Finite Group Databasebeta

← Group #287213

Character table — Group #287213

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444888888888888888822224444488888888888888882244888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
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
χ911111111111-1-1-1-11111111-1-1-1-1111111111111-1-1-1-111-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111111-1-1-1-11111111-1-1-1-1111111111111-1-1-1-111-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-11
χ1111111111111-1-1-1-11111111-1-1-1-111111111-1-1-1-11111-1-111-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-11
χ1211111111111-1-1-1-11111111-1-1-1-111111111-1-1-1-11111-1-111-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-11111-1-11-1
χ1311111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-11
χ1411111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1111-1
χ1511111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-11111-1-1111111-1-1-1-1-1-111-1-1111-1
χ1611111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-11111-1-111-1-1-1-1111111-1-111-1-1-11
χ172222222222-222222-2-2-22-2-2-2-22200000000000000002222-2-2-2-2-200000000000000000000000000
χ182222222222-222222-2-2-22-2-2-2-2220000000000000000-2-2-2-2-2222200000000000000000000000000
χ192222222222-2-2-2-2-22-2-2-22-2-222-2-2000000000000000022-2-22-2-22200000000000000000000000000
χ202222222222-2-2-2-2-22-2-2-22-2-222-2-20000000000000000-2-222222-2-200000000000000000000000000
χ2122222222-2-222222-2222-2-2-222-2-200000000222222220000-200000000-2-2-2-2000000000000000000
χ2222222222-2-222222-2222-2-2-222-2-200000000-2-2-2-2-2-2-2-20000-2000000002222000000000000000000
χ2322222222-2-22-2-2-2-2-2222-2-2-2-2-222000000002222-2-2-2-20000200000000-2-222000000000000000000
χ2422222222-2-22-2-2-2-2-2222-2-2-2-2-22200000000-2-2-2-22222000020000000022-2-2000000000000000000
χ2522222222-2-2-22222-2-2-2-2-222-2-2-2-22i2i2i2i−2i−2i−2i−2i000000000000200002i2i−2i−2i0000000000000000000000
χ2622222222-2-2-22222-2-2-2-2-222-2-2-2-2−2i−2i−2i−2i2i2i2i2i00000000000020000−2i−2i2i2i0000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222222i2i2i2i−2i−2i−2i−2i000000000000-20000−2i−2i2i2i0000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222−2i−2i−2i−2i2i2i2i2i000000000000-200002i2i−2i−2i0000000000000000000000
χ29222-2-22-2-22-220000-22-2-222-200002i2i−2i−2i2i2i−2i−2i00000000000000000000000002i2i−2i−2i00002-200000000
χ30222-2-22-2-22-220000-22-2-222-200002i2i−2i−2i2i2i−2i−2i0000000000000000000000000−2i−2i2i2i0000-2200000000
χ31222-2-22-2-22-220000-22-2-222-20000−2i−2i2i2i−2i−2i2i2i00000000000000000000000002i2i−2i−2i0000-2200000000
χ32222-2-22-2-22-220000-22-2-222-20000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000−2i−2i2i2i00002-200000000
χ33222-2-22-2-2-22-200002-222-22-2000022-2-2-2-222000000000000000000000000000002i2i−2i−2i002i−2i000000
χ34222-2-22-2-2-22-200002-222-22-2000022-2-2-2-22200000000000000000000000000000−2i−2i2i2i00−2i2i000000
χ35222-2-22-2-2-22-200002-222-22-20000-2-22222-2-2000000000000000000000000000002i2i−2i−2i00−2i2i000000
χ36222-2-22-2-2-22-200002-222-22-20000-2-22222-2-200000000000000000000000000000−2i−2i2i2i002i−2i000000
χ3722-2-2-2-22222022-2-2-2000-200002-2i2−i2i2−i2i2−i2i2−i222−2−222−2−2000002i−2i2i−2ii2−i2i2−i22−22−2000000000000000000
χ3822-2-2-2-22222022-2-2-2000-200002-2i2−i2i2−i2i2−i2i2−i2−2−222−2−22200000−2i2i−2i2ii2−i2i2−i2−22−22000000000000000000
χ3922-2-2-2-22222022-2-2-2000-200002-2−i2i2−i2i2−i2i2−i2i222−2−222−2−200000−2i2i−2i2i−i2i2−i2i22−22−2000000000000000000
χ4022-2-2-2-22222022-2-2-2000-200002-2−i2i2−i2i2−i2i2−i2i2−2−222−2−222000002i−2i2i−2i−i2i2−i2i2−22−22000000000000000000
χ4122-2-2-2-222220-2-222-2000-20000-22i2−i2i2−i2i2−i2i2−i222−2−2−2−222000002i−2i−2i2i−i2i2−i2i22−2−22000000000000000000
