Finite Group Databasebeta

← Group #287809

Character table — Group #287809

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444888888888888888822444444488888888888888884444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11111111111-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1-1-111111111-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-111111111-1-1-1-1111111-1-1-1-111111111-1-111-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-111111111-1-1-1-1111111-1-1-1-111111111-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-11
χ1111111111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-11
χ1211111111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1
χ1311111111-1-1-1-111111111-1-1-1-111-1-1-1-111111111111111-1-111-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-11
χ1411111111-1-1-1-111111111-1-1-1-111-1-1-1-111111111111111-1-111-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ1511111111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-111111111-1-1-1-1-1-1111111-1-111-1-1-11
χ172222222222222-222-2-22-222-2-2-2-2000000000000000022-2-2-2-2-22200000000000000000000000000
χ182222222222222-222-2-22-222-2-2-2-20000000000000000-2-22222-2-2-200000000000000000000000000
χ19222222222222-22-2-222-22-2-222-2-22222222200000000000000-200-2-200000000-2-200000000000000
χ20222222222222-22-2-222-22-2-222-2-2-2-2-2-2-2-2-2-200000000000000-20022000000002200000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-222000000002i2i2i2i−2i−2i−2i−2i000000200002i2i−2i−2i00000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-22200000000−2i−2i−2i−2i2i2i2i2i00000020000−2i−2i2i2i00000000000000000000
χ2322222222-2-2-2-22-222-2-22-2-2-222-2-200000000000000002222-2-22-2-200000000000000000000000000
χ2422222222-2-2-2-22-222-2-22-2-2-222-2-20000000000000000-2-2-2-22222200000000000000000000000000
χ2522222222-2-2-2-2-22-2-222-2222-2-2-2-22222-2-2-2-2000000000000002002200000000-2-200000000000000
χ2622222222-2-2-2-2-22-2-222-2222-2-2-2-2-2-2-2-2222200000000000000200-2-2000000002200000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000002i2i2i2i−2i−2i−2i−2i000000-20000−2i−2i2i2i00000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000−2i−2i−2i−2i2i2i2i2i000000-200002i2i−2i−2i00000000000000000000
χ2922-2-22-22-22i2i−2i−2i0-200220-2002i−2i0022-2-22i2i−2i−2i00000000000000000000000i2i2−i2−i20022−2−20000i2−i22−200
χ3022-2-22-22-22i2i−2i−2i0-200220-2002i−2i0022-2-22i2i−2i−2i00000000000000000000000−i2−i2i2i200−2−2220000−i2i2−2200
χ3122-2-22-22-22i2i−2i−2i0-200220-2002i−2i00-2-222−2i−2i2i2i00000000000000000000000i2i2−i2−i20022−2−20000−i2i2−2200
χ3222-2-22-22-22i2i−2i−2i0-200220-2002i−2i00-2-222−2i−2i2i2i00000000000000000000000−i2−i2i2i200−2−2220000i2−i22−200
χ3322-2-22-22-2−2i−2i2i2i0-200220-200−2i2i0022-2-2−2i−2i2i2i00000000000000000000000i2i2−i2−i200−2−2220000i2−i2−2200
χ3422-2-22-22-2−2i−2i2i2i0-200220-200−2i2i0022-2-2−2i−2i2i2i00000000000000000000000−i2−i2i2i20022−2−20000−i2i22−200
χ3522-2-22-22-2−2i−2i2i2i0-200220-200−2i2i00-2-2222i2i−2i−2i00000000000000000000000i2i2−i2−i200−2−2220000−i2i22−200
χ3622-2-22-22-2−2i−2i2i2i0-200220-200−2i2i00-2-2222i2i−2i−2i00000000000000000000000−i2−i2i2i20022−2−20000i2−i2−2200
χ372-22-2-222-22i−2i2i−2i20-2-200202i−2i00002−22−2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i22-2000002i−2ii2−i22−22−200002−200000000000000
χ382-22-2-222-22i−2i2i−2i20-2-200202i−2i00002−22−2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2-2200000−2i2ii2−i2−22−2200002−200000000000000
χ392-22-2-222-22i−2i2i−2i20-2-200202i−2i0000−22−22−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2-2200000−2i2i−i2i22−22−20000−2200000000000000
χ402-22-2-222-22i−2i2i−2i20-2-200202i−2i0000−22−22−i2i2−i2i2−i2−i2i2i2−i2−i2i2i22-2000002i−2i−i2i2−22−220000−2200000000000000
χ412-22-2-222-22i−2i2i−2i-202200-20−2i2i00002−22−2i2−i2i2−i222−2−2−2−222002-22i−2i000−i2i2−i2i2i2−i20000−2200000000000000
