Finite Group Databasebeta

← Group #397244

Character table — Group #397244

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222222224444444444442244444444444444444444444444888888882224444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1
χ911111111111-1-1-1-1111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111-111-1-11-1-1-111-1-1
χ1011111111111-1-1-1-1111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-11-1-111-1111-1-111
χ1111111111111-1-1-1-1111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1111-1-1-11-1-1-1-111
χ1211111111111-1-1-1-1111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11-1-1-1111-11111-1-1
χ1311111111111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111111-1-1-1-1-11-111-1-111
χ1411111111111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-111111-11-1-111-1-1
χ1511111111111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-111-11-1-1-1-1-111111-1-1
χ1611111111111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-11-111111-1-1-1-1-111
χ172222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2000000000000000000000000000000002-200002-200000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-200000000000000000000000000000000-220000-2200000000
χ1922222222222-2-2-2-22-2-2-2-2-22222-2-2-2-2-222000000000000000000000000000000002-20000-2200000000
χ2022222222222-2-2-2-22-2-2-2-2-22222-2-2-2-2-22200000000000000000000000000000000-2200002-200000000
χ2122222222-2-2-22222-2222-2-22222-2-22-2-2-2-200000000000000000000000000000000002-20000-22000000
χ2222222222-2-2-22222-2222-2-22222-2-22-2-2-2-20000000000000000000000000000000000-2200002-2000000
χ2322222222-2-2-22222-2-2-2-222-2-2-2-222-2-2-22200000000000000002222-2-2-2-2000000000000000000000000
χ2422222222-2-2-22222-2-2-2-222-2-2-2-222-2-2-2220000000000000000-2-2-2-22222000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-2222220000000000000000000000000000000000220000-2-2000000
χ2622222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-2222220000000000000000000000000000000000-2-2000022000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-222222222-222-2-2000000000000000022-2-2-2-222000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-222222222-222-2-20000000000000000-2-22222-2-2000000000000000000000000
χ2922-22-22-2-222-20000-22-2-22-200002-220000000000002i2i2i2i−2i−2i−2i−2i002i−2i002i−2i22-2-200000000000000000000
χ3022-22-22-2-222-20000-22-2-22-200002-220000000000002i2i2i2i−2i−2i−2i−2i00−2i2i00−2i2i-2-22200000000000000000000
χ3122-22-22-2-222-20000-22-2-22-200002-22000000000000−2i−2i−2i−2i2i2i2i2i002i−2i002i−2i-2-22200000000000000000000
χ3222-22-22-2-222-20000-22-2-22-200002-22000000000000−2i−2i−2i−2i2i2i2i2i00−2i2i00−2i2i22-2-200000000000000000000
χ3322-22-22-2-2-2-2200002-2222-200002-2-200002222-2-2-2-200000000002i−2i00−2i2i00002i2i−2i−2i0000000000000000
χ3422-22-22-2-2-2-2200002-2222-200002-2-200002222-2-2-2-20000000000−2i2i002i−2i0000−2i−2i2i2i0000000000000000
χ3522-22-22-2-2-2-2200002-2222-200002-2-20000-2-2-2-2222200000000002i−2i00−2i2i0000−2i−2i2i2i0000000000000000
χ3622-22-22-2-2-2-2200002-2222-200002-2-20000-2-2-2-222220000000000−2i2i002i−2i00002i2i−2i−2i0000000000000000
χ372-22-2-222-22-2222-2-2-222-2-2-222-2-222-22-22-20000000000000000000000000000000000002i−2i00002i−2i0000
χ382-22-2-222-22-2222-2-2-222-2-2-222-2-222-22-22-2000000000000000000000000000000000000−2i2i0000−2i2i0000
χ392-22-2-222-22-2222-2-2-2-2-2222-2-222-2-222-2-222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ402-22-2-222-22-2222-2-2-2-2-2222-2-222-2-222-2-22−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ412-22-2-222-22-22-2-222-222-2-2-2-2-22222-2-22-220000000000000000000000000000000000002i−2i0000−2i2i0000
χ422-22-2-222-22-22-2-222-222-2-2-2-2-22222-2-22-22000000000000000000000000000000000000−2i2i00002i−2i0000
