Finite Group Databasebeta

← Group #243458

Character table — Group #243458

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444444444422444444888888888888888888888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ9111111111-1-1-1-1-1-1-1-11111111-1-111-1-111-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ10111111111-1-1-1-1-1-1-1-11111111-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-11111-1-1
χ11111111111-1-1-1-1-1-1-1-11111111-1-111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111
χ12111111111-1-1-1-1-1-1-1-11111111-1-111-1-111-1-111-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-1-1-111
χ13111111111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-111-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ14111111111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-111-1-1-1-111
χ15111111111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-11111-1-111-1-1
χ16111111111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-11111-1-1
χ172222222222222-2-2-2-2-2-222-2-22-2-2-2-2222222-2-2-2-2000000000000000000000000000000000000
χ182222222222222-2-2-2-2-2-222-2-22-2-2-2-222-2-2-2-22222000000000000000000000000000000000000
χ19222222222-2-2-2-22222-2-222-2-2222-2-2-2-222-2-2-2-222000000000000000000000000000000000000
χ20222222222-2-2-2-22222-2-222-2-2222-2-2-2-2-2-22222-2-2000000000000000000000000000000000000
χ2122222222-22222222222-2-222-2-2-2-2-2-2-200000000222200000000-2-2-2-200000000000000000000
χ2222222222-22222222222-2-222-2-2-2-2-2-2-200000000-2-2-2-200000000222200000000000000000000
χ2322222222-22222-2-2-2-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000000000002i−2i2i−2i
χ2422222222-22222-2-2-2-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000000000−2i2i−2i2i
χ2522222222-2-2-2-2-22222-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000002i−2i−2i2i
χ2622222222-2-2-2-2-22222-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000−2i2i2i−2i
χ2722222222-2-2-2-2-2-2-2-2-222-2-222-222-2-2220000000022-2-200000000-2-22200000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-222-2-222-222-2-22200000000-2-2220000000022-2-200000000000000000000
χ2922-2-22-22-202i2i−2i−2i2i2i−2i−2i2-2002-20000000000000002-22i−2i22−2−222−2−20000i2i2−i2−i2i2i2−i2−i2000000000000
χ3022-2-22-22-202i2i−2i−2i2i2i−2i−2i2-2002-20000000000000002-22i−2i−2−222−2−2220000−i2−i2i2i2−i2−i2i2i2000000000000
χ3122-2-22-22-202i2i−2i−2i2i2i−2i−2i2-2002-2000000000000000-22−2i2i22−2−2−2−2220000i2i2−i2−i2−i2−i2i2i2000000000000
χ3222-2-22-22-202i2i−2i−2i2i2i−2i−2i2-2002-2000000000000000-22−2i2i−2−22222−2−20000−i2−i2i2i2i2i2−i2−i2000000000000
χ3322-2-22-22-20−2i−2i2i2i−2i−2i2i2i2-2002-20000000000000002-2−2i2i22−2−222−2−20000−i2−i2i2i2−i2−i2i2i2000000000000
χ3422-2-22-22-20−2i−2i2i2i−2i−2i2i2i2-2002-20000000000000002-2−2i2i−2−222−2−2220000i2i2−i2−i2i2i2−i2−i2000000000000
χ3522-2-22-22-20−2i−2i2i2i−2i−2i2i2i2-2002-2000000000000000-222i−2i22−2−2−2−2220000−i2−i2i2i2i2i2−i2−i2000000000000
χ3622-2-22-22-20−2i−2i2i2i−2i−2i2i2i2-2002-2000000000000000-222i−2i−2−22222−2−20000i2i2−i2−i2−i2−i2i2i2000000000000
χ372-22-2-222-222i−2i2i−2i2i−2i2i−2i2-2-2-2-2222i−2i2-22i−2i0000000000002i−2i2i−2i000000002-22-20000000000000000
χ382-22-2-222-222i−2i2i−2i2i−2i2i−2i2-2-2-2-2222i−2i2-22i−2i000000000000−2i2i−2i2i00000000-22-220000000000000000
χ392-22-2-222-222i−2i2i−2i−2i2i−2i2i-22-2-22-22−2i2i-222i−2i000000000000000000000000000000002i−2i2-200000000
χ402-22-2-222-222i−2i2i−2i−2i2i−2i2i-22-2-22-22−2i2i-222i−2i00000000000000000000000000000000−2i2i-2200000000
