Finite Group Databasebeta

← Group #499239

Character table — Group #499239

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order122222224444444444448888888822444444888888888888161616161616161616161616161616164444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1
χ911111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111
χ1011111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1
χ1111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-111-1-1
χ1211111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111-1-111
χ1311111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1
χ1411111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111
χ1511111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111111
χ1611111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ1722222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000022−2−222−2−222−2−222−2−20000000000000000
χ20222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000−2−222−2−222−2−222−2−2220000000000000000
χ21222222222222-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000000022−2−222−2−2−2−222−2−2220000000000000000
χ22222222222222-2-2-2-2-2-2-2-200000000-2-2-2-22222000000000000−2−222−2−22222−2−222−2−20000000000000000
χ2322222222-2-2-2-22222-2-2-2-20000000022-2-222-2-200000000000022−2−2−2−22222−2−2−2−2220000000000000000
χ2422222222-2-2-2-22222-2-2-2-20000000022-2-222-2-2000000000000−2−22222−2−2−2−22222−2−20000000000000000
χ2522222222-2-2-2-22222-2-2-2-200000000-2-222-2-22200000000000022−2−2−2−222−2−22222−2−20000000000000000
χ2622222222-2-2-2-22222-2-2-2-200000000-2-222-2-222000000000000−2−22222−2−222−2−2−2−2220000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-2222222-2-2-2-2222200000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-222222222-2-2-2-200000000000000000000000000000000
χ2922-22-2-2-222i2i−2i−2i2i2i−2i−2i2-22-2000000000000000000002i2i−2i−2i22-2-2i2−i2i2−i22−22−22−22−2i2−i2i2−i20000000000000000
χ3022-22-2-2-222i2i−2i−2i2i2i−2i−2i2-22-2000000000000000000002i2i−2i−2i22-2-2−i2i2−i2i2−22−22−22−22−i2i2−i2i20000000000000000
χ3122-22-2-2-222i2i−2i−2i2i2i−2i−2i2-22-200000000000000000000−2i−2i2i2i-2-222i2−i2i2−i22−22−2−22−22−i2i2−i2i20000000000000000
χ3222-22-2-2-222i2i−2i−2i2i2i−2i−2i2-22-200000000000000000000−2i−2i2i2i-2-222−i2i2−i2i2−22−222−22−2i2−i2i2−i20000000000000000
χ3322-22-2-2-222i2i−2i−2i−2i−2i2i2i-22-222222-2-2-2-2000000002i2i−2i−2i00000000000000002-2-222i−2i−2i2i0000000000000000
χ3422-22-2-2-222i2i−2i−2i−2i−2i2i2i-22-222222-2-2-2-2000000002i2i−2i−2i0000000000000000-222-2−2i2i2i−2i0000000000000000
χ3522-22-2-2-222i2i−2i−2i−2i−2i2i2i-22-22-2-2-2-2222200000000−2i−2i2i2i000000002i−2i−2i2i2-2-22000000000000000000000000
χ3622-22-2-2-222i2i−2i−2i−2i−2i2i2i-22-22-2-2-2-2222200000000−2i−2i2i2i00000000−2i2i2i−2i-222-2000000000000000000000000
χ3722-22-2-2-22−2i−2i2i2i2i2i−2i−2i-22-222222-2-2-2-200000000−2i−2i2i2i00000000000000002-2-22−2i2i2i−2i0000000000000000
χ3822-22-2-2-22−2i−2i2i2i2i2i−2i−2i-22-222222-2-2-2-200000000−2i−2i2i2i0000000000000000-222-22i−2i−2i2i0000000000000000
χ3922-22-2-2-22−2i−2i2i2i2i2i−2i−2i-22-22-2-2-2-22222000000002i2i−2i−2i000000002i−2i−2i2i-222-2000000000000000000000000
χ4022-22-2-2-22−2i−2i2i2i2i2i−2i−2i-22-22-2-2-2-22222000000002i2i−2i−2i00000000−2i2i2i−2i2-2-22000000000000000000000000
χ4122-22-2-2-22−2i−2i2i2i−2i−2i2i2i2-22-2000000000000000000002i2i−2i−2i-2-222i2−i2i2−i2−22−222−22−2−i2i2−i2i20000000000000000
χ4222-22-2-2-22−2i−2i2i2i−2i−2i2i2i2-22-2000000000000000000002i2i−2i−2i-2-222−i2i2−i2i22−22−2−22−22i2−i2i2−i20000000000000000
χ4322-22-2-2-22−2i−2i2i2i−2i−2i2i2i2-22-200000000000000000000−2i−2i2i2i22-2-2i2−i2i2−i2−22−22−22−22i2−i2i2−i20000000000000000
χ4422-22-2-2-22−2i−2i2i2i−2i−2i2i2i2-22-200000000000000000000−2i−2i2i2i22-2-2−i2i2−i2i22−22−22−22−2−i2i2−i2i20000000000000000
χ452-22-22-2-222i−2i2i−2i2i−2i2i−2i2-2-2222-2-222-2-2000000002i−2i2i−2i0000000000000000000000002i−2i2-2000000000000
