Finite Group Databasebeta

← Group #285665

Character table — Group #285665

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444224444888888888888888844444444488888888888888884444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
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
χ9111111111-1-1-1-11111111-1-111-1-11111-1-1-1-111111111-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ10111111111-1-1-1-11111111-1-111-1-11111-1-1-1-111111111-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ11111111111-1-1-1-11111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-11111-1-1-11
χ12111111111-1-1-1-11111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1111-1
χ13111111111-1-1-1-11111111-1-111-1-1-1-1-1-1111111111111-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ14111111111-1-1-1-11111111-1-111-1-1-1-1-1-1111111111111-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ15111111111-1-1-1-11111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-111-1-1111-1
χ16111111111-1-1-1-11111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-111-1-1-11
χ172222222222222-2-222-2-2222-2-2-2-20000000000000000-22222-2-2-2-200000000000000000000000000
χ182222222222222-2-222-2-2222-2-2-2-20000000000000000-2-2-2-2-2222200000000000000000000000000
χ19222222222-2-2-2-2-2-222-2-22-2-2-2-2220000000000000000222-2-222-2-200000000000000000000000000
χ20222222222-2-2-2-2-2-222-2-22-2-2-2-22200000000000000002-2-222-2-22200000000000000000000000000
χ2122222222-2222222-2-222-2-2-2-2-2222222222200000000-200000000-2-2-2-20000000000000000000000
χ2222222222-2222222-2-222-2-2-2-2-222-2-2-2-2-2-2-2-200000000-20000000022220000000000000000000000
χ2322222222-22222-2-2-2-2-2-2-2-2-222-2-2000000002i2i2i2i−2i−2i−2i−2i20000000000002i2i−2i−2i000000000000000000
χ2422222222-22222-2-2-2-2-2-2-2-2-222-2-200000000−2i−2i−2i−2i2i2i2i2i2000000000000−2i−2i2i2i000000000000000000
χ2522222222-2-2-2-2-222-2-222-222-2-2-2-22222-2-2-2-200000000200000000-2-2220000000000000000000000
χ2622222222-2-2-2-2-222-2-222-222-2-2-2-2-2-2-2-222220000000020000000022-2-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000002i2i2i2i−2i−2i−2i−2i-2000000000000−2i−2i2i2i000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000−2i−2i−2i−2i2i2i2i2i-20000000000002i2i−2i−2i000000000000000000
χ2922-2-2-22-22222-2-200-2-20022-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000002-22-2i2−i2i2−i2i2−i2i2−i2000000000000000000
χ3022-2-2-22-22222-2-200-2-20022-20000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000-22-22i2−i2i2−i2−i2i2−i2i2000000000000000000
χ3122-2-2-22-22222-2-200-2-20022-20000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000-22-22−i2i2−i2i2i2−i2i2−i2000000000000000000
χ3222-2-2-22-22222-2-200-2-20022-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000002-22-2−i2i2−i2i2−i2i2−i2i2000000000000000000
χ3322-2-2-22-222-2-22200-2-2002-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000002-2-22i2−i2−i2i2−i2i2−i2i2000000000000000000
χ3422-2-2-22-222-2-22200-2-2002-220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000-222-2i2−i2−i2i2i2−i2i2−i2000000000000000000
χ3522-2-2-22-222-2-22200-2-2002-220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000-222-2−i2i2i2−i2−i2i2−i2i2000000000000000000
χ3622-2-2-22-222-2-22200-2-2002-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000002-2-22−i2i2i2−i2i2−i2i2−i2000000000000000000
χ3722-2-2-22-22-222-2-2002200-2-220000i2i2−i2−i2i2i2−i2−i222−2−2−2−22202i−2i2i−2i0000−i2i2−i2i22−2−22000000000000000000
χ3822-2-2-22-22-222-2-2002200-2-220000i2i2−i2−i2i2i2−i2−i2−2−22222−2−20−2i2i−2i2i0000−i2i2−i2i2−222−2000000000000000000
χ3922-2-2-22-22-222-2-2002200-2-220000−i2−i2i2i2−i2−i2i2i222−2−2−2−2220−2i2i−2i2i0000i2−i2i2−i22−2−22000000000000000000
χ4022-2-2-22-22-222-2-2002200-2-220000−i2−i2i2i2−i2−i2i2i2−2−22222−2−202i−2i2i−2i0000i2−i2i2−i2−222−2000000000000000000
