Finite Group Databasebeta

← Group #234005

Character table — Group #234005

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444444444444444888888888888888844444444888888882444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-11-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-111-1-1-1-1
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11111111-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-11111
χ911111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111-1-1-1-1111-1-111-1-1
χ1011111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-11111-1-1-111-1-111
χ1111111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111-1-111-1-1-1-111111-1-1
χ1211111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-111-1-11111-1-1-1-1-111
χ1311111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111111-1-1-1-1-1-1111-1-111
χ1411111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1111111-1-1-111-1-1
χ1511111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-11-1-111-1-1111-1-1-1-111
χ1611111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-111-1-111-1-1-11111-1-1
χ172222222222222222222-2-2-2-2-2-2-2-22-2-2-2-200000000000000000000000000000000200002-200-2000000
χ182222222222222222222-2-2-2-2-2-2-2-22-2-2-2-200000000000000000000000000000000-20000-22002000000
χ19222222222222-2-2-2-2-2-2-22222-2-2-2-2-22-2-220000000000000000000000000000000002-22-200000000000
χ20222222222222-2-2-2-2-2-2-22222-2-2-2-2-22-2-22000000000000000000000000000000000-22-2200000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-22222-2-222-200000000000000002222-2-2-2-2000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-22222-2-222-20000000000000000-2-2-2-22222000000000000000000000000
χ2322222222-2-2-2-2222-2-2-2-22222-2-2-2-22-222-20000000000000000000000000000000020000-2200-2000000
χ2422222222-2-2-2-2222-2-2-2-22222-2-2-2-22-222-200000000000000000000000000000000-200002-2002000000
χ2522222222-2-2-2-2-2-2-2222222222222-2-2-2-2-2000000000000000022-2-2-2-222000000000000000000000000
χ2622222222-2-2-2-2-2-2-2222222222222-2-2-2-2-20000000000000000-2-22222-2-2000000000000000000000000
χ2722222222-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-222220000000000000000000000000000000002-2-2200000000000
χ2822222222-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000-222-200000000000
χ2922-22-2-2-2200000002i2i−2i−2i2i2i−2i−2i2-22-200000i2i2i2i2−i2−i2−i2−i22222−2−2−2−2002i−2i2-200i2i2−i2−i222−2−20000000000000000
χ3022-22-2-2-2200000002i2i−2i−2i2i2i−2i−2i2-22-200000i2i2i2i2−i2−i2−i2−i22222−2−2−2−200−2i2i-2200−i2−i2i2i2−2−2220000000000000000
χ3122-22-2-2-2200000002i2i−2i−2i2i2i−2i−2i2-22-200000−i2−i2−i2−i2i2i2i2i2−2−2−2−22222002i−2i2-200−i2−i2i2i2−2−2220000000000000000
χ3222-22-2-2-2200000002i2i−2i−2i2i2i−2i−2i2-22-200000−i2−i2−i2−i2i2i2i2i2−2−2−2−2222200−2i2i-2200i2i2−i2−i222−2−20000000000000000
χ3322-22-2-2-220000000−2i−2i2i2i−2i−2i2i2i2-22-200000i2i2i2i2−i2−i2−i2−i2−2−2−2−22222002i−2i-2200−i2−i2i2i222−2−20000000000000000
χ3422-22-2-2-220000000−2i−2i2i2i−2i−2i2i2i2-22-200000i2i2i2i2−i2−i2−i2−i2−2−2−2−2222200−2i2i2-200i2i2−i2−i2−2−2220000000000000000
χ3522-22-2-2-220000000−2i−2i2i2i−2i−2i2i2i2-22-200000−i2−i2−i2−i2i2i2i2i22222−2−2−2−2002i−2i-2200i2i2−i2−i2−2−2220000000000000000
χ3622-22-2-2-220000000−2i−2i2i2i−2i−2i2i2i2-22-200000−i2−i2−i2−i2i2i2i2i22222−2−2−2−200−2i2i2-200−i2−i2i2i222−2−20000000000000000
χ372-22-22-2-2200000002i−2i2i−2i2i−2i2i−2i2-2-220000022−2−222−2−2i2i2−i2−i2i2i2−i2−i22i−2i00002-2i2−i2i2−i22−22−20000000000000000
χ382-22-22-2-2200000002i−2i2i−2i2i−2i2i−2i2-2-220000022−2−222−2−2i2i2−i2−i2i2i2−i2−i2−2i2i0000-22−i2i2−i2i2−22−220000000000000000
χ392-22-22-2-2200000002i−2i2i−2i2i−2i2i−2i2-2-2200000−2−222−2−222−i2−i2i2i2−i2−i2i2i22i−2i00002-2−i2i2−i2i2−22−220000000000000000
χ402-22-22-2-2200000002i−2i2i−2i2i−2i2i−2i2-2-2200000−2−222−2−222−i2−i2i2i2−i2−i2i2i2−2i2i0000-22i2−i2i2−i22−22−20000000000000000
χ412-22-22-2-220000000−2i2i−2i2i−2i2i−2i2i2-2-220000022−2−222−2−2−i2−i2i2i2−i2−i2i2i22i−2i0000-22i2−i2i2−i2−22−220000000000000000