χ432-22-2-222-22-22-2-222-2-2-222222-2-2-2-22-222-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ442-22-2-222-22-22-2-222-2-2-222222-2-2-2-22-222-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ452-22-2-222-2-22-222-2-2222-22222-2-2-2-2-2-22-220000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ462-22-2-222-2-22-222-2-2222-22222-2-2-2-2-2-22-22000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ472-22-2-222-2-22-222-2-22-2-22-2-2-2-222222-222-2000000000000000000000000000000000000000000002-22-2
χ482-22-2-222-2-22-222-2-22-2-22-2-2-2-222222-222-200000000000000000000000000000000000000000000-22-22
χ492-22-2-222-2-22-2-2-222222-222-2-222-2-2-22-22-20000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ502-22-2-222-2-22-2-2-222222-222-2-222-2-2-22-22-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ512-22-2-222-2-22-2-2-2222-2-22-2-222-2-22222-2-22000000000000000000000000000000000000000000002-2-22
χ522-22-2-222-2-22-2-2-2222-2-22-2-222-2-22222-2-2200000000000000000000000000000000000000000000-222-2
χ532-2-2-222-222-2-200002-22-22-20000-22200000000000022-2-2-2-2222-2002-20000002-2-220000000000000000
χ542-2-2-222-222-2-200002-22-22-20000-22200000000000022-2-2-2-222-2200-22000000-222-20000000000000000
χ552-2-2-222-222-2-200002-22-22-20000-222000000000000-2-22222-2-22-2002-2000000-222-20000000000000000
χ562-2-2-222-222-2-200002-22-22-20000-222000000000000-2-22222-2-2-2200-220000002-2-220000000000000000
χ572-2-2-222-22-2220000-22-222-20000-22-200002i2i−2i−2i−2i−2i2i2i000000002-200-2200−2i2i2i−2i00000000000000000000
χ582-2-2-222-22-2220000-22-222-20000-22-200002i2i−2i−2i−2i−2i2i2i00000000-22002-2002i−2i−2i2i00000000000000000000
χ592-2-2-222-22-2220000-22-222-20000-22-20000−2i−2i2i2i2i2i−2i−2i000000002-200-22002i−2i−2i2i00000000000000000000
χ602-2-2-222-22-2220000-22-222-20000-22-20000−2i−2i2i2i2i2i−2i−2i00000000-22002-200−2i2i2i−2i00000000000000000000
χ61444-4-4-4-4400000000000004i−4i4i−4i00000002i−2i2i−2i2i−2i2i−2i2-22-22-22-200000000000000000000000000000000
χ62444-4-4-4-4400000000000004i−4i4i−4i0000000−2i2i−2i2i−2i2i−2i2i-22-22-22-2200000000000000000000000000000000
χ63444-4-4-4-440000000000000−4i4i−4i4i00000002i−2i2i−2i2i−2i2i−2i-22-22-22-2200000000000000000000000000000000
χ64444-4-4-4-440000000000000−4i4i−4i4i0000000−2i2i−2i2i−2i2i−2i2i2-22-22-22-200000000000000000000000000000000
χ6544-44-44-4-444-40000-4-444-440000-44-40000000000000000000000000000000000000000000000000000
χ6644-44-44-4-4-4-44000044-4-4-440000-4440000000000000000000000000000000000000000000000000000
χ6744-4-44-44-40004-44-4000000000000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ6844-4-44-44-40004-44-400000000000000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ6944-4-44-44-4000-44-44000000000000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ7044-4-44-44-4000-44-4400000000000000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ714-4444-4-4-400000000000004i−4i−4i4i00000002-2-222-2-222i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ724-4444-4-4-400000000000004i−4i−4i4i0000000-222-2-222-2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ734-4444-4-4-40000000000000−4i4i4i−4i00000002-2-222-2-22−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ744-4444-4-4-40000000000000−4i4i4i−4i0000000-222-2-222-22i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ754-4-44-4-4440004-4-44000000000000000002-2-22-222-22-2-22-222-200000000000000000000000000000000
χ764-4-44-4-4440004-4-4400000000000000000-222-22-2-22-222-22-2-2200000000000000000000000000000000
χ774-4-44-4-444000-444-4000000000000000002-2-22-222-2-222-22-2-2200000000000000000000000000000000
χ784-4-44-4-444000-444-400000000000000000-222-22-2-222-2-22-222-200000000000000000000000000000000
χ794-4-4-444-444-4-4000044-44-4400004-4-40000000000000000000000000000000000000000000000000000
χ804-4-4-444-44-4440000-4-44-4-4400004-440000000000000000000000000000000000000000000000000000

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