Finite Group Databasebeta

← Group #277014

Character table — Group #277014

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444222244444444448888888844444888888888888888888884444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ911111111-1-1-1-111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-111-11
χ1111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-11
χ1211111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-11111-1-11-1
χ1311111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-11
χ1411111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1111-1
χ1511111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-11111-1-1111111-1-1-1-111-1-111-1-1-11
χ172222222222222-2-2222-2-22222-2-222-2-2-2-2-2-200000000-222-2-2000000000000000000000000000000
χ182222222222222-2-2222-2-2-2-2-2-2-2-222-2-2222200000000-2-2-222000000000000000000000000000000
χ19222222222222-222-2-2-2220000-2-2-2-222000022222222-2000000000000-2-2-2-2000000000000000000
χ20222222222222-222-2-2-2220000-2-2-2-2220000-2-2-2-2-2-2-2-2-20000000000002222000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2000022-2-2-2-2000000000000200000000000000002i2i−2i−2i2i2i−2i−2i0000000000
χ22222222222222-2-2-2-2-2-2-2-2000022-2-2-2-200000000000020000000000000000−2i−2i2i2i−2i−2i2i2i0000000000
χ2322222222-2-2-2-22-2-2222-2-22222-2-2-2-222-2-2-2-2000000002-2-222000000000000000000000000000000
χ2422222222-2-2-2-22-2-2222-2-2-2-2-2-2-2-2-2-222222200000000222-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-222-2-2-2220000-2-222-2-200002222-2-2-2-22000000000000-2-222000000000000000000
χ2622222222-2-2-2-2-222-2-2-2220000-2-222-2-20000-2-2-2-22222200000000000022-2-2000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-20000222222000000000000-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000222222000000000000-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ29222-2-2-22-22i2i−2i−2i02-20002-2000000002i−2i000022-2-22i2i−2i−2i0000022−2−2i2i2−i2−i200000000000000002−2i2−i200
χ30222-2-2-22-22i2i−2i−2i02-20002-2000000002i−2i000022-2-22i2i−2i−2i00000−2−222−i2−i2i2i20000000000000000−22−i2i200
χ31222-2-2-22-22i2i−2i−2i02-20002-2000000002i−2i0000-2-222−2i−2i2i2i0000022−2−2i2i2−i2−i20000000000000000−22−i2i200
χ32222-2-2-22-22i2i−2i−2i02-20002-2000000002i−2i0000-2-222−2i−2i2i2i00000−2−222−i2−i2i2i200000000000000002−2i2−i200
χ33222-2-2-22-2−2i−2i2i2i02-20002-200000000−2i2i000022-2-2−2i−2i2i2i0000022−2−2−i2−i2i2i200000000000000002−2−i2i200
χ34222-2-2-22-2−2i−2i2i2i02-20002-200000000−2i2i000022-2-2−2i−2i2i2i00000−2−222i2i2−i2−i20000000000000000−22i2−i200
χ35222-2-2-22-2−2i−2i2i2i02-20002-200000000−2i2i0000-2-2222i2i−2i−2i0000022−2−2−i2−i2i2i20000000000000000−22i2−i200
χ36222-2-2-22-2−2i−2i2i2i02-20002-200000000−2i2i0000-2-2222i2i−2i−2i00000−2−222i2i2−i2−i200000000000000002−2−i2i200
χ3722-2-222-2-22-22-2200-2-220022-2-2002-2000000i2−i2i2−i2i2−i2i2−i202-20000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000
χ3822-2-222-2-22-22-2200-2-220022-2-2002-2000000−i2i2−i2i2−i2i2−i2i202-20000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000
χ3922-2-222-2-22-22-2200-2-2200-2-222002-2000000i2−i2i2−i2i2−i2i2−i20-220000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000
χ4022-2-222-2-22-22-2200-2-2200-2-222002-2000000−i2i2−i2i2−i2i2−i2i20-220000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000
χ4122-2-222-2-22-22-2-20022-200000000-22002i2i−2i−2ii2−i2i2−i2i2−i2i2−i20002i−2i00000000−i2i2−i2i22−2−222−2−220000000000
χ4222-2-222-2-22-22-2-20022-200000000-22002i2i−2i−2i−i2i2−i2i2−i2i2−i2i20002i−2i00000000i2−i2i2−i2−222−2−222−20000000000
χ4322-2-222-2-22-22-2-20022-200000000-2200−2i−2i2i2ii2−i2i2−i2i2−i2i2−i2000−2i2i00000000−i2i2−i2i2−222−2−222−20000000000
