Finite Group Databasebeta

← Group #394169

Character table — Group #394169

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222222222222444444442222222244444444444444444444444444442244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-11-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111-111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1111-111-1-1-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-11-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11-1-1-1111-1-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1111-1-1-1111-1-1-1-111
χ1722222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-20000000022-2-222-2-2000000000000000000000000
χ1822222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-200000000-2-222-2-222000000000000000000000000
χ1922222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-20000000022220000000022-2-2-2-222000000000000000000000000
χ2022222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-200000000222200000000-2-22222-2-2000000000000000000000000
χ2122222222-2-2-222-2-222-2-2-22222-2-2-2-20000000022-2-200000000000000000000000002002-20-200000000
χ2222222222-2-2-222-2-222-2-2-22222-2-2-2-20000000022-2-20000000000000000000000000-200-220200000000
χ2322222222-2-2-222-2-222-2-2-2-2-2-2-2222200000000-2-2220000000000000000000000000200-220-200000000
χ2422222222-2-2-222-2-222-2-2-2-2-2-2-2222200000000-2-2220000000000000000000000000-2002-20200000000
χ2522222222-2-2-2-2-222-2-222-22222-2-2-2-200000000-2-222000000000000000000000000202-200-2000000000
χ2622222222-2-2-2-2-222-2-222-22222-2-2-2-200000000-2-222000000000000000000000000-20-22002000000000
χ2722222222-2-2-2-2-222-2-222-2-2-2-2-222220000000022-2-200000000000000000000000020-2200-2000000000
χ2822222222-2-2-2-2-222-2-222-2-2-2-2-222220000000022-2-2000000000000000000000000-202-2002000000000
χ29222-2-2-2-2222-22-22-22-22-2-2000000000000000000002222-2-2-2-200002i−2i2i−2i2i2i−2i−2i00000000000000000000
χ30222-2-2-2-2222-22-22-22-22-2-2000000000000000000002222-2-2-2-20000−2i2i−2i2i−2i−2i2i2i00000000000000000000
χ31222-2-2-2-2222-22-22-22-22-2-200000000000000000000-2-2-2-2222200002i−2i2i−2i−2i−2i2i2i00000000000000000000
χ32222-2-2-2-2222-22-22-22-22-2-200000000000000000000-2-2-2-222220000−2i2i−2i2i2i2i−2i−2i00000000000000000000
χ33222-2-2-2-2222-2-22-22-22-22-2000000002222-2-2-2-200000000000000002i−2i−2i2i00002i2i−2i−2i0000000000000000
χ34222-2-2-2-2222-2-22-22-22-22-2000000002222-2-2-2-20000000000000000−2i2i2i−2i0000−2i−2i2i2i0000000000000000
χ35222-2-2-2-2222-2-22-22-22-22-200000000-2-2-2-2222200000000000000002i−2i−2i2i0000−2i−2i2i2i0000000000000000
χ36222-2-2-2-2222-2-22-22-22-22-200000000-2-2-2-222220000000000000000−2i2i2i−2i00002i2i−2i−2i0000000000000000
χ372-2-222-2-222-222222-2-2-2-2-222-2-222-2-2000000002-22-200000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ382-2-222-2-222-222222-2-2-2-2-222-2-222-2-2000000002-22-20000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ392-2-222-2-222-222222-2-2-2-2-2-2-222-2-22200000000-22-2200000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ402-2-222-2-222-222222-2-2-2-2-2-2-222-2-22200000000-22-220000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ412-2-222-2-222-22-2-2-2-22222-222-2-222-2-222-2-222-2-2-22-2222-2-222-2-200000000000000000000000000000000
χ422-2-222-2-222-22-2-2-2-22222-222-2-222-2-2-2-222-2-222-22-22-2-222-2-22200000000000000000000000000000000
χ432-2-222-2-222-22-2-2-2-22222-2-2-222-2-22222-2-222-2-22-22-2-2-222-2-22200000000000000000000000000000000
χ442-2-222-2-222-22-2-2-2-22222-2-2-222-2-222-2-222-2-2222-22-222-2-222-2-200000000000000000000000000000000
χ452-2-222-2-22-22-222-2-2-2-222222-2-2-2-222000000002-2-22000000000000000000000000000000002-22-20000
