Finite Group Databasebeta

← Group #270975

Character table — Group #270975

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222222244444444444422224444448888888888888888224444444488888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1
χ911111111-1-1-1-111111-1-1-1-111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1111-1-111-1-11-1
χ1011111111-1-1-1-111111-1-1-1-111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-111-1-111-11
χ1111111111-1-1-1-111111-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-11111-1111-1-1-1-111-11
χ1211111111-1-1-1-111111-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111111-1-1-11111-1-11-1
χ1311111111-1-1-1-111111-1-1-1-1111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-11-1-11111-1-1-11
χ1411111111-1-1-1-111111-1-1-1-1111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111111-111-1-1-1-1111-1
χ1511111111-1-1-1-111111-1-1-1-1111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-11-1-111-1-1111-1
χ1611111111-1-1-1-111111-1-1-1-1111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1111111-1-1-1-11-111-1-111-1-1-11
χ1722222222222222-2-2-2-2-2-2-222-22222-2-2-222-20000000000000000220000-2-2-2-200000000000000000000
χ1822222222222222-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222-20000000000000000-2-20000222200000000000000000000
χ19222222222222-2-22222222-2-220000-2-2-2-2-2-20000000000000000002222000000000000-2-20000000000
χ20222222222222-2-22222222-2-220000-2-2-2-2-2-2000000000000000000-2-2-2-2000000000000220000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-20000222-2-220000000000000000000000000000000000002-22-2000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-20000222-2-22000000000000000000000000000000000000-22-22000000
χ2322222222-2-2-2-222-2-2-2222222-22222-222-2-2-20000000000000000-2-20000-2-22200000000000000000000
χ2422222222-2-2-2-222-2-2-2222222-2-2-2-2-2-222-2-2-2000000000000000022000022-2-200000000000000000000
χ2522222222-2-2-2-2-2-2222-2-2-2-2-2-220000-22222-200000000000000000022-2-20000000000002-20000000000
χ2622222222-2-2-2-2-2-2222-2-2-2-2-2-220000-22222-2000000000000000000-2-222000000000000-220000000000
χ2722222222-2-2-2-2-2-2-2-2-22222-2-2-200002-2-22220000000000000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-22222-2-2-200002-2-2222000000000000000000000000000000000000-222-2000000
χ2922-2-22-22-200002-20002i2i−2i−2i2-2022-2-202i−2i000i2i2i2i2−i2−i2−i2−i22222−2−2−2−2000000002i−2ii2i2−i2−i222−2−2000000000000
χ3022-2-22-22-200002-20002i2i−2i−2i2-2022-2-202i−2i000−i2−i2−i2−i2i2i2i2i2−2−2−2−22222000000002i−2i−i2−i2i2i2−2−222000000000000
χ3122-2-22-22-200002-20002i2i−2i−2i2-20-2-22202i−2i000i2i2i2i2−i2−i2−i2−i22222−2−2−2−200000000−2i2i−i2−i2i2i2−2−222000000000000
χ3222-2-22-22-200002-20002i2i−2i−2i2-20-2-22202i−2i000−i2−i2−i2−i2i2i2i2i2−2−2−2−2222200000000−2i2ii2i2−i2−i222−2−2000000000000
χ3322-2-22-22-200002-2000−2i−2i2i2i2-2022-2-20−2i2i000i2i2i2i2−i2−i2−i2−i2−2−2−2−2222200000000−2i2ii2i2−i2−i2−2−222000000000000
χ3422-2-22-22-200002-2000−2i−2i2i2i2-2022-2-20−2i2i000−i2−i2−i2−i2i2i2i2i22222−2−2−2−200000000−2i2i−i2−i2i2i222−2−2000000000000
χ3522-2-22-22-200002-2000−2i−2i2i2i2-20-2-2220−2i2i000i2i2i2i2−i2−i2−i2−i2−2−2−2−22222000000002i−2i−i2−i2i2i222−2−2000000000000
χ3622-2-22-22-200002-2000−2i−2i2i2i2-20-2-2220−2i2i000−i2−i2−i2−i2i2i2i2i22222−2−2−2−2000000002i−2ii2i2−i2−i2−2−222000000000000
χ372-22-22-2-2222-2-20022-22-22-200-20000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002i−2i2i−2i0000000000000000002−22−200
χ382-22-22-2-2222-2-20022-22-22-200-20000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200−2i2i−2i2i000000000000000000−22−2200
χ392-22-22-2-2222-2-20022-22-22-200-20000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002i−2i2i−2i000000000000000000−22−2200
χ402-22-22-2-2222-2-20022-22-22-200-20000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200−2i2i−2i2i0000000000000000002−22−200
χ412-22-22-2-22-2-2220022-2-22-2200-20000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2002i−2i−2i2i0000000000000000002−2−2200
χ422-22-22-2-22-2-2220022-2-22-2200-20000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200−2i2i2i−2i000000000000000000−222−200
χ432-22-22-2-22-2-2220022-2-22-2200-20000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2002i−2i−2i2i000000000000000000−222−200
