Finite Group Databasebeta

← Group #285644

Character table — Group #285644

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444224444888888888888888844444444488888888888888884444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ9111111111-1-1-1-11111111-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-11
χ10111111111-1-1-1-11111111-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-1
χ11111111111-1-1-1-11111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-111-1-1111-1
χ12111111111-1-1-1-11111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-111-1-1-11
χ13111111111-1-1-1-11111111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111-1-111-1-11-1
χ14111111111-1-1-1-11111111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-11
χ15111111111-1-1-1-11111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-11
χ16111111111-1-1-1-11111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111-1
χ172222222222222-2-2-2222-2-2-2-2-222000000000000000022-2-2-222-2-200000000000000000000000000
χ182222222222222-2-2-2222-2-2-2-2-2220000000000000000-2-222-2-2-22200000000000000000000000000
χ19222222222-2-2-2-2-2-2-2222-222-2-2-2-2000000000000000022-2-22-2-22200000000000000000000000000
χ20222222222-2-2-2-2-2-2-2222-222-2-2-2-20000000000000000-2-222222-2-200000000000000000000000000
χ2122222222-22222222-2-2-2222-2-2-2-222222222000000000000-20000-2-200000000-2-200000000000000
χ2222222222-22222222-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-2000000000000-2000022000000002200000000000000
χ2322222222-22222-2-2-2-2-2-2-2-2-222-2-2000000002i2i2i2i−2i−2i−2i−2i0000200000000000000002i2i−2i−2i0000000000
χ2422222222-22222-2-2-2-2-2-2-2-2-222-2-200000000−2i−2i−2i−2i2i2i2i2i000020000000000000000−2i−2i2i2i0000000000
χ2522222222-2-2-2-2-2222-2-2-22-2-2-2-2222222-2-2-2-200000000000020000-2-2000000002200000000000000
χ2622222222-2-2-2-2-2222-2-2-22-2-2-2-222-2-2-2-22222000000000000200002200000000-2-200000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000002i2i2i2i−2i−2i−2i−2i0000-20000000000000000−2i−2i2i2i0000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000−2i−2i−2i−2i2i2i2i2i0000-200000000000000002i2i−2i−2i0000000000
χ2922-22-2-2-2222i2i−2i−2i000-2-22000002i−2ii2i2−i2−i222−2−222−2−222−2−2002i−2i0002-2i2−i2000000002−2i2−i2i2−i20000000000
χ3022-22-2-2-2222i2i−2i−2i000-2-22000002i−2ii2i2−i2−i222−2−2−2−222−2−22200−2i2i000-22i2−i2000000002−2−i2i2−i2i20000000000
χ3122-22-2-2-2222i2i−2i−2i000-2-22000002i−2i−i2−i2i2i2−2−22222−2−222−2−200−2i2i000-22−i2i200000000−22i2−i2i2−i20000000000
χ3222-22-2-2-2222i2i−2i−2i000-2-22000002i−2i−i2−i2i2i2−2−222−2−222−2−222002i−2i0002-2−i2i200000000−22−i2i2−i2i20000000000
χ3322-22-2-2-222−2i−2i2i2i000-2-2200000−2i2ii2i2−i2−i2−2−22222−2−222−2−2002i−2i000-22i2−i200000000−22−i2i2−i2i20000000000
χ3422-22-2-2-222−2i−2i2i2i000-2-2200000−2i2ii2i2−i2−i2−2−222−2−222−2−22200−2i2i0002-2i2−i200000000−22i2−i2i2−i20000000000
χ3522-22-2-2-222−2i−2i2i2i000-2-2200000−2i2i−i2−i2i2i222−2−222−2−222−2−200−2i2i0002-2−i2i2000000002−2−i2i2−i2i20000000000
χ3622-22-2-2-222−2i−2i2i2i000-2-2200000−2i2i−i2−i2i2i222−2−2−2−222−2−222002i−2i000-22−i2i2000000002−2i2−i2i2−i20000000000
χ3722-22-2-2-22-22i2i−2i−2i00022-200000−2i2ii2i2−i2−i222−2−2i2i2−i2−i2−i2−i2i2i22-20002i−2i00−i2i200000000−22−222−20000000000
χ3822-22-2-2-22-22i2i−2i−2i00022-200000−2i2ii2i2−i2−i222−2−2−i2−i2i2i2i2i2−i2−i2-22000−2i2i00−i2i200000000−222−2−220000000000
χ3922-22-2-2-22-22i2i−2i−2i00022-200000−2i2i−i2−i2i2i2−2−222i2i2−i2−i2−i2−i2i2i2-22000−2i2i00i2−i2000000002−2−222−20000000000
χ4022-22-2-2-22-22i2i−2i−2i00022-200000−2i2i−i2−i2i2i2−2−222−i2−i2i2i2i2i2−i2−i22-20002i−2i00i2−i2000000002−22−2−220000000000
χ4122-22-2-2-22-2−2i−2i2i2i00022-2000002i−2ii2i2−i2−i2−2−222i2i2−i2−i2−i2−i2i2i22-2000−2i2i00−i2i2000000002−22−2−220000000000
