Finite Group Databasebeta

← Group #292256

Character table — Group #292256

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444444444444422444444448888888888888888224444444488888888224444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ611111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ711111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1
χ911111111-1-1-1-111-1-1-1-1111111-1-11-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11-11111-1-11-1
χ1011111111-1-1-1-111-1-1-1-1111111-1-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-11-1-1-1-111-11
χ1111111111-1-1-1-111-1-1-1-1111111-1-11-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-11-111-1-111-11
χ1211111111-1-1-1-111-1-1-1-1111111-1-11-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1111111-11-1-111-1-11-1
χ1311111111-1-1-1-111-1-1-1-1111111-1-11-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111-1-1-111-1-1-11
χ1411111111-1-1-1-111-1-1-1-1111111-1-11-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1111-1-1111-1
χ1511111111-1-1-1-111-1-1-1-1111111-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1111-1
χ1611111111-1-1-1-111-1-1-1-1111111-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1111111-1-1-1-1-1-1-111111-1-1-11
χ1722222222222222-2-2-2-2-2-222-2-2-2-2-2222222-200000000000000000022-2-2-2-20000000000000000000000
χ1822222222222222-2-2-2-2-2-222-2-2-2-2-222-2-2-2-2-2000000000000000000-2-222220000000000000000000000
χ19222222222222-2-2222222-2-222-2-2-2-2-20000-2000000000000000022000000220000000000-2-200000000
χ20222222222222-2-2222222-2-222-2-2-2-2-20000-20000000000000000-2-2000000-2-200000000002200000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-20000200000000000000000000000000000000002-2002-2000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-2000020000000000000000000000000000000000-2200-22000000
χ2322222222-2-2-2-2222222-2-222-2-222-2-2-22222-2000000000000000000-2-222-2-20000000000000000000000
χ2422222222-2-2-2-2222222-2-222-2-222-2-2-2-2-2-2-2-200000000000000000022-2-2220000000000000000000000
χ2522222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-22220000200000000000000000000000000000000002-200-22000000
χ2622222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222000020000000000000000000000000000000000-22002-2000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-22222-2220000-2000000000000000022000000-2-20000000000-2200000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-22222-2220000-20000000000000000-2-20000002200000000002-200000000
χ2922-22-22-2-200002-20000222-2-2-200-2002i2i−2i−2i2000000002222-2-2-2-20000002i−2i0000002i2i−2i−2i000000000000
χ3022-22-22-2-200002-20000222-2-2-200-2002i2i−2i−2i200000000-2-2-2-222220000002i−2i000000−2i−2i2i2i000000000000
χ3122-22-22-2-200002-20000222-2-2-200-200−2i−2i2i2i2000000002222-2-2-2-2000000−2i2i000000−2i−2i2i2i000000000000
χ3222-22-22-2-200002-20000222-2-2-200-200−2i−2i2i2i200000000-2-2-2-22222000000−2i2i0000002i2i−2i−2i000000000000
χ3322-22-22-2-200002-20000-2-22-222002002i2i−2i−2i-22i2i2i2i−2i−2i−2i−2i00000000000000−2i2i0022-2-20000000000000000
χ3422-22-22-2-200002-20000-2-22-222002002i2i−2i−2i-2−2i−2i−2i−2i2i2i2i2i00000000000000−2i2i00-2-2220000000000000000
χ3522-22-22-2-200002-20000-2-22-22200200−2i−2i2i2i-22i2i2i2i−2i−2i−2i−2i000000000000002i−2i00-2-2220000000000000000
χ3622-22-22-2-200002-20000-2-22-22200200−2i−2i2i2i-2−2i−2i−2i−2i2i2i2i2i000000000000002i−2i0022-2-20000000000000000
χ372-222-2-22-22i2i−2i−2i2-2000000-22000002i−2i2i−2i2i−2i022−2−222−2−2i2i2−i2−i2i2i2−i2−i2002-2000000i2−i2i2−i22−22−2000000000000
χ382-222-2-22-22i2i−2i−2i2-2000000-22000002i−2i2i−2i2i−2i0−2−222−2−222−i2−i2i2i2−i2−i2i2i2002-2000000−i2i2−i2i2−22−22000000000000
χ392-222-2-22-22i2i−2i−2i2-2000000-22000002i−2i−2i2i−2i2i022−2−222−2−2i2i2−i2−i2i2i2−i2−i200-22000000−i2i2−i2i2−22−22000000000000
χ402-222-2-22-22i2i−2i−2i2-2000000-22000002i−2i−2i2i−2i2i0−2−222−2−222−i2−i2i2i2−i2−i2i2i200-22000000i2−i2i2−i22−22−2000000000000
χ412-222-2-22-2−2i−2i2i2i2-2000000-2200000−2i2i2i−2i2i−2i022−2−222−2−2−i2−i2i2i2−i2−i2i2i200-22000000i2−i2i2−i2−22−22000000000000
χ422-222-2-22-2−2i−2i2i2i2-2000000-2200000−2i2i2i−2i2i−2i0−2−222−2−222i2i2−i2−i2i2i2−i2−i200-22000000−i2i2−i2i22−22−2000000000000
χ432-222-2-22-2−2i−2i2i2i2-2000000-2200000−2i2i−2i2i−2i2i022−2−222−2−2−i2−i2i2i2−i2−i2i2i2002-2000000−i2i2−i2i22−22−2000000000000
