Finite Group Databasebeta

← Group #286706

Character table — Group #286706

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444888888888888888844444444488888888888888884444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
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
χ9111111111-1-1-1-11111111-1-111-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-11-1
χ10111111111-1-1-1-11111111-1-111-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-11
χ11111111111-1-1-1-11111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11
χ12111111111-1-1-1-11111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11-1
χ13111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-111-1-111-1-1-11
χ14111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-111-1-1111-1
χ15111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1111-1
χ16111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-111-1-1-1-11111-1-11111-1-11111-1-1-11
χ172222222222222-222-2-22-222-2-2-2-20000000000000000-222-2-222-2-200000000000000000000000000
χ182222222222222-222-2-22-222-2-2-2-20000000000000000-2-2-222-2-22200000000000000000000000000
χ19222222222-2-2-2-2-222-2-22-2-2-2-2-2220000000000000000222-2-2-2-22200000000000000000000000000
χ20222222222-2-2-2-2-222-2-22-2-2-2-2-22200000000000000002-2-22222-2-200000000000000000000000000
χ2122222222-222222-2-222-22-2-2-2-2220000000022222222-200000000-2-200000000-2-200000000000000
χ2222222222-222222-2-222-22-2-2-2-22200000000-2-2-2-2-2-2-2-2-20000000022000000002200000000000000
χ2322222222-22222-2-2-2-2-2-2-2-2-222-2-22i2i2i2i−2i−2i−2i−2i000000002000000000000002i2i−2i−2i0000000000000000
χ2422222222-22222-2-2-2-2-2-2-2-2-222-2-2−2i−2i−2i−2i2i2i2i2i00000000200000000000000−2i−2i2i2i0000000000000000
χ2522222222-2-2-2-2-22-2-222-2222-2-2-2-2000000002222-2-2-2-22000000002200000000-2-200000000000000
χ2622222222-2-2-2-2-22-2-222-2222-2-2-2-200000000-2-2-2-22222200000000-2-2000000002200000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222222i2i2i2i−2i−2i−2i−2i00000000-200000000000000−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222−2i−2i−2i−2i2i2i2i2i00000000-2000000000000002i2i−2i−2i0000000000000000
χ29222-2-2-2-2222i2i−2i−2i0-2-200202i−2i0000i2i2−i2−i2i2i2−i2−i222−2−2i2i2−i2−i20002i−2i002-2i2−i200002−22−22−200000000000000
χ30222-2-2-2-2222i2i−2i−2i0-2-200202i−2i0000i2i2−i2−i2i2i2−i2−i2−2−222−i2−i2i2i2000−2i2i00-22−i2i200002−22−2−2200000000000000
χ31222-2-2-2-2222i2i−2i−2i0-2-200202i−2i0000−i2−i2i2i2−i2−i2i2i222−2−2i2i2−i2−i2000−2i2i00-22i2−i20000−22−222−200000000000000
χ32222-2-2-2-2222i2i−2i−2i0-2-200202i−2i0000−i2−i2i2i2−i2−i2i2i2−2−222−i2−i2i2i20002i−2i002-2−i2i20000−22−22−2200000000000000
χ33222-2-2-2-222−2i−2i2i2i0-2-20020−2i2i0000i2i2−i2−i2i2i2−i2−i222−2−2−i2−i2i2i20002i−2i00-22−i2i20000−22−222−200000000000000
χ34222-2-2-2-222−2i−2i2i2i0-2-20020−2i2i0000i2i2−i2−i2i2i2−i2−i2−2−222i2i2−i2−i2000−2i2i002-2i2−i20000−22−22−2200000000000000
χ35222-2-2-2-222−2i−2i2i2i0-2-20020−2i2i0000−i2−i2i2i2−i2−i2i2i222−2−2−i2−i2i2i2000−2i2i002-2−i2i200002−22−22−200000000000000
χ36222-2-2-2-222−2i−2i2i2i0-2-20020−2i2i0000−i2−i2i2i2−i2−i2i2i2−2−222i2i2−i2−i20002i−2i00-22i2−i200002−22−2−2200000000000000
χ37222-2-2-2-22-22i2i−2i−2i02200-20−2i2i000022−2−2−2−22222−2−2i2i2−i2−i202-2002i−2i00−i2i20000−i2i2i2−i2−2200000000000000
χ38222-2-2-2-22-22i2i−2i−2i02200-20−2i2i000022−2−2−2−222−2−222−i2−i2i2i20-2200−2i2i00i2−i20000−i2i2i2−i22−200000000000000
χ39222-2-2-2-22-22i2i−2i−2i02200-20−2i2i0000−2−22222−2−222−2−2i2i2−i2−i20-2200−2i2i00−i2i20000i2−i2−i2i2−2200000000000000
χ40222-2-2-2-22-22i2i−2i−2i02200-20−2i2i0000−2−22222−2−2−2−222−i2−i2i2i202-2002i−2i00i2−i20000i2−i2−i2i22−200000000000000
χ41222-2-2-2-22-2−2i−2i2i2i02200-202i−2i000022−2−2−2−22222−2−2−i2−i2i2i202-200−2i2i00i2−i20000i2−i2−i2i2−2200000000000000