χ462-22-22-2-222i−2i2i−2i2i−2i2i−2i2-2-2222-2-222-2-2000000002i−2i2i−2i000000000000000000000000−2i2i-22000000000000
χ472-22-22-2-222i−2i2i−2i2i−2i2i−2i2-2-22-2-222-2-22200000000−2i2i−2i2i00000000000000000000000000002i−2i00002-20000
χ482-22-22-2-222i−2i2i−2i2i−2i2i−2i2-2-22-2-222-2-22200000000−2i2i−2i2i0000000000000000000000000000−2i2i0000-220000
χ492-22-22-2-22−2i2i−2i2i−2i2i−2i2i2-2-2222-2-222-2-200000000−2i2i−2i2i0000000000000000000000002i−2i-22000000000000
χ502-22-22-2-22−2i2i−2i2i−2i2i−2i2i2-2-2222-2-222-2-200000000−2i2i−2i2i000000000000000000000000−2i2i2-2000000000000
χ512-22-22-2-22−2i2i−2i2i−2i2i−2i2i2-2-22-2-222-2-222000000002i−2i2i−2i00000000000000000000000000002i−2i0000-220000
χ522-22-22-2-22−2i2i−2i2i−2i2i−2i2i2-2-22-2-222-2-222000000002i−2i2i−2i0000000000000000000000000000−2i2i00002-20000
χ532-2-2-2-22222-2-22-222-2-2-22222-2-2-2-222000000002-2-22000000000000000000000000000000002-200002-2
χ542-2-2-2-22222-2-22-222-2-2-22222-2-2-2-222000000002-2-2200000000000000000000000000000000-220000-22
χ552-2-2-2-22222-2-22-222-2-2-222-2-22222-2-200000000-222-20000000000000000000000000000002-200002-200
χ562-2-2-2-22222-2-22-222-2-2-222-2-22222-2-200000000-222-2000000000000000000000000000000-220000-2200
χ572-2-2-2-2222-222-22-2-22-2-22222-2-2-2-22200000000-222-2000000000000000000000000000000002-20000-22
χ582-2-2-2-2222-222-22-2-22-2-22222-2-2-2-22200000000-222-200000000000000000000000000000000-2200002-2
χ592-2-2-2-2222-222-22-2-22-2-222-2-22222-2-2000000002-2-220000000000000000000000000000002-20000-2200
χ602-2-2-2-2222-222-22-2-22-2-222-2-22222-2-2000000002-2-22000000000000000000000000000000-2200002-200
χ61444-4-4-44-400000000000022−2222−2222−2222−2200004-4000000000022−2222−2200000000000000000000000000000000
χ62444-4-4-44-400000000000022−2222−2222−2222−220000-440000000000−2222−222200000000000000000000000000000000
χ63444-4-4-44-4000000000000−2222−2222−2222−222200004-40000000000−2222−222200000000000000000000000000000000
χ64444-4-4-44-4000000000000−2222−2222−2222−22220000-44000000000022−2222−2200000000000000000000000000000000
χ6544-4-444-4-400000000000022−2222−22−2222−2222004-400000000000022−22−222200000000000000000000000000000000
χ6644-4-444-4-400000000000022−2222−22−2222−222200-44000000000000−222222−2200000000000000000000000000000000
χ6744-4-444-4-4000000000000−2222−222222−2222−22004-4000000000000−222222−2200000000000000000000000000000000
χ6844-4-444-4-4000000000000−2222−222222−2222−2200-4400000000000022−22−222200000000000000000000000000000000
χ694-444-44-4-400000000000022−22−222222−22−22224-4000000000022−2222−22000000000000000000000000000000000000
χ704-444-44-4-400000000000022−22−222222−22−2222-440000000000−2222−2222000000000000000000000000000000000000
χ714-444-44-4-4000000000000−222222−22−222222−224-40000000000−2222−2222000000000000000000000000000000000000
χ724-444-44-4-4000000000000−222222−22−222222−22-44000000000022−2222−22000000000000000000000000000000000000
χ734-44-44-4-444i−4i4i−4i−4i4i−4i4i-444-4000000000000000000000000000000000000000000000000000000000000
χ744-44-44-4-44−4i4i−4i4i4i−4i4i−4i-444-4000000000000000000000000000000000000000000000000000000000000
χ754-4-444-44-400000000000022−22−2222−222222−220000004i−4i00002i2−2i2−2i22i2000000000000000000000000000000000000
χ764-4-444-44-400000000000022−22−2222−222222−22000000−4i4i0000−2i22i22i2−2i2000000000000000000000000000000000000
χ774-4-444-44-4000000000000−222222−2222−22−22220000004i−4i0000−2i22i22i2−2i2000000000000000000000000000000000000
χ784-4-444-44-4000000000000−222222−2222−22−2222000000−4i4i00002i2−2i2−2i22i2000000000000000000000000000000000000
χ794-4-4-4-44444-4-444-4-4444-4-4000000000000000000000000000000000000000000000000000000000000
χ804-4-4-4-4444-444-4-444-444-4-4000000000000000000000000000000000000000000000000000000000000

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