χ422-22-22-2-220000000−2i2i−2i2i−2i2i−2i2i2-2-220000022−2−222−2−2−i2−i2i2i2−i2−i2i2i2−2i2i00002-2−i2i2−i2i22−22−20000000000000000
χ432-22-22-2-220000000−2i2i−2i2i−2i2i−2i2i2-2-2200000−2−222−2−222i2i2−i2−i2i2i2−i2−i22i−2i0000-22−i2i2−i2i22−22−20000000000000000
χ442-22-22-2-220000000−2i2i−2i2i−2i2i−2i2i2-2-2200000−2−222−2−222i2i2−i2−i2i2i2−i2−i2−2i2i00002-2i2−i2i2−i2−22−220000000000000000
χ452-2-2-2-222222-2-222-22-2-222-2-2222-2-2-222-2-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ462-2-2-2-222222-2-222-22-2-222-2-2222-2-2-222-2-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ472-2-2-2-222222-2-222-22-2-22-222-2-2-222-2-2-222000000000000000000000000000000000000000000002-22-2
χ482-2-2-2-222222-2-222-22-2-22-222-2-2-222-2-2-22200000000000000000000000000000000000000000000-22-22
χ492-2-2-2-222222-2-2-2-22-222-22-2-22-2-22222-22-20000000000000000000000000000000000000002-202-20000
χ502-2-2-2-222222-2-2-2-22-222-22-2-22-2-22222-22-2000000000000000000000000000000000000000-220-220000
χ512-2-2-2-222222-2-2-2-22-222-2-222-222-2-22-22-220000000000000000000000002-2-22-222-20000000000000000
χ522-2-2-2-222222-2-2-2-22-222-2-222-222-2-22-22-22000000000000000000000000-222-22-2-220000000000000000
χ532-2-2-2-2222-2-22222-2-222-22-2-22-2-222-2-22-22000000000000000000000000000000000000000000002-2-22
χ542-2-2-2-2222-2-22222-2-222-22-2-22-2-222-2-22-2200000000000000000000000000000000000000000000-222-2
χ552-2-2-2-2222-2-22222-2-222-2-222-222-2-2-22-22-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ562-2-2-2-2222-2-22222-2-222-2-222-222-2-2-22-22-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ572-2-2-2-2222-2-222-2-222-2-222-2-2222-2-22-2-2220000000000000000000000002-2-222-2-220000000000000000
χ582-2-2-2-2222-2-222-2-222-2-222-2-2222-2-22-2-222000000000000000000000000-222-2-222-20000000000000000
χ592-2-2-2-2222-2-222-2-222-2-22-222-2-2-222222-2-20000000000000000000000000000000000000002-20-220000
χ602-2-2-2-2222-2-222-2-222-2-22-222-2-2-222222-2-2000000000000000000000000000000000000000-2202-20000
χ61444-4-44-4-44-44-4000000000000000000002-22-22-22-22-22-22-22-200000000000000000000000000000000
χ62444-4-44-4-44-44-400000000000000000000-22-22-22-22-22-22-22-2200000000000000000000000000000000
χ63444-4-44-4-4-44-44000000000000000000002-22-22-22-2-22-22-22-2200000000000000000000000000000000
χ64444-4-44-4-4-44-4400000000000000000000-22-22-22-222-22-22-22-200000000000000000000000000000000
χ6544-44-4-4-4400000004i4i−4i−4i−4i−4i4i4i-44-4400000000000000000000000000000000000000000000000000000
χ6644-44-4-4-440000000−4i−4i4i4i4i4i−4i−4i-44-4400000000000000000000000000000000000000000000000000000
χ6744-4-44-44-400004-44000000000000-400000000000022−2222−22−2222−222200000000000000000000000000000000
χ6844-4-44-44-400004-44000000000000-4000000000000−2222−222222−2222−2200000000000000000000000000000000
χ6944-4-44-44-40000-44-4000000000000400002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000
χ7044-4-44-44-40000-44-400000000000040000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000
χ714-444-4-44-400004-4-400000000000040000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000
χ724-444-4-44-400004-4-40000000000004000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000
χ734-444-4-44-40000-444000000000000-4000022−22−222222−22−22220000000000000000000000000000000000000000
χ744-444-4-44-40000-444000000000000-40000−222222−22−222222−220000000000000000000000000000000000000000
χ754-44-44-4-4400000004i−4i4i−4i−4i4i−4i4i-444-400000000000000000000000000000000000000000000000000000
χ764-44-44-4-440000000−4i4i−4i4i4i−4i4i−4i-444-400000000000000000000000000000000000000000000000000000
χ774-4-4444-4-44-4-44000000000000000000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ784-4-4444-4-44-4-4400000000000000000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ794-4-4444-4-4-444-4000000000000000000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ804-4-4444-4-4-444-400000000000000000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000

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