Finite Group Databasebeta

← Group #316232

Character table — Group #316232

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444888888882244444488888888888822444444888888884444444488888888
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
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-11111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-11111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-11111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111
χ172222222222222-2-2-2-222222222222-2-2-2-222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ182222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-2222200000000000000000000000000000000
χ19222222222222-22222-2-2-20000000022-2-2-2-2-2-200000000000022-2-222-2-2000000000000000000000000
χ20222222222222-22222-2-2-20000000022-2-2-2-2-2-2000000000000-2-222-2-222000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-200000000-2-222-2-222000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ22222222222222-2-2-2-2-2-2-2-200000000-2-222-2-22200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-2-2-22-2-2-2-22222222222222-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2422222222-2-2-2-22-2-2-2-2222-2-2-2-2-2-2-2-222-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
χ2522222222-2-2-2-2-22222-2-2-200000000-2-2-2-222220000000000002222-2-2-2-2000000000000000000000000
χ2622222222-2-2-2-2-22222-2-2-200000000-2-2-2-22222000000000000-2-2-2-22222000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-2000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2922-2-22-2-222i2i−2i−2i-2000022-22i2i2i2i−2i−2i−2i−2i00002i−2i00000022-2-200000000000000000000000000002−2i2−i2i2−i22−2
χ3022-2-22-2-222i2i−2i−2i-2000022-22i2i2i2i−2i−2i−2i−2i00002i−2i00000022-2-20000000000000000000000000000−22−i2i2−i2i2−22
χ3122-2-22-2-222i2i−2i−2i-2000022-2−2i−2i−2i−2i2i2i2i2i00002i−2i000000-2-22200000000000000000000000000002−2i2−i2−i2i2−22
χ3222-2-22-2-222i2i−2i−2i-2000022-2−2i−2i−2i−2i2i2i2i2i00002i−2i000000-2-2220000000000000000000000000000−22−i2i2i2−i22−2
χ3322-2-22-2-22−2i−2i2i2i-2000022-22i2i2i2i−2i−2i−2i−2i0000−2i2i000000-2-22200000000000000000000000000002−2−i2i2i2−i2−22
χ3422-2-22-2-22−2i−2i2i2i-2000022-22i2i2i2i−2i−2i−2i−2i0000−2i2i000000-2-2220000000000000000000000000000−22i2−i2−i2i22−2
χ3522-2-22-2-22−2i−2i2i2i-2000022-2−2i−2i−2i−2i2i2i2i2i0000−2i2i00000022-2-200000000000000000000000000002−2−i2i2−i2i22−2
χ3622-2-22-2-22−2i−2i2i2i-2000022-2−2i−2i−2i−2i2i2i2i2i0000−2i2i00000022-2-20000000000000000000000000000−22i2−i2i2−i2−22
χ372-22-222-2-22-22-2022-2-2000i2i2−i2−i2i2i2−i2−i22-2000000i2i2−i2−i2i2−i2i2−i2i2i2−i2−i2002i−2i002i−2i2−22−22−22−20000000000000000
χ382-22-222-2-22-22-2022-2-2000i2i2−i2−i2i2i2−i2−i22-2000000i2i2−i2−i2i2−i2i2−i2i2i2−i2−i200−2i2i00−2i2i−22−22−22−220000000000000000
χ392-22-222-2-22-22-2022-2-2000−i2−i2i2i2−i2−i2i2i22-2000000−i2−i2i2i2−i2i2−i2i2−i2−i2i2i2002i−2i002i−2i−22−22−22−220000000000000000
χ402-22-222-2-22-22-2022-2-2000−i2−i2i2i2−i2−i2i2i22-2000000−i2−i2i2i2−i2i2−i2i2−i2−i2i2i200−2i2i00−2i2i2−22−22−22−20000000000000000
χ412-22-222-2-22-22-20-2-222000i2i2−i2−i2i2i2−i2−i2-22000000−i2−i2i2i2i2−i2i2−i2−i2−i2i2i22-2002-200i2−i2−i2i2i2−i2−i2i20000000000000000
χ422-22-222-2-22-22-20-2-222000i2i2−i2−i2i2i2−i2−i2-22000000−i2−i2i2i2i2−i2i2−i2−i2−i2i2i2-2200-2200−i2i2i2−i2−i2i2i2−i20000000000000000
χ432-22-222-2-22-22-20-2-222000−i2−i2i2i2−i2−i2i2i2-22000000i2i2−i2−i2−i2i2−i2i2i2i2−i2−i22-2002-200−i2i2i2−i2−i2i2i2−i20000000000000000
χ442-22-222-2-22-22-20-2-222000−i2−i2i2i2−i2−i2i2i2-22000000i2i2−i2−i2−i2i2−i2i2i2i2−i2−i2-2200-2200i2−i2−i2i2i2−i2−i2i20000000000000000
χ452-22-222-2-2-22-22022-2-2000i2i2−i2−i2i2i2−i2−i2-22000000i2i2−i2−i2−i2i2−i2i2−i2−i2i2i2002i−2i00−2i2i2−22−2−22−220000000000000000
χ462-22-222-2-2-22-22022-2-2000i2i2−i2−i2i2i2−i2−i2-22000000i2i2−i2−i2−i2i2−i2i2−i2−i2i2i200−2i2i002i−2i−22−222−22−20000000000000000
