Finite Group Databasebeta

← Group #274129

Character table — Group #274129

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444448888888824444888888888888888888884444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
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
χ51111111111111111111111-1-1-1-111-1-1-1-111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ911111111-1-1-1-111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-11
χ1111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ1211111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-11-1
χ1311111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ1411111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1
χ1511111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-11
χ172222222222222-2-222-2-22-2-22222-2-2-2-2-2-22200000000-222-2-2000000000000000000000000000000
χ182222222222222-2-222-2-22-2-2-2-2-2-2-2-222222200000000-2-2-222000000000000000000000000000000
χ19222222222222-222-2-222-2-2-20000220000-2-222222222-20000-2-2-2-200000000000000000000000000
χ20222222222222-222-2-222-2-2-20000220000-2-2-2-2-2-2-2-2-2-2-20000222200000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2220000-2-20000-2-20000000020000000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ22222222222222-2-2-2-2-2-2-2-2220000-2-20000-2-2000000002000000000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2322222222-2-2-2-22-2-222-2-22-2-2222222-2-2-2-2-2-2000000002-2-222000000000000000000000000000000
χ2422222222-2-2-2-22-2-222-2-22-2-2-2-2-2-2222222-2-200000000222-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-222-2-222-2-2-20000-2-20000222222-2-2-2-220000-2-22200000000000000000000000000
χ2622222222-2-2-2-2-222-2-222-2-2-20000-2-2000022-2-2-2-222222000022-2-200000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22200002200002200000000-20000000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22200002200002200000000-2000000000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ29222-2-2-2-222i2i−2i−2i02-2002-200000002i−2i00000022-2-22i2i−2i−2i00000000022−2−200000000i2i2−i2−i200002−2i2−i200
χ30222-2-2-2-222i2i−2i−2i02-2002-200000002i−2i00000022-2-22i2i−2i−2i000000000−2−22200000000−i2−i2i2i20000−22−i2i200
χ31222-2-2-2-222i2i−2i−2i02-2002-200000002i−2i000000-2-222−2i−2i2i2i00000000022−2−200000000i2i2−i2−i20000−22−i2i200
χ32222-2-2-2-222i2i−2i−2i02-2002-200000002i−2i000000-2-222−2i−2i2i2i000000000−2−22200000000−i2−i2i2i200002−2i2−i200
χ33222-2-2-2-22−2i−2i2i2i02-2002-20000000−2i2i00000022-2-2−2i−2i2i2i00000000022−2−200000000−i2−i2i2i200002−2−i2i200
χ34222-2-2-2-22−2i−2i2i2i02-2002-20000000−2i2i00000022-2-2−2i−2i2i2i000000000−2−22200000000i2i2−i2−i20000−22i2−i200
χ35222-2-2-2-22−2i−2i2i2i02-2002-20000000−2i2i000000-2-2222i2i−2i−2i00000000022−2−200000000−i2−i2i2i20000−22i2−i200