χ42222-2-2-2-22-2−2i−2i2i2i02200-202i−2i000022−2−2−2−222−2−222i2i2−i2−i20-22002i−2i00−i2i20000i2−i2−i2i22−200000000000000
χ43222-2-2-2-22-2−2i−2i2i2i02200-202i−2i0000−2−22222−2−222−2−2−i2−i2i2i20-22002i−2i00i2−i20000−i2i2i2−i2−2200000000000000
χ44222-2-2-2-22-2−2i−2i2i2i02200-202i−2i0000−2−22222−2−2−2−222i2i2−i2−i202-200−2i2i00−i2i20000−i2i2i2−i22−200000000000000
χ4522-2-2-222-220000-22-22-2-22002-2002i−2i2i−2i2i−2i2i−2i000000000000000000000000000002i2i−2i−2i2-200000000
χ4622-2-2-222-220000-22-22-2-22002-2002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000−2i−2i2i2i-2200000000
χ4722-2-2-222-220000-22-22-2-22002-200−2i2i−2i2i−2i2i−2i2i000000000000000000000000000002i2i−2i−2i-2200000000
χ4822-2-2-222-220000-22-22-2-22002-200−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000−2i−2i2i2i2-200000000
χ4922-2-2-222-2-200002-22-222-2002-2002-22-2-22-2200000000000000000002i2i−2i−2i0000000000002i−2i000000
χ5022-2-2-222-2-200002-22-222-2002-2002-22-2-22-220000000000000000000−2i−2i2i2i000000000000−2i2i000000
χ5122-2-2-222-2-200002-22-222-2002-200-22-222-22-200000000000000000002i2i−2i−2i000000000000−2i2i000000
χ5222-2-2-222-2-200002-22-222-2002-200-22-222-22-20000000000000000000−2i−2i2i2i0000000000002i−2i000000
χ532-222-22-2-202i−2i2i−2i200-2-20200002i−2i000000002i−2i2i−2i2-22-2000000000002−22−2000000i2−i2i2−i20000i2−i22−200
χ542-222-22-2-202i−2i2i−2i200-2-20200002i−2i000000002i−2i2i−2i2-22-200000000000−22−22000000−i2i2−i2i20000−i2i2−2200
χ552-222-22-2-202i−2i2i−2i200-2-20200002i−2i00000000−2i2i−2i2i-22-22000000000002−22−2000000i2−i2i2−i20000−i2i2−2200
χ562-222-22-2-202i−2i2i−2i200-2-20200002i−2i00000000−2i2i−2i2i-22-2200000000000−22−22000000−i2i2−i2i20000i2−i22−200
χ572-222-22-2-20−2i2i−2i2i200-2-2020000−2i2i000000002i−2i2i−2i-22-22000000000002−22−2000000−i2i2−i2i20000i2−i2−2200
χ582-222-22-2-20−2i2i−2i2i200-2-2020000−2i2i000000002i−2i2i−2i-22-2200000000000−22−22000000i2−i2i2−i20000−i2i22−200
χ592-222-22-2-20−2i2i−2i2i200-2-2020000−2i2i00000000−2i2i−2i2i2-22-2000000000002−22−2000000−i2i2−i2i20000−i2i22−200
χ602-222-22-2-20−2i2i−2i2i200-2-2020000−2i2i00000000−2i2i−2i2i2-22-200000000000−22−22000000i2−i2i2−i20000i2−i2−2200
χ6144-444-4-4-4400000-4400-4000000022−22−222222−22−22220000000000000000000000000000000000000000000
χ6244-444-4-4-4400000-4400-40000000−222222−22−222222−220000000000000000000000000000000000000000000
χ6344-444-4-4-4-4000004-400400000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000
χ6444-444-4-4-4-4000004-40040000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000
χ6544-4-4-444-44000044-4-44-4-400-4400000000000000000000000000000000000000000000000000000
χ6644-4-4-444-4-40000-4-444-44400-4400000000000000000000000000000000000000000000000000000
χ674-444-44-4-404i−4i4i−4i-400440-40000−4i4i000000000000000000000000000000000000000000000000000
χ684-444-44-4-40−4i4i−4i4i-400440-400004i−4i000000000000000000000000000000000000000000000000000
χ694-44-44-44-404-4-440000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000
χ704-44-44-44-404-4-44000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000
χ714-44-44-44-40-444-40000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ724-44-44-44-40-444-4000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ734-4-4-444-44000004004-40-40000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ744-4-4-444-44000004004-40-4000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ754-4-4-444-4400000-400-4404000000000000000000000000000000000000000000022−22−22220000000000
χ764-4-4-444-4400000-400-44040000000000000000000000000000000000000000000−222222−220000000000
χ778-8-88-8-888000000000000000000000000000000000000000000000000000000000000000000000

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