χ4222-2-2-2-222220-2-222-2000-20000-22i2−i2i2−i2i2−i2i2−i2−2−22222−2−200000−2i2i2i−2i−i2i2−i2i2−222−2000000000000000000
χ4322-2-2-2-222220-2-222-2000-20000-22−i2i2−i2i2−i2i2−i2i222−2−2−2−22200000−2i2i2i−2ii2−i2i2−i22−2−22000000000000000000
χ4422-2-2-2-222220-2-222-2000-20000-22−i2i2−i2i2−i2i2−i2i2−2−22222−2−2000002i−2i−2i2ii2−i2i2−i2−222−2000000000000000000
χ4522-2-2-2-222-2-2022-2-2200020000-222−22−2−22−2222−2−222−2−22-22-2000002−2−22−22−22000000000000000000
χ4622-2-2-2-222-2-2022-2-2200020000-222−22−2−22−22−2−222−2−222-22-22000002−2−222−22−2000000000000000000
χ4722-2-2-2-222-2-2022-2-2200020000-22−22−222−22−222−2−222−2−2-22-2200000−222−2−22−22000000000000000000
χ4822-2-2-2-222-2-2022-2-2200020000-22−22−222−22−2−2−222−2−2222-22-200000−222−22−22−2000000000000000000
χ4922-2-2-2-222-2-20-2-2222000200002-22−22−2−22−2222−2−2−2−2222-2-2200000−222−2−222−2000000000000000000
χ5022-2-2-2-222-2-20-2-2222000200002-22−22−2−22−22−2−22222−2−2-222-200000−222−22−2−22000000000000000000
χ5122-2-2-2-222-2-20-2-2222000200002-2−22−222−22−222−2−2−2−222-222-2000002−2−22−222−2000000000000000000
χ5222-2-2-2-222-2-20-2-2222000200002-2−22−222−22−2−2−22222−2−22-2-22000002−2−222−2−22000000000000000000
χ532-2-22-222-20022-22-20-22-20002-200000000002i−2i2i−2i2i−2i2i−2i00000000000000000i2−i2i2−i2i2−i2i2−i200002−22−200
χ542-2-22-222-20022-22-20-22-20002-200000000002i−2i2i−2i2i−2i2i−2i00000000000000000−i2i2−i2i2−i2i2−i2i20000−22−2200
χ552-2-22-222-20022-22-20-22-20002-20000000000−2i2i−2i2i−2i2i−2i2i00000000000000000i2−i2i2−i2i2−i2i2−i20000−22−2200
χ562-2-22-222-20022-22-20-22-20002-20000000000−2i2i−2i2i−2i2i−2i2i00000000000000000−i2i2−i2i2−i2i2−i2i200002−22−200
χ572-2-22-222-2002-22-220-22-2000-2200000000002i−2i2i−2i−2i2i−2i2i00000000000000000i2−i2i2−i2−i2i2−i2i200002−2−2200
χ582-2-22-222-2002-22-220-22-2000-2200000000002i−2i2i−2i−2i2i−2i2i00000000000000000−i2i2−i2i2i2−i2i2−i20000−222−200
χ592-2-22-222-2002-22-220-22-2000-220000000000−2i2i−2i2i2i−2i2i−2i00000000000000000i2−i2i2−i2−i2i2−i2i20000−222−200
χ602-2-22-222-2002-22-220-22-2000-220000000000−2i2i−2i2i2i−2i2i−2i00000000000000000−i2i2−i2i2i2−i2i2−i200002−2−2200
χ61444-4-44-4-44-4-40000-4-4444-440000000000000000000000000000000000000000000000000000000
χ62444-4-44-4-4-444000044-4-4-4-440000000000000000000000000000000000000000000000000000000
χ6344-444-4-4-44-4000004000-400000022−22−222222−22−22220000000000000000000000000000000000000000000
χ6444-444-4-4-44-4000004000-4000000−222222−22−222222−220000000000000000000000000000000000000000000
χ6544-444-4-4-4-4400000-400040000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000
χ6644-444-4-4-4-4400000-40004000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000
χ674-44-44-44-40004-4-4400000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ684-44-44-44-40004-4-440000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ694-44-44-44-4000-444-400000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000
χ704-44-44-44-4000-444-40000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000
χ714-4-44-444-400-44-44-404-44000-4400000000000000000000000000000000000000000000000000000
χ724-4-44-444-400-4-44-4404-440004-400000000000000000000000000000000000000000000000000000
χ734-4-4-444-4400400000-4-44000000000000000000000000000000000000000022−22−222200000000000000
χ744-4-4-444-4400400000-4-440000000000000000000000000000000000000000−222222−2200000000000000
χ754-4-4-444-4400-40000044-40000000000000000000000000000000000000000000022−22−22220000000000
χ764-4-4-444-4400-40000044-400000000000000000000000000000000000000000000−222222−220000000000
χ778-888-8-8-88000000000000000000000000000000000000000000000000000000000000000000000

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