Finite Group Databasebeta

← Group #419203

Character table — Group #419203

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12222222222244444444444444448888888888888888222244444444244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-11111-1-1
χ311111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-11-1-1-1-11-1-1-111-1-1-1-111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-111-1-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-111-1-111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-11-1-111111-11111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11-1-1-111-1111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-1111-1-111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-11-1-1111-1-1-1-1-1-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-111-111-1-11111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11111-1-111-1-1-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-1-111111-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111111-1-11-1-1-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-1-1-1-1111-1-1-1111111
χ1722222222-2-2-2-222-2-22-22-200000000000000002222-2-2-2-22200-2-2000000200000000-200000000
χ1822222222-2-2-2-222-2-22-22-200000000000000002222-2-2-2-2-2-20022000000-200000000200000000
χ1922222222-2-2-2-222-2-22-22-20000000000000000-2-2-2-222222200-2-2000000-200000000200000000
χ2022222222-2-2-2-222-2-22-22-20000000000000000-2-2-2-22222-2-20022000000200000000-200000000
χ2122222222-2-2-2-2-2-222-22-22000000002222-2-2-2-200000000002200-2-20000020000-200000000000
χ2222222222-2-2-2-2-2-222-22-22000000002222-2-2-2-20000000000-2-2002200000-20000200000000000
χ2322222222-2-2-2-2-2-222-22-2200000000-2-2-2-2222200000000002200-2-200000-20000200000000000
χ2422222222-2-2-2-2-2-222-22-2200000000-2-2-2-222220000000000-2-200220000020000-200000000000
χ2522-2-22-2-2222-2-22-222-2-22-2000000002i2i−2i−2i2i2i−2i−2i000000002-2002-2000000000000000000002i−2i00
χ2622-2-22-2-2222-2-22-222-2-22-2000000002i2i−2i−2i2i2i−2i−2i00000000-2200-2200000000000000000000−2i2i00
χ2722-2-22-2-2222-2-22-222-2-22-200000000−2i−2i2i2i−2i−2i2i2i000000002-2002-200000000000000000000−2i2i00
χ2822-2-22-2-2222-2-22-222-2-22-200000000−2i−2i2i2i−2i−2i2i2i00000000-2200-22000000000000000000002i−2i00
χ2922-2-22-2-22-2-2222-2-2-2-22222222-2-2-2-200000000000000002-200-220000000000000000002-20000
χ3022-2-22-2-22-2-2222-2-2-2-22222222-2-2-2-20000000000000000-22002-2000000000000000000-220000
χ3122-2-22-2-22-2-2222-2-2-2-2222-2-2-2-2222200000000000000002-200-22000000000000000000-220000
χ3222-2-22-2-22-2-2222-2-2-2-2222-2-2-2-222220000000000000000-22002-20000000000000000002-20000
χ3322-2-22-2-22-2-222-22222-2-2-2000000002i2i−2i−2i−2i−2i2i2i000000000000000022-2-200002i−2i000000000000
χ3422-2-22-2-22-2-222-22222-2-2-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000-2-2220000−2i2i000000000000
χ3522-2-22-2-22-2-222-22222-2-2-200000000−2i−2i2i2i2i2i−2i−2i000000000000000022-2-20000−2i2i000000000000
χ3622-2-22-2-22-2-222-22222-2-2-200000000−2i−2i2i2i2i2i−2i−2i0000000000000000-2-22200002i−2i000000000000
χ372-22-2-22-222-22-22-22-222-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000002-22-2002i−2i00000000000000
χ382-22-2-22-222-22-22-22-222-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000-22-2200−2i2i00000000000000
χ392-22-2-22-222-22-22-22-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000002-22-200−2i2i00000000000000
χ402-22-2-22-222-22-22-22-222-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000-22-22002i−2i00000000000000