χ442-22-22-2-22-2-2220022-2-22-2200-20000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200−2i2i2i−2i0000000000000000002−2−2200
χ452-22-2-222-22-22-2220000000-2-202-22-20002-20i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22-200000000i2−i2i2−i2i2−i2i2−i2000000000000
χ462-22-2-222-22-22-2220000000-2-202-22-20002-20−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22-200000000−i2i2−i2i2−i2i2−i2i2000000000000
χ472-22-2-222-22-22-2220000000-2-20-22-220002-20i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2-2200000000−i2i2−i2i2−i2i2−i2i2000000000000
χ482-22-2-222-22-22-2220000000-2-20-22-220002-20−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2-2200000000i2−i2i2−i2i2−i2i2−i2000000000000
χ492-22-2-222-2-22-22220000000-2-202-22-2000-220i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2-2200000000i2−i2i2−i2−i2i2−i2i2000000000000
χ502-22-2-222-2-22-22220000000-2-202-22-2000-220−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2-2200000000−i2i2−i2i2i2−i2i2−i2000000000000
χ512-22-2-222-2-22-22220000000-2-20-22-22000-220i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i22-200000000−i2i2−i2i2i2−i2i2−i2000000000000
χ522-22-2-222-2-22-22220000000-2-20-22-22000-220−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i22-200000000i2−i2i2−i2−i2i2−i2i2000000000000
χ532-2-22-2-22200002-22-220000-22-22-2-2220000-2000000002i−2i2i−2i−2i2i−2i2i0000002-20000002i−2i−2i2i000000000000
χ542-2-22-2-22200002-22-220000-22-22-2-2220000-200000000−2i2i−2i2i2i−2i2i−2i0000002-2000000−2i2i2i−2i000000000000
χ552-2-22-2-22200002-22-220000-22-2-222-220000-2000000002i−2i2i−2i−2i2i−2i2i000000-22000000−2i2i2i−2i000000000000
χ562-2-22-2-22200002-22-220000-22-2-222-220000-200000000−2i2i−2i2i2i−2i2i−2i000000-220000002i−2i−2i2i000000000000
χ572-2-22-2-22200002-2-22-20000-2222-2-22-2000022-22-2-22-2200000000000000-22002-2-220000000000000000
χ582-2-22-2-22200002-2-22-20000-2222-2-22-200002-22-222-22-200000000000000-2200-222-20000000000000000
χ592-2-22-2-22200002-2-22-20000-222-222-2-2000022-22-2-22-22000000000000002-200-222-20000000000000000
χ602-2-22-2-22200002-2-22-20000-222-222-2-200002-22-222-22-2000000000000002-2002-2-220000000000000000
χ614444-4-4-4-44-4-4400000000000000000000002-2-222-2-222-2-222-2-22000000000000000000000000000000
χ624444-4-4-4-44-4-440000000000000000000000-222-2-222-2-222-2-222-2000000000000000000000000000000
χ634444-4-4-4-4-444-400000000000000000000002-2-222-2-22-222-2-222-2000000000000000000000000000000
χ644444-4-4-4-4-444-40000000000000000000000-222-2-222-22-2-222-2-22000000000000000000000000000000
χ6544-4-44-44-40000-440004i4i−4i−4i-44000000−4i4i0000000000000000000000000000000000000000000000000
χ6644-4-44-44-40000-44000−4i−4i4i4i-440000004i−4i0000000000000000000000000000000000000000000000000
χ6744-4-4-44-440000004-4-4000000400000000000000000022−22−2222−222222−22000000000000000000000000000000
χ6844-4-4-44-440000004-4-40000004000000000000000000−222222−2222−22−2222000000000000000000000000000000
χ6944-4-4-44-44000000-444000000-400000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ7044-4-4-44-44000000-444000000-40000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ714-44-44-4-4444-4-400-4-44-44-4400400000000000000000000000000000000000000000000000000000000
χ724-44-44-4-44-4-44400-4-444-44-400400000000000000000000000000000000000000000000000000000000
χ734-44-4-444-44-44-4-4-400000004400000000-4400000000000000000000000000000000000000000000000
χ744-44-4-444-4-44-44-4-4000000044000000004-400000000000000000000000000000000000000000000000
χ754-4-4444-4-40000000004i−4i−4i4i000000000000022-2-2-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ764-4-4444-4-40000000004i−4i−4i4i0000000000000-2-22222-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ774-4-4444-4-4000000000−4i4i4i−4i000000000000022-2-2-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ784-4-4444-4-4000000000−4i4i4i−4i0000000000000-2-22222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ794-4-44-4-4440000-444-4400004-4-40000-4000040000000000000000000000000000000000000000000000
χ804-4-44-4-4440000-44-44-400004-44000040000-40000000000000000000000000000000000000000000000

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