Finite Group Databasebeta

← Group #414508

Character table — Group #414508

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444888888884444444488888888888844444444888888882244444488888888
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111-1-1111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ17222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ18222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ19222222222222-2-2-2-2-2-2-2-200000000-2-2-2-22222000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ20222222222222-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2122222222-2-2-2-2222-2-2-2-222222222222-2-222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2222222222-2-2-2-2222-2-2-2-2222222222-2-222-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2322222222-2-2-2-2222-2-2-2-22-2-2-2-2-2-2-2-222-2-222-2-22222-2-2-2-2222200000000000000000000000000000000
χ2422222222-2-2-2-2222-2-2-2-22-2-2-2-2-2-2-2-2-2-222-2-22222222222-2-2-2-200000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-22222-20000000022-2-2-2-2220000000000002222-2-2-2-2000000000000000000000000
χ2622222222-2-2-2-2-2-2-22222-20000000022-2-2-2-222000000000000-2-2-2-22222000000000000000000000000
χ2722222222-2-2-2-2-2-2-22222-200000000-2-22222-2-200000000000022-2-2-2-222000000000000000000000000
χ2822222222-2-2-2-2-2-2-22222-200000000-2-22222-2-2000000000000-2-22222-2-2000000000000000000000000
χ29222-22-2-2-222-2-2-22-222-2-222i2i2i2i−2i−2i−2i−2i000000002i2i−2i−2i0000000000000000000000000000000000002i−2i2-2
χ30222-22-2-2-222-2-2-22-222-2-222i2i2i2i−2i−2i−2i−2i000000002i2i−2i−2i000000000000000000000000000000000000−2i2i-22
χ31222-22-2-2-222-2-2-22-222-2-22−2i−2i−2i−2i2i2i2i2i00000000−2i−2i2i2i0000000000000000000000000000000000002i−2i-22
χ32222-22-2-2-222-2-2-22-222-2-22−2i−2i−2i−2i2i2i2i2i00000000−2i−2i2i2i000000000000000000000000000000000000−2i2i2-2
χ33222-22-2-2-2-2-222-22-2-2-22222i2i2i2i−2i−2i−2i−2i00000000−2i−2i2i2i000000000000000000000000000000002i−2i2-20000
χ34222-22-2-2-2-2-222-22-2-2-22222i2i2i2i−2i−2i−2i−2i00000000−2i−2i2i2i00000000000000000000000000000000−2i2i-220000
χ35222-22-2-2-2-2-222-22-2-2-2222−2i−2i−2i−2i2i2i2i2i000000002i2i−2i−2i000000000000000000000000000000002i−2i-220000
χ36222-22-2-2-2-2-222-22-2-2-2222−2i−2i−2i−2i2i2i2i2i000000002i2i−2i−2i00000000000000000000000000000000−2i2i2-20000
χ372-222-2-22-22-22-22-2-22-22-22000000000000000000002i2i−2i−2i2i2i−2i−2i002i−2i002i−2i2-22-200000000000000000000
χ382-222-2-22-22-22-22-2-22-22-22000000000000000000002i2i−2i−2i2i2i−2i−2i00−2i2i00−2i2i-22-2200000000000000000000
χ392-222-2-22-22-22-22-2-22-22-2200000000000000000000−2i−2i2i2i−2i−2i2i2i002i−2i002i−2i-22-2200000000000000000000
χ402-222-2-22-22-22-22-2-22-22-2200000000000000000000−2i−2i2i2i−2i−2i2i2i00−2i2i00−2i2i2-22-200000000000000000000
χ412-222-2-22-22-22-2-222-22-22-222-2-222-2-2000000002-22-2000000002i−2i002i−2i002i−2i−2i2i00000000000000000000
χ422-222-2-22-22-22-2-222-22-22-222-2-222-2-2000000002-22-200000000−2i2i00−2i2i00−2i2i2i−2i00000000000000000000
χ432-222-2-22-22-22-2-222-22-22-2-2-222-2-22200000000-22-22000000002i−2i002i−2i00−2i2i2i−2i00000000000000000000
χ442-222-2-22-22-22-2-222-22-22-2-2-222-2-22200000000-22-2200000000−2i2i00−2i2i002i−2i−2i2i00000000000000000000
χ452-222-2-22-2-22-222-2-2-22-222000000000000000000002i2i−2i−2i−2i−2i2i2i2i−2i00−2i2i0000002-22-20000000000000000
χ462-222-2-22-2-22-222-2-2-22-222000000000000000000002i2i−2i−2i−2i−2i2i2i−2i2i002i−2i000000-22-220000000000000000
χ472-222-2-22-2-22-222-2-2-22-22200000000000000000000−2i−2i2i2i2i2i−2i−2i2i−2i00−2i2i000000-22-220000000000000000
χ482-222-2-22-2-22-222-2-2-22-22200000000000000000000−2i−2i2i2i2i2i−2i−2i−2i2i002i−2i0000002-22-20000000000000000