χ442-222-2-22-2−2i−2i2i2i2-2000000-2200000−2i2i−2i2i−2i2i0−2−222−2−222i2i2−i2−i2i2i2−i2−i2002-2000000i2−i2i2−i2−22−22000000000000
χ452-22-222-2-22i−2i2i−2i002i2i−2i−2i2-2002-20000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−22-20000002i−2i00000000000000i2−i22−200
χ462-22-222-2-22i−2i2i−2i002i2i−2i−2i2-2002-20000000000i2−i2i2−i2i2−i2i2−i22−22−22−22−2-22000000−2i2i00000000000000−i2i2−2200
χ472-22-222-2-22i−2i2i−2i002i2i−2i−2i2-2002-20000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−222-20000002i−2i00000000000000−i2i2−2200
χ482-22-222-2-22i−2i2i−2i002i2i−2i−2i2-2002-20000000000−i2i2−i2i2−i2i2−i2i2−22−22−22−22-22000000−2i2i00000000000000i2−i22−200
χ492-22-222-2-2−2i2i−2i2i00−2i−2i2i2i2-2002-20000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−222-2000000−2i2i00000000000000i2−i2−2200
χ502-22-222-2-2−2i2i−2i2i00−2i−2i2i2i2-2002-20000000000i2−i2i2−i2i2−i2i2−i2−22−22−22−22-220000002i−2i00000000000000−i2i22−200
χ512-22-222-2-2−2i2i−2i2i00−2i−2i2i2i2-2002-20000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−22-2000000−2i2i00000000000000−i2i22−200
χ522-22-222-2-2−2i2i−2i2i00−2i−2i2i2i2-2002-20000000000−i2i2−i2i2−i2i2−i2i22−22−22−22−2-220000002i−2i00000000000000i2−i2−2200
χ532-2-222-2-220000222-22-200-2-2002-20002-2-220i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200002-20000−i2i2i2−i2−i2i2i2−i2000000000000
χ542-2-222-2-220000222-22-200-2-2002-20002-2-220−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200002-20000i2−i2−i2i2i2−i2−i2i2000000000000
χ552-2-222-2-220000222-22-200-2-2002-2000-222-20i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000-220000i2−i2−i2i2i2−i2−i2i2000000000000
χ562-2-222-2-220000222-22-200-2-2002-2000-222-20−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000-220000−i2i2i2−i2−i2i2i2−i2000000000000
χ572-2-222-2-22000022-22-2200-2-200-220002-2-220i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000-220000−i2i2i2−i2i2−i2−i2i2000000000000
χ582-2-222-2-22000022-22-2200-2-200-220002-2-220−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000-220000i2−i2−i2i2−i2i2i2−i2000000000000
χ592-2-222-2-22000022-22-2200-2-200-22000-222-20i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200002-20000i2−i2−i2i2−i2i2i2−i2000000000000
χ602-2-222-2-22000022-22-2200-2-200-22000-222-20−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200002-20000−i2i2i2−i2i2−i2−i2i2000000000000
χ61444-4-4-4-444-4-4400000000000000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ62444-4-4-4-444-4-440000000000000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ63444-4-4-4-44-444-400000000000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ64444-4-4-4-44-444-40000000000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ6544-44-44-4-40000-44000044-44-4-4004000000-40000000000000000000000000000000000000000000000
χ6644-44-44-4-40000-440000-4-4-444400-400000040000000000000000000000000000000000000000000000
χ6744-4-44-44-40000004i−4i−4i4i00000000000000002-2-22-222-2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ6844-4-44-44-40000004i−4i−4i4i0000000000000000-222-22-2-222i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ6944-4-44-44-4000000−4i4i4i−4i00000000000000002-2-22-222-22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ7044-4-44-44-4000000−4i4i4i−4i0000000000000000-222-22-2-22−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ714-444-4-44-44i4i−4i−4i-440000004-400000−4i4i000000000000000000000000000000000000000000000000000
χ724-444-4-44-4−4i−4i4i4i-440000004-4000004i−4i000000000000000000000000000000000000000000000000000
χ734-44-444-4-44i−4i4i−4i00−4i−4i4i4i-4400-4400000000000000000000000000000000000000000000000000000000
χ744-44-444-4-4−4i4i−4i4i004i4i−4i−4i-4400-4400000000000000000000000000000000000000000000000000000000
χ754-4-444-4-440000-4-44-44-4004400-44000000000000000000000000000000000000000000000000000000
χ764-4-444-4-440000-4-4-44-440044004-4000000000000000000000000000000000000000000000000000000
χ774-4-4-4-444400000000004-400-4400000000000000000022−2222−22−2222−2222000000000000000000000000000000
χ784-4-4-4-444400000000004-400-44000000000000000000−2222−222222−2222−22000000000000000000000000000000
χ794-4-4-4-44440000000000-44004-4000000000022−2222−22−2222−222200000000000000000000000000000000000000
χ804-4-4-4-44440000000000-44004-40000000000−2222−222222−2222−2200000000000000000000000000000000000000

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