-200−2i2i−2i2i000000−2i2i−2i2i00002-202i−2i002i−2i002-2-220000000000000000000000
χ614444-4-4-4-4440044-4-4-4-400-440000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-44400-4-444-4-4004-40000000000000000000000000000000000000000000000000000000
χ6344-4-44-4-440044000000-4-400000000000000004-4-440000000000000000000000000000000000000
χ6444-4-44-4-440044000000-4-40000000000000000-444-40000000000000000000000000000000000000
χ6544-4-44-4-4400-4-4000000440000000000004i−4i−4i4i00000000000000000000000000000000000000000
χ6644-4-44-4-4400-4-400000044000000000000−4i4i4i−4i00000000000000000000000000000000000000000
χ674-44-444-4-400-444i−4i4i−4i00-44000000−4i4i0000000000000000000000000000000000000000000000000
χ684-44-444-4-400-44−4i4i−4i4i00-440000004i−4i0000000000000000000000000000000000000000000000000
χ694-44-4-4-44400004i−4i−4i4i00000000000000000000000000000000000000000002-2-22−2i2i2i−2i0000000000
χ704-44-4-4-44400004i−4i−4i4i0000000000000000000000000000000000000000000-222-22i−2i−2i2i0000000000
χ714-44-4-4-4440000−4i4i4i−4i00000000000000000000000000000000000000000002-2-222i−2i−2i2i0000000000
χ724-44-4-4-4440000−4i4i4i−4i0000000000000000000000000000000000000000000-222-2−2i2i2i−2i0000000000
χ734-4-44-44-444-4000000-4400004i−4i−4i4i000000000000000000000000000000000000000000000000000
χ744-4-44-44-444-4000000-440000−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ754-4-44-44-44-440000004-400000000004i−4i−4i4i000000000000000000000000000000000000000000000
χ764-4-44-44-44-440000004-40000000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ7788-8-8-888-8000000000000000000000000000000000000000000000000000000000000000000000

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