χ492-222-2-22-2-22-22-2222-22-2-222-2-222-2-200000000-22-2200000000002i−2i00−2i2i00002i−2i−2i2i0000000000000000
χ502-222-2-22-2-22-22-2222-22-2-222-2-222-2-200000000-22-220000000000−2i2i002i−2i0000−2i2i2i−2i0000000000000000
χ512-222-2-22-2-22-22-2222-22-2-2-2-222-2-222000000002-22-200000000002i−2i00−2i2i0000−2i2i2i−2i0000000000000000
χ522-222-2-22-2-22-22-2222-22-2-2-2-222-2-222000000002-22-20000000000−2i2i002i−2i00002i−2i−2i2i0000000000000000
χ532-22-2-22-222-2-2222-2-222-2-22i2i−2i−2i−2i−2i2i2i000000002i−2i−2i2i000000000000000000000000002i−2i002-200000000
χ542-22-2-22-222-2-2222-2-222-2-22i2i−2i−2i−2i−2i2i2i000000002i−2i−2i2i00000000000000000000000000−2i2i00-2200000000
χ552-22-2-22-222-2-2222-2-222-2-2−2i−2i2i2i2i2i−2i−2i00000000−2i2i2i−2i000000000000000000000000002i−2i00-2200000000
χ562-22-2-22-222-2-2222-2-222-2-2−2i−2i2i2i2i2i−2i−2i00000000−2i2i2i−2i00000000000000000000000000−2i2i002-200000000
χ572-22-2-22-22-222-222-22-2-22-22i2i−2i−2i−2i−2i2i2i00000000−2i2i2i−2i0000000000000000000000002-2002i−2i0000000000
χ582-22-2-22-22-222-222-22-2-22-22i2i−2i−2i−2i−2i2i2i00000000−2i2i2i−2i000000000000000000000000-2200−2i2i0000000000
χ592-22-2-22-22-222-222-22-2-22-2−2i−2i2i2i2i2i−2i−2i000000002i−2i−2i2i0000000000000000000000002-200−2i2i0000000000
χ602-22-2-22-22-222-222-22-2-22-2−2i−2i2i2i2i2i−2i−2i000000002i−2i−2i2i000000000000000000000000-22002i−2i0000000000
χ61444-44-4-4-444-4-44-44-4-444-4000000000000000000000000000000000000000000000000000000000000
χ62444-44-4-4-4-4-4444-4444-4-4-4000000000000000000000000000000000000000000000000000000000000
χ6344-44-4-4-440000000000002i2−2i22i2−2i22i2−2i22i2−2i200004i−4i00000022−2222−22000000000000000000000000000000000000
χ6444-44-4-4-440000000000002i2−2i22i2−2i22i2−2i22i2−2i20000−4i4i000000−2222−2222000000000000000000000000000000000000
χ6544-44-4-4-44000000000000−2i22i2−2i22i2−2i22i2−2i22i200004i−4i000000−2222−2222000000000000000000000000000000000000
χ6644-44-4-4-44000000000000−2i22i2−2i22i2−2i22i2−2i22i20000−4i4i00000022−2222−22000000000000000000000000000000000000
χ6744-4-4-444-400000000000022−2222−22−2222−2222004i−4i0000000000002i2−2i22i2−2i200000000000000000000000000000000
χ6844-4-4-444-400000000000022−2222−22−2222−222200−4i4i000000000000−2i22i2−2i22i200000000000000000000000000000000
χ6944-4-4-444-4000000000000−2222−222222−2222−22004i−4i000000000000−2i22i2−2i22i200000000000000000000000000000000
χ7044-4-4-444-4000000000000−2222−222222−2222−2200−4i4i0000000000002i2−2i22i2−2i200000000000000000000000000000000
χ714-44-4-44-444-4-44-4-444-4-444000000000000000000000000000000000000000000000000000000000000
χ724-44-4-44-44-444-4-4-44-444-44000000000000000000000000000000000000000000000000000000000000
χ734-4-4444-4-40000000000002i2−2i2−2i22i22i2−2i2−2i22i24-400000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ744-4-4444-4-40000000000002i2−2i2−2i22i22i2−2i2−2i22i2-440000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ754-4-4444-4-4000000000000−2i22i22i2−2i2−2i22i22i2−2i24-40000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ764-4-4444-4-4000000000000−2i22i22i2−2i2−2i22i22i2−2i2-4400000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ774-4-4-44-44400000000000022−22−2222−222222−220000004-40000000022−22−222200000000000000000000000000000000
χ784-4-4-44-44400000000000022−22−2222−222222−22000000-4400000000−222222−2200000000000000000000000000000000
χ794-4-4-44-444000000000000−222222−2222−22−22220000004-400000000−222222−2200000000000000000000000000000000
χ804-4-4-44-444000000000000−222222−2222−22−2222000000-440000000022−22−222200000000000000000000000000000000

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