χ422-22-2-222-22i−2i2i−2i-202200-20−2i2i00002−22−2i2−i2i2−i2−2−22222−2−200-22−2i2i000−i2i2i2−i2−i2i20000−2200000000000000
χ432-22-2-222-22i−2i2i−2i-202200-20−2i2i0000−22−22−i2i2−i2i222−2−2−2−22200-22−2i2i000i2−i2−i2i2i2−i200002−200000000000000
χ442-22-2-222-22i−2i2i−2i-202200-20−2i2i0000−22−22−i2i2−i2i2−2−22222−2−2002-22i−2i000i2−i2i2−i2−i2i200002−200000000000000
χ452-22-2-222-2−2i2i−2i2i20-2-20020−2i2i00002−22−2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2-22000002i−2i−i2i2−22−2200002−200000000000000
χ462-22-2-222-2−2i2i−2i2i20-2-20020−2i2i00002−22−2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i22-200000−2i2i−i2i22−22−200002−200000000000000
χ472-22-2-222-2−2i2i−2i2i20-2-20020−2i2i0000−22−22i2−i2i2−i2i2i2−i2−i2i2i2−i2−i22-200000−2i2ii2−i2−22−220000−2200000000000000
χ482-22-2-222-2−2i2i−2i2i20-2-20020−2i2i0000−22−22i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2-22000002i−2ii2−i22−22−20000−2200000000000000
χ492-22-2-222-2−2i2i−2i2i-202200-202i−2i00002−22−2−i2i2−i2i222−2−2−2−222002-2−2i2i000i2−i2i2−i2−i2i20000−2200000000000000
χ502-22-2-222-2−2i2i−2i2i-202200-202i−2i00002−22−2−i2i2−i2i2−2−22222−2−200-222i−2i000i2−i2−i2i2i2−i20000−2200000000000000
χ512-22-2-222-2−2i2i−2i2i-202200-202i−2i0000−22−22i2−i2i2−i222−2−2−2−22200-222i−2i000−i2i2i2−i2−i2i200002−200000000000000
χ522-22-2-222-2−2i2i−2i2i-202200-202i−2i0000−22−22i2−i2i2−i2−2−22222−2−2002-2−2i2i000−i2i2−i2i2i2−i200002−200000000000000
χ532-2-2-222-220000222-22-2-2-200002-2000000002i−2i2i−2i2i−2i2i−2i0000000000000002-22-20000002i−2i00000000
χ542-2-2-222-220000222-22-2-2-200002-2000000002i−2i2i−2i2i−2i2i−2i000000000000000-22-22000000−2i2i00000000
χ552-2-2-222-220000222-22-2-2-200002-200000000−2i2i−2i2i−2i2i−2i2i0000000000000002-22-2000000−2i2i00000000
χ562-2-2-222-220000222-22-2-2-200002-200000000−2i2i−2i2i−2i2i−2i2i000000000000000-22-220000002i−2i00000000
χ572-2-2-222-220000-2-2-22-222200002-2000000002-22-2-22-220000000000000000000002-22-2002-2000000
χ582-2-2-222-220000-2-2-22-222200002-2000000002-22-2-22-22000000000000000000000-22-2200-22000000
χ592-2-2-222-220000-2-2-22-222200002-200000000-22-222-22-20000000000000000000002-22-200-22000000
χ602-2-2-222-220000-2-2-22-222200002-200000000-22-222-22-2000000000000000000000-22-22002-2000000
χ6144-44-44-4-4000040-4400-400000000000000022−22−222222−22−222200000000000000000000000000000000000
χ6244-44-44-4-4000040-4400-4000000000000000−222222−22−222222−2200000000000000000000000000000000000
χ6344-44-44-4-40000-404-40040000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000
χ6444-44-44-4-40000-404-4004000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000
χ6544-4-44-44-44i4i−4i−4i0400-4-40400−4i4i00000000000000000000000000000000000000000000000000000
χ6644-4-44-44-4−4i−4i4i4i0400-4-404004i−4i00000000000000000000000000000000000000000000000000000
χ674-4444-4-4-400000400-440-4000000000000000000000000000000000000000000022−22−22220000000000
χ684-4444-4-4-400000400-440-40000000000000000000000000000000000000000000−222222−220000000000
χ694-4444-4-4-400000-4004-40400000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ704-4444-4-4-400000-4004-4040000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ714-4-44-4-4444-4-440000000000000022−22−222222−22−22220000000000000000000000000000000000000000000
χ724-4-44-4-4444-4-4400000000000000−222222−22−222222−220000000000000000000000000000000000000000000
χ734-4-44-4-444-444-40000000000000022−22−2222−222222−220000000000000000000000000000000000000000000
χ744-4-44-4-444-444-400000000000000−222222−2222−22−22220000000000000000000000000000000000000000000
χ754-4-4-444-4400004-44-4-44-440000-44000000000000000000000000000000000000000000000000000
χ764-4-4-444-440000-44-444-44-40000-44000000000000000000000000000000000000000000000000000
χ77888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000000000

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