χ412-22-2-222-22−2i2i−2i2i2i−2i2i−2i-22-2-22-222i−2i-22−2i2i000000000000000000000000000000002i−2i-2200000000
χ422-22-2-222-22−2i2i−2i2i2i−2i2i−2i-22-2-22-222i−2i-22−2i2i00000000000000000000000000000000−2i2i2-200000000
χ432-22-2-222-22−2i2i−2i2i−2i2i−2i2i2-2-2-2-222−2i2i2-2−2i2i0000000000002i−2i2i−2i00000000-22-220000000000000000
χ442-22-2-222-22−2i2i−2i2i−2i2i−2i2i2-2-2-2-222−2i2i2-2−2i2i000000000000−2i2i−2i2i000000002-22-20000000000000000
χ452-22-2-222-2-22i−2i2i−2i2i−2i2i−2i2-222-22-2−2i2i-22−2i2i00000000000000002-22-2000000002i−2i2i−2i000000000000
χ462-22-2-222-2-22i−2i2i−2i2i−2i2i−2i2-222-22-2−2i2i-22−2i2i0000000000000000-22-2200000000−2i2i−2i2i000000000000
χ472-22-2-222-2-22i−2i2i−2i−2i2i−2i2i-22222-2-22i−2i2-2−2i2i0000000000000000000000000000000000002-22i−2i0000
χ482-22-2-222-2-22i−2i2i−2i−2i2i−2i2i-22222-2-22i−2i2-2−2i2i000000000000000000000000000000000000-22−2i2i0000
χ492-22-2-222-2-2−2i2i−2i2i2i−2i2i−2i-22222-2-2−2i2i2-22i−2i0000000000000000000000000000000000002-2−2i2i0000
χ502-22-2-222-2-2−2i2i−2i2i2i−2i2i−2i-22222-2-2−2i2i2-22i−2i000000000000000000000000000000000000-222i−2i0000
χ512-22-2-222-2-2−2i2i−2i2i−2i2i−2i2i2-222-22-22i−2i-222i−2i00000000000000002-22-200000000−2i2i−2i2i000000000000
χ522-22-2-222-2-2−2i2i−2i2i−2i2i−2i2i2-222-22-22i−2i-222i−2i0000000000000000-22-22000000002i−2i2i−2i000000000000
χ532-2-22-2-22202-2-222-2-222200-2-20000000000000000000i2−i2−i2i22−2−222i−2i2i−2i−i2i2i2−i22−2−22000000000000
χ542-2-22-2-22202-2-222-2-222200-2-20000000000000000000i2−i2−i2i2−222−2−2i2i−2i2i−i2i2i2−i2−222−2000000000000
χ552-2-22-2-22202-2-222-2-222200-2-20000000000000000000−i2i2i2−i22−2−22−2i2i−2i2ii2−i2−i2i22−2−22000000000000
χ562-2-22-2-22202-2-222-2-222200-2-20000000000000000000−i2i2i2−i2−222−22i−2i2i−2ii2−i2−i2i2−222−2000000000000
χ572-2-22-2-2220-222-2-222-22200-2-20000000000000000000i2−i2−i2i22−2−222i−2i−2i2ii2−i2−i2i2−222−2000000000000
χ582-2-22-2-2220-222-2-222-22200-2-20000000000000000000i2−i2−i2i2−222−2−2i2i2i−2ii2−i2−i2i22−2−22000000000000
χ592-2-22-2-2220-222-2-222-22200-2-20000000000000000000−i2i2i2−i22−2−22−2i2i2i−2i−i2i2i2−i2−222−2000000000000
χ602-2-22-2-2220-222-2-222-22200-2-20000000000000000000−i2i2i2−i2−222−22i−2i−2i2i−i2i2i2−i22−2−22000000000000
χ61444-4-4-4-44400000000004-400-40000000000004-4000000000000000000000000000000000000
χ62444-4-4-4-44400000000004-400-4000000000000-44000000000000000000000000000000000000
χ63444-4-4-4-44-40000000000-44004000000004i−4i0000000000000000000000000000000000000000
χ64444-4-4-4-44-40000000000-4400400000000−4i4i0000000000000000000000000000000000000000
χ6544-4-44-44-404i4i−4i−4i−4i−4i4i4i-4400-44000000000000000000000000000000000000000000000000000
χ6644-4-44-44-40−4i−4i4i4i4i4i−4i−4i-4400-44000000000000000000000000000000000000000000000000000
χ674-4444-4-4-440000000000-4400-40000004-4000000000000000000000000000000000000000000
χ684-4444-4-4-440000000000-4400-4000000-44000000000000000000000000000000000000000000
χ694-4444-4-4-4-400000000004-400400000000004i−4i00000000000000000000000000000000000000
χ704-4444-4-4-4-400000000004-40040000000000−4i4i00000000000000000000000000000000000000
χ714-4-44-4-44404-4-44-444-4-4-40044000000000000000000000000000000000000000000000000000
χ724-4-44-4-4440-444-44-4-44-4-40044000000000000000000000000000000000000000000000000000
χ7388-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000
χ748-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000

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