χ4222-22-2-2-22-2−2i−2i2i2i00022-2000002i−2ii2i2−i2−i2−2−222−i2−i2i2i2i2i2−i2−i2-220002i−2i00−i2i2000000002−2−222−20000000000
χ4322-22-2-2-22-2−2i−2i2i2i00022-2000002i−2i−i2−i2i2i222−2−2i2i2−i2−i2−i2−i2i2i2-220002i−2i00i2−i200000000−222−2−220000000000
χ4422-22-2-2-22-2−2i−2i2i2i00022-2000002i−2i−i2−i2i2i222−2−2−i2−i2i2i2i2i2−i2−i22-2000−2i2i00i2−i200000000−22−222−20000000000
χ452-2-222-22-2200002-2-22-2-22002-200000000002-22-22-22-20000000000000002i2i−2i−2i000000002i−2i000000
χ462-2-222-22-2200002-2-22-2-22002-200000000002-22-22-22-2000000000000000−2i−2i2i2i00000000−2i2i000000
χ472-2-222-22-2200002-2-22-2-22002-20000000000-22-22-22-220000000000000002i2i−2i−2i00000000−2i2i000000
χ482-2-222-22-2200002-2-22-2-22002-20000000000-22-22-22-22000000000000000−2i−2i2i2i000000002i−2i000000
χ492-2-222-22-2-20000-222-222-2002-200000000002i−2i2i−2i−2i2i−2i2i0000000000022-2-200000000002i−2i00000000
χ502-2-222-22-2-20000-222-222-2002-200000000002i−2i2i−2i−2i2i−2i2i00000000000-2-2220000000000−2i2i00000000
χ512-2-222-22-2-20000-222-222-2002-20000000000−2i2i−2i2i2i−2i2i−2i0000000000022-2-20000000000−2i2i00000000
χ522-2-222-22-2-20000-222-222-2002-20000000000−2i2i−2i2i2i−2i2i−2i00000000000-2-22200000000002i−2i00000000
χ532-2-2-2-222202-22-222-2000-22-200002-22-22-22-20000000000000000000i2−i2i2−i2i2−i2i2−i20000000000i2−i2i2−i200
χ542-2-2-2-222202-22-222-2000-22-200002-22-22-22-20000000000000000000−i2i2−i2i2−i2i2−i2i20000000000−i2i2−i2i200
χ552-2-2-2-222202-22-222-2000-22-20000-22-22-22-220000000000000000000i2−i2i2−i2i2−i2i2−i20000000000−i2i2−i2i200
χ562-2-2-2-222202-22-222-2000-22-20000-22-22-22-220000000000000000000−i2i2−i2i2−i2i2−i2i20000000000i2−i2i2−i200
χ572-2-2-2-22220-22-2222-2000-2-2200002-22-2-22-220000000000000000000i2−i2i2−i2−i2i2−i2i20000000000−i2i2i2−i200
χ582-2-2-2-22220-22-2222-2000-2-2200002-22-2-22-220000000000000000000−i2i2−i2i2i2−i2i2−i20000000000i2−i2−i2i200
χ592-2-2-2-22220-22-2222-2000-2-220000-22-222-22-20000000000000000000i2−i2i2−i2−i2i2−i2i20000000000i2−i2−i2i200
χ602-2-2-2-22220-22-2222-2000-2-220000-22-222-22-20000000000000000000−i2i2−i2i2i2−i2i2−i20000000000−i2i2i2−i200
χ61444-4-4-44-4000004-44000-4000000000000000000000000000000000000022−22−22220000000000000000
χ62444-4-4-44-4000004-44000-40000000000000000000000000000000000000−222222−220000000000000000
χ63444-4-4-44-400000-44-400040000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ64444-4-4-44-400000-44-40004000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ654-444-44-4-440000000-44-400000000000000022−22−222222−22−222200000000000000000000000000000000000
χ664-444-44-4-440000000-44-4000000000000000−222222−22−222222−2200000000000000000000000000000000000
χ674-444-44-4-4-400000004-440000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000
χ684-444-44-4-4-400000004-44000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000
χ694-44-44-4-4404i−4i−4i4i00000000000002i2−2i2−2i22i222−22−22220000000000000000000000000000000000000000000
χ704-44-44-4-4404i−4i−4i4i0000000000000−2i22i22i2−2i2−222222−220000000000000000000000000000000000000000000
χ714-44-44-4-440−4i4i4i−4i00000000000002i2−2i2−2i22i2−222222−220000000000000000000000000000000000000000000
χ724-44-44-4-440−4i4i4i−4i0000000000000−2i22i22i2−2i222−22−22220000000000000000000000000000000000000000000
χ734-4-444-44-440000-4444-4-4-400-4400000000000000000000000000000000000000000000000000000
χ744-4-444-44-4-400004-4-4-444400-4400000000000000000000000000000000000000000000000000000
χ754-4-4-4-444404-44-4-4-440004-440000000000000000000000000000000000000000000000000000000
χ764-4-4-4-44440-44-44-4-4400044-40000000000000000000000000000000000000000000000000000000
χ7788-8-888-8-8000000000000000000000000000000000000000000000000000000000000000000000

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