χ412-2-22-2-2222-2-22-2-2-22222-2000000000000000022-2-222-2-2002-2002-2000000000000002-2000000
χ422-2-22-2-2222-2-22-2-2-22222-2000000000000000022-2-222-2-200-2200-2200000000000000-22000000
χ432-2-22-2-2222-2-22-2-2-22222-20000000000000000-2-222-2-222002-2002-200000000000000-22000000
χ442-2-22-2-2222-2-22-2-2-22222-20000000000000000-2-222-2-22200-2200-22000000000000002-2000000
χ452-2-22-2-222-222-222-22-22-2-22i2i−2i−2i−2i−2i2i2i0000000000000000002-200-22000000000000000000002i−2i
χ462-2-22-2-222-222-222-22-22-2-22i2i−2i−2i−2i−2i2i2i000000000000000000-22002-200000000000000000000−2i2i
χ472-2-22-2-222-222-222-22-22-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000002-200-2200000000000000000000−2i2i
χ482-2-22-2-222-222-222-22-22-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000-22002-2000000000000000000002i−2i
χ492-2-22-2-222-222-2-2-22-22-222000000000000000022-2-2-2-222000000002-2-2200000002-2000000000
χ502-2-22-2-222-222-2-2-22-22-222000000000000000022-2-2-2-22200000000-222-20000000-22000000000
χ512-2-22-2-222-222-2-2-22-22-2220000000000000000-2-22222-2-2000000002-2-220000000-22000000000
χ522-2-22-2-222-222-2-2-22-22-2220000000000000000-2-22222-2-200000000-222-200000002-2000000000
χ53444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000
χ544444-4-4-4-40000000000002-22-22-22-222−2222−22000022−2222−220000000000000000000000000000000000
χ554444-4-4-4-40000000000002-22-22-22-2−2222−22220000−2222−22220000000000000000000000000000000000
χ564444-4-4-4-4000000000000-22-22-22-2222−2222−220000−2222−22220000000000000000000000000000000000
χ574444-4-4-4-4000000000000-22-22-22-22−2222−2222000022−2222−220000000000000000000000000000000000
χ5844-4-44-4-4444-4-4-44-4-444-44000000000000000000000000000000000000000000000000000000
χ5944-4-4-444-40000000000002-22-2-22-222i2−2i2−2i22i2000000002i2−2i22i2−2i2000000000000000000000000000000
χ6044-4-4-444-40000000000002-22-2-22-22−2i22i22i2−2i200000000−2i22i2−2i22i2000000000000000000000000000000
χ6144-4-4-444-4000000000000-22-222-22-22i2−2i2−2i22i200000000−2i22i2−2i22i2000000000000000000000000000000
χ6244-4-4-444-4000000000000-22-222-22-2−2i22i22i2−2i2000000002i2−2i22i2−2i2000000000000000000000000000000
χ634-44-44-44-40000000000002i−2i−2i2i2i−2i−2i2i000022−2222−2200002i2−2i2−2i22i2000000000000000000000000000000
χ644-44-44-44-40000000000002i−2i−2i2i2i−2i−2i2i0000−2222−22220000−2i22i22i2−2i2000000000000000000000000000000
χ654-44-44-44-4000000000000−2i2i2i−2i−2i2i2i−2i000022−2222−220000−2i22i22i2−2i2000000000000000000000000000000
χ664-44-44-44-4000000000000−2i2i2i−2i−2i2i2i−2i0000−2222−222200002i2−2i2−2i22i2000000000000000000000000000000
χ674-44-4-44-444-44-4-44-44-4-444000000000000000000000000000000000000000000000000000000
χ684-44-4-44-44-44-444-4-444-4-44000000000000000000000000000000000000000000000000000000
χ694-44-4-44-44-44-44-444-4-444-4000000000000000000000000000000000000000000000000000000
χ704-4-4444-4-40000000000002i−2i−2i2i−2i2i2i−2i00002i2−2i2−2i22i2−222222−220000000000000000000000000000000000
χ714-4-4444-4-40000000000002i−2i−2i2i−2i2i2i−2i0000−2i22i22i2−2i222−22−22220000000000000000000000000000000000
χ724-4-4444-4-4000000000000−2i2i2i−2i2i−2i−2i2i00002i2−2i2−2i22i222−22−22220000000000000000000000000000000000
χ734-4-4444-4-4000000000000−2i2i2i−2i2i−2i−2i2i0000−2i22i22i2−2i2−222222−220000000000000000000000000000000000
χ744-4-44-4-4444-4-44444-4-4-4-44000000000000000000000000000000000000000000000000000000

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