χ4122-2-2-22-22-2-2-222002200-22-20000i2i2−i2−i2−i2−i2i2i222−2−2−2−2220−2i2i2i−2i0000−i2i2i2−i2−222−2000000000000000000
χ4222-2-2-22-22-2-2-222002200-22-20000i2i2−i2−i2−i2−i2i2i2−2−22222−2−202i−2i−2i2i0000−i2i2i2−i22−2−22000000000000000000
χ4322-2-2-22-22-2-2-222002200-22-20000−i2−i2i2i2i2i2−i2−i222−2−2−2−22202i−2i−2i2i0000i2−i2−i2i2−222−2000000000000000000
χ4422-2-2-22-22-2-2-222002200-22-20000−i2−i2i2i2i2i2−i2−i2−2−22222−2−20−2i2i2i−2i0000i2−i2−i2i22−2−22000000000000000000
χ452-222-2-2-2220000-2-22-222-2002-200000000002-22-22-22-20000000000000000000002i2i−2i−2i002i−2i000000
χ462-222-2-2-2220000-2-22-222-2002-200000000002-22-22-22-2000000000000000000000−2i−2i2i2i00−2i2i000000
χ472-222-2-2-2220000-2-22-222-2002-20000000000-22-22-22-220000000000000000000002i2i−2i−2i00−2i2i000000
χ482-222-2-2-2220000-2-22-222-2002-20000000000-22-22-22-22000000000000000000000−2i−2i2i2i002i−2i000000
χ492-222-2-2-22-2000022-22-2-22002-200000000002i−2i2i−2i−2i2i−2i2i0000000000000000022-2-200002i−2i00000000
χ502-222-2-2-22-2000022-22-2-22002-200000000002i−2i2i−2i−2i2i−2i2i00000000000000000-2-2220000−2i2i00000000
χ512-222-2-2-22-2000022-22-2-22002-20000000000−2i2i−2i2i2i−2i2i−2i0000000000000000022-2-20000−2i2i00000000
χ522-222-2-2-22-2000022-22-2-22002-20000000000−2i2i−2i2i2i−2i2i−2i00000000000000000-2-22200002i−2i00000000
χ532-22-2-222-202i−2i2i−2i2-2002-2000002i−2i2i−2i2i−2i2-22-200000000000000000000000002−22−2i2−i2i2−i20000i2−i22−200
χ542-22-2-222-202i−2i2i−2i2-2002-2000002i−2i2i−2i2i−2i2-22-20000000000000000000000000−22−22−i2i2−i2i20000−i2i2−2200
χ552-22-2-222-202i−2i2i−2i2-2002-2000002i−2i−2i2i−2i2i-22-2200000000000000000000000002−22−2i2−i2i2−i20000−i2i2−2200
χ562-22-2-222-202i−2i2i−2i2-2002-2000002i−2i−2i2i−2i2i-22-220000000000000000000000000−22−22−i2i2−i2i20000i2−i22−200
χ572-22-2-222-20−2i2i−2i2i2-2002-200000−2i2i2i−2i2i−2i-22-2200000000000000000000000002−22−2−i2i2−i2i20000i2−i2−2200
χ582-22-2-222-20−2i2i−2i2i2-2002-200000−2i2i2i−2i2i−2i-22-220000000000000000000000000−22−22i2−i2i2−i20000−i2i22−200
χ592-22-2-222-20−2i2i−2i2i2-2002-200000−2i2i−2i2i−2i2i2-22-200000000000000000000000002−22−2−i2i2−i2i20000−i2i22−200
χ602-22-2-222-20−2i2i−2i2i2-2002-200000−2i2i−2i2i−2i2i2-22-20000000000000000000000000−22−22i2−i2i2−i20000i2−i2−2200
χ61444-44-4-4-4000004-400-44000000000000000000000000000000000000000022−22−222200000000000000
χ62444-44-4-4-4000004-400-440000000000000000000000000000000000000000−222222−2200000000000000
χ63444-44-4-4-400000-44004-40000000000000000000000000000000000000000000022−22−22220000000000
χ64444-44-4-4-400000-44004-400000000000000000000000000000000000000000000−222222−220000000000
χ654-444-4-4-4440000444-4-4-4-400-4400000000000000000000000000000000000000000000000000000
χ664-444-4-4-44-40000-4-4-4444400-4400000000000000000000000000000000000000000000000000000
χ674-44-4-444-404i−4i4i−4i-4400-4400000−4i4i000000000000000000000000000000000000000000000000000
χ684-44-4-444-40−4i4i−4i4i-4400-44000004i−4i000000000000000000000000000000000000000000000000000
χ694-4-4444-4-404i−4i−4i4i000000000000022−22−2222−2i22i22i2−2i20000000000000000000000000000000000000000000
χ704-4-4444-4-404i−4i−4i4i0000000000000−222222−222i2−2i2−2i22i20000000000000000000000000000000000000000000
χ714-4-4444-4-40−4i4i4i−4i000000000000022−22−22222i2−2i2−2i22i20000000000000000000000000000000000000000000
χ724-4-4444-4-40−4i4i4i−4i0000000000000−222222−22−2i22i22i2−2i20000000000000000000000000000000000000000000
χ734-4-4-44-4444000000-4400-4000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ744-4-4-44-4444000000-4400-400000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ754-4-4-44-444-40000004-40040000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ764-4-4-44-444-40000004-400400000000000000−222222−2222−22−222200000000000000000000000000000000000
χ7788-88-8-88-8000000000000000000000000000000000000000000000000000000000000000000000

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