χ4422-2-222-2-22-22-2-20022-200000000-2200−2i−2i2i2i−i2i2−i2i2−i2i2−i2i2000−2i2i00000000i2−i2i2−i22−2−222−2−220000000000
χ4522-2-222-2-2-22-22200-2-220022-2-200-22000000i2−i2i2−i2−i2i2−i2i20-220000000000i2−i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000
χ4622-2-222-2-2-22-22200-2-220022-2-200-22000000−i2i2−i2i2i2−i2i2−i20-220000000000−i2i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000
χ4722-2-222-2-2-22-22200-2-2200-2-22200-22000000i2−i2i2−i2−i2i2−i2i202-20000000000i2−i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000
χ4822-2-222-2-2-22-22200-2-2200-2-22200-22000000−i2i2−i2i2i2−i2i2−i202-20000000000−i2i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000
χ4922-2-222-2-2-22-22-20022-2000000002-2002i2i−2i−2ii2−i2i2−i2−i2i2−i2i2000−2i2i00000000−i2i2i2−i22−2−22−222−20000000000
χ5022-2-222-2-2-22-22-20022-2000000002-2002i2i−2i−2i−i2i2−i2i2i2−i2i2−i2000−2i2i00000000i2−i2−i2i2−222−22−2−220000000000
χ5122-2-222-2-2-22-22-20022-2000000002-200−2i−2i2i2ii2−i2i2−i2−i2i2−i2i20002i−2i00000000−i2i2i2−i2−222−22−2−220000000000
χ5222-2-222-2-2-22-22-20022-2000000002-200−2i−2i2i2i−i2i2−i2i2i2−i2i2−i20002i−2i00000000i2−i2−i2i22−2−22−222−20000000000
χ532-2-22-222-20000-2222-22-2-22-22-22-200002-22-2000000000000000002i−2i2i−2i000000000000002i−2i000000
χ542-2-22-222-20000-2222-22-2-22-22-22-200002-22-200000000000000000−2i2i−2i2i00000000000000−2i2i000000
χ552-2-22-222-20000-2222-22-2-2-22-222-20000-22-22000000000000000002i−2i2i−2i00000000000000−2i2i000000
χ562-2-22-222-20000-2222-22-2-2-22-222-20000-22-2200000000000000000−2i2i−2i2i000000000000002i−2i000000
χ572-2-22-222-20000-2-2-22-22222-22-2-220000-22-2200000000000002-22-200000000000000002-200000000
χ582-2-22-222-20000-2-2-22-22222-22-2-220000-22-220000000000000-22-220000000000000000-2200000000
χ592-2-22-222-20000-2-2-22-2222-22-22-2200002-22-200000000000002-22-20000000000000000-2200000000
χ602-2-22-222-20000-2-2-22-2222-22-22-2200002-22-20000000000000-22-2200000000000000002-200000000
χ61444-4-4-44-44i4i−4i−4i0-44000-4400000000−4i4i00000000000000000000000000000000000000000000000
χ62444-4-4-44-4−4i−4i4i4i0-44000-44000000004i−4i00000000000000000000000000000000000000000000000
χ6344-44-4-4-444i−4i−4i4i00000000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000000000000000000
χ6444-44-4-4-444i−4i−4i4i0000000000000000000000−2i22i22i2−2i222−22−222200000000000000000000000000000000000
χ6544-44-4-4-44−4i4i4i−4i00000000000000000000002i2−2i2−2i22i222−22−222200000000000000000000000000000000000
χ6644-44-4-4-44−4i4i4i−4i0000000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000000000000000000
χ674-44-4-44-4400004004-4-40000000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ684-44-4-44-4400004004-4-4000000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ694-44-4-44-440000-400-444004-4-4400000000000000000000000000000000000000000000000000000
χ704-44-4-44-440000-400-44400-444-400000000000000000000000000000000000000000000000000000
χ714-4-44-444-40000444-44-4-4-40000-44000000000000000000000000000000000000000000000000000
χ724-4-44-444-400004-4-4-44-44400004-4000000000000000000000000000000000000000000000000000
χ734-4-4-44-444000004-4000-44000000000000000000000000000000022−22−22220000000000000000000000
χ744-4-4-44-444000004-4000-440000000000000000000000000000000−222222−220000000000000000000000
χ754-4-4-44-44400000-440004-400000000000000000000000000022−22−222200000000000000000000000000
χ764-4-4-44-44400000-440004-4000000000000000000000000000−222222−2200000000000000000000000000
χ778-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000000000

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