χ472-22-222-2-2-22-22022-2-2000−i2−i2i2i2−i2−i2i2i2-22000000−i2−i2i2i2i2−i2i2−i2i2i2−i2−i2002i−2i00−2i2i−22−222−22−20000000000000000
χ482-22-222-2-2-22-22022-2-2000−i2−i2i2i2−i2−i2i2i2-22000000−i2−i2i2i2i2−i2i2−i2i2i2−i2−i200−2i2i002i−2i2−22−2−22−220000000000000000
χ492-22-222-2-2-22-220-2-222000i2i2−i2−i2i2i2−i2−i22-2000000−i2−i2i2i2−i2i2−i2i2i2i2−i2−i22-200-2200−i2i2i2−i2i2−i2−i2i20000000000000000
χ502-22-222-2-2-22-220-2-222000i2i2−i2−i2i2i2−i2−i22-2000000−i2−i2i2i2−i2i2−i2i2i2i2−i2−i2-22002-200i2−i2−i2i2−i2i2i2−i20000000000000000
χ512-22-222-2-2-22-220-2-222000−i2−i2i2i2−i2−i2i2i22-2000000i2i2−i2−i2i2−i2i2−i2−i2−i2i2i22-200-2200i2−i2−i2i2−i2i2i2−i20000000000000000
χ522-22-222-2-2-22-220-2-222000−i2−i2i2i2−i2−i2i2i22-2000000i2i2−i2−i2i2−i2i2−i2−i2−i2i2i2-22002-200−i2i2i2−i2i2−i2−i2i20000000000000000
χ532-22-2-2-222000022-22-22-2-22i−2i2i−2i2i−2i2i−2i002-200002i−2i2i−2i000000000000000000000000002i−2i002-200000000
χ542-22-2-2-222000022-22-22-2-22i−2i2i−2i2i−2i2i−2i002-200002i−2i2i−2i00000000000000000000000000−2i2i00-2200000000
χ552-22-2-2-222000022-22-22-2-2−2i2i−2i2i−2i2i−2i2i002-20000−2i2i−2i2i000000000000000000000000002i−2i00-2200000000
χ562-22-2-2-222000022-22-22-2-2−2i2i−2i2i−2i2i−2i2i002-20000−2i2i−2i2i00000000000000000000000000−2i2i002-200000000
χ572-22-2-2-22200002-22-222-2-22i−2i2i−2i2i−2i2i−2i00-220000−2i2i−2i2i0000000000000000000000002i−2i002-20000000000
χ582-22-2-2-22200002-22-222-2-22i−2i2i−2i2i−2i2i−2i00-220000−2i2i−2i2i000000000000000000000000−2i2i00-220000000000
χ592-22-2-2-22200002-22-222-2-2−2i2i−2i2i−2i2i−2i2i00-2200002i−2i2i−2i0000000000000000000000002i−2i00-220000000000
χ602-22-2-2-22200002-22-222-2-2−2i2i−2i2i−2i2i−2i2i00-2200002i−2i2i−2i000000000000000000000000−2i2i002-20000000000
χ614444-4-4-4-4000004-4-4400022−22−222222−22−22220000000022−22−22220000000000000000000000000000000000000000
χ624444-4-4-4-4000004-4-44000−222222−22−222222−2200000000−222222−220000000000000000000000000000000000000000
χ634444-4-4-4-400000-444-400022−22−222222−22−222200000000−222222−220000000000000000000000000000000000000000
χ644444-4-4-4-400000-444-4000−222222−22−222222−220000000022−22−22220000000000000000000000000000000000000000
χ6544-4-44-4-444i4i−4i−4i40000-4-44000000000000−4i4i0000000000000000000000000000000000000000000000
χ6644-4-44-4-44−4i−4i4i4i40000-4-440000000000004i−4i0000000000000000000000000000000000000000000000
χ6744-4-4-444-40000000000002i2−2i2−2i22i2−2i22i22i2−2i20000004i−4i0000000022−2222−2200000000000000000000000000000000
χ6844-4-4-444-40000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000−4i4i00000000−2222−222200000000000000000000000000000000
χ6944-4-4-444-4000000000000−2i22i22i2−2i22i2−2i2−2i22i20000004i−4i00000000−2222−222200000000000000000000000000000000
χ7044-4-4-444-4000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000−4i4i0000000022−2222−2200000000000000000000000000000000
χ714-44-4-4-4440000-44-44-4-4440000000000-44000000000000000000000000000000000000000000000000
χ724-44-4-4-4440000-4-44-44-44400000000004-4000000000000000000000000000000000000000000000000
χ734-4-444-44-44i−4i−4i4i000000002222−22−22−22−222222000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ744-4-444-44-44i−4i−4i4i00000000−22−2222222222−22−220000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ754-4-444-44-4−4i4i4i−4i000000002222−22−22−22−2222220000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ764-4-444-44-4−4i4i4i−4i00000000−22−2222222222−22−22000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ774-4-44-44-44000040000-44-40000000000000000000000004i−4i−4i4i00000000000000000000000000000000
χ784-4-44-44-44000040000-44-4000000000000000000000000−4i4i4i−4i00000000000000000000000000000000
χ794-4-44-44-440000-400004-444-44-4-44-440000000000000000000000000000000000000000000000000000
χ804-4-44-44-440000-400004-44-44-444-44-40000000000000000000000000000000000000000000000000000

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