χ462-2-222-2-22-22-222-2-2-2-222222-2-2-2-222000000002-2-2200000000000000000000000000000000-22-220000
χ472-2-222-2-22-22-222-2-2-2-2222-2-22222-2-200000000-222-2000000000000000000000000000000002-2-220000
χ482-2-222-2-22-22-222-2-2-2-2222-2-22222-2-200000000-222-200000000000000000000000000000000-222-20000
χ492-2-222-2-22-22-2-2-22222-2-2222-2-2-2-22200000000-222-20000000000000000000000000000000000002-22-2
χ502-2-222-2-22-22-2-2-22222-2-2222-2-2-2-22200000000-222-2000000000000000000000000000000000000-22-22
χ512-2-222-2-22-22-2-2-22222-2-22-2-22222-2-2000000002-2-220000000000000000000000000000000000002-2-22
χ522-2-222-2-22-22-2-2-22222-2-22-2-22222-2-2000000002-2-22000000000000000000000000000000000000-222-2
χ532-2-2-2-22222-2-22-22-2-22-2220000000022-2-2-2-2220000000000002-22-200002-2-2200000000000000000000
χ542-2-2-2-22222-2-22-22-2-22-2220000000022-2-2-2-222000000000000-22-220000-222-200000000000000000000
χ552-2-2-2-22222-2-22-22-2-22-22200000000-2-22222-2-20000000000002-22-20000-222-200000000000000000000
χ562-2-2-2-22222-2-22-22-2-22-22200000000-2-22222-2-2000000000000-22-2200002-2-2200000000000000000000
χ572-2-2-2-22222-2-2-22-222-22-220000000000000000000022-2-2-2-2222-2-22000000002-2-220000000000000000
χ582-2-2-2-22222-2-2-22-222-22-220000000000000000000022-2-2-2-222-222-200000000-222-20000000000000000
χ592-2-2-2-22222-2-2-22-222-22-2200000000000000000000-2-22222-2-22-2-2200000000-222-20000000000000000
χ602-2-2-2-22222-2-2-22-222-22-2200000000000000000000-2-22222-2-2-222-2000000002-2-220000000000000000
χ61444-4-4-4-44-4-444-4-444-4-444000000000000000000000000000000000000000000000000000000000000
χ62444-4-4-4-44-4-44-444-4-444-44000000000000000000000000000000000000000000000000000000000000
χ6344-44-44-4-400000000000000004i−4i4i−4i2-22-22-22-200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ6444-44-44-4-400000000000000004i−4i4i−4i-22-22-22-220000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ6544-44-44-4-40000000000000000−4i4i−4i4i2-22-22-22-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ6644-44-44-4-40000000000000000−4i4i−4i4i-22-22-22-2200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ6744-4-44-44-40000000000004i−4i4i−4i00002-22-2-22-2200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ6844-4-44-44-40000000000004i−4i4i−4i0000-22-222-22-20000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ6944-4-44-44-4000000000000−4i4i−4i4i00002-22-2-22-220000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ7044-4-44-44-4000000000000−4i4i−4i4i0000-22-222-22-200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ714-444-4-44-400000000000000004i−4i−4i4i2-2-222-2-2200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ724-444-4-44-400000000000000004i−4i−4i4i-222-2-222-20000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ734-444-4-44-40000000000000000−4i4i4i−4i2-2-222-2-220000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ744-444-4-44-40000000000000000−4i4i4i−4i-222-2-222-200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ754-44-444-4-40000000000004i−4i−4i4i00002-2-22-222-200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ764-44-444-4-40000000000004i−4i−4i4i0000-222-22-2-220000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ774-44-444-4-4000000000000−4i4i4i−4i00002-2-22-222-20000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ784-44-444-4-4000000000000−4i4i4i−4i0000-222-22-2-2200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ794-4-4-4-4444-4444-4-44-444-4-4000000000000000000000000000000000000000000000000000000000000
χ804-4-4-4-4444-444-444-44-4-44-4000000000000000000000000000000000000000000000000000000000000

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