χ36222-2-2-2-22−2i−2i2i2i02-2002-20000000−2i2i000000-2-2222i2i−2i−2i000000000−2−22200000000i2i2−i2−i200002−2−i2i200
χ3722-2-2-222-22i−2i2i−2i200-2-2002002i2i−2i−2i0000002i−2i2−22−2i2−i2i2−i202-2002−2i2−i20000i2−i2i2−i22−22−200000000000000
χ3822-2-2-222-22i−2i2i−2i200-2-2002002i2i−2i−2i0000002i−2i−22−22−i2i2−i2i202-200−22−i2i20000−i2i2−i2i2−22−2200000000000000
χ3922-2-2-222-22i−2i2i−2i200-2-200200−2i−2i2i2i0000002i−2i2−22−2i2−i2i2−i20-22002−2i2−i20000−i2i2−i2i2−22−2200000000000000
χ4022-2-2-222-22i−2i2i−2i200-2-200200−2i−2i2i2i0000002i−2i−22−22−i2i2−i2i20-2200−22−i2i20000i2−i2i2−i22−22−200000000000000
χ4122-2-2-222-22i−2i2i−2i-2002200-20000000022-2-2−2i2i2−22−2i2−i2i2−i20002i−2i−22−i2i200002−2−22−i2i2i2−i200000000000000
χ4222-2-2-222-22i−2i2i−2i-2002200-20000000022-2-2−2i2i−22−22−i2i2−i2i20002i−2i2−2i2−i20000−222−2i2−i2−i2i200000000000000
χ4322-2-2-222-22i−2i2i−2i-2002200-200000000-2-222−2i2i2−22−2i2−i2i2−i2000−2i2i−22−i2i20000−222−2i2−i2−i2i200000000000000
χ4422-2-2-222-22i−2i2i−2i-2002200-200000000-2-222−2i2i−22−22−i2i2−i2i2000−2i2i2−2i2−i200002−2−22−i2i2i2−i200000000000000
χ4522-2-2-222-2−2i2i−2i2i200-2-2002002i2i−2i−2i000000−2i2i2−22−2−i2i2−i2i20-22002−2−i2i20000i2−i2i2−i2−22−2200000000000000
χ4622-2-2-222-2−2i2i−2i2i200-2-2002002i2i−2i−2i000000−2i2i−22−22i2−i2i2−i20-2200−22i2−i20000−i2i2−i2i22−22−200000000000000
χ4722-2-2-222-2−2i2i−2i2i200-2-200200−2i−2i2i2i000000−2i2i2−22−2−i2i2−i2i202-2002−2−i2i20000−i2i2−i2i22−22−200000000000000
χ4822-2-2-222-2−2i2i−2i2i200-2-200200−2i−2i2i2i000000−2i2i−22−22i2−i2i2−i202-200−22i2−i20000i2−i2i2−i2−22−2200000000000000
χ4922-2-2-222-2−2i2i−2i2i-2002200-20000000022-2-22i−2i2−22−2−i2i2−i2i2000−2i2i−22i2−i200002−2−22i2−i2−i2i200000000000000
χ5022-2-2-222-2−2i2i−2i2i-2002200-20000000022-2-22i−2i−22−22i2−i2i2−i2000−2i2i2−2−i2i20000−222−2−i2i2i2−i200000000000000
χ5122-2-2-222-2−2i2i−2i2i-2002200-200000000-2-2222i−2i2−22−2−i2i2−i2i20002i−2i−22i2−i20000−222−2−i2i2i2−i200000000000000
χ5222-2-2-222-2−2i2i−2i2i-2002200-200000000-2-2222i−2i−22−22i2−i2i2−i20002i−2i2−2−i2i200002−2−22i2−i2−i2i200000000000000
χ532-2-22-22-22000022-22-2-22-22-22i−2i2i−2i002i−2i2i−2i00000000000000000002i−2i2i−2i0000000000002-200000000
χ542-2-22-22-22000022-22-2-22-22-22i−2i2i−2i002i−2i2i−2i0000000000000000000−2i2i−2i2i000000000000-2200000000
χ552-2-22-22-22000022-22-2-22-22-2−2i2i−2i2i00−2i2i−2i2i00000000000000000002i−2i2i−2i000000000000-2200000000
χ562-2-22-22-22000022-22-2-22-22-2−2i2i−2i2i00−2i2i−2i2i0000000000000000000−2i2i−2i2i0000000000002-200000000
χ572-2-22-22-2200002-222-22-2-2-222i−2i2i−2i00−2i2i−2i2i00000000000000000000000000000002i−2i2i−2i002-2000000
χ582-2-22-22-2200002-222-22-2-2-222i−2i2i−2i00−2i2i−2i2i0000000000000000000000000000000−2i2i−2i2i00-22000000
χ592-2-22-22-2200002-222-22-2-2-22−2i2i−2i2i002i−2i2i−2i00000000000000000000000000000002i−2i2i−2i00-22000000
χ602-2-22-22-2200002-222-22-2-2-22−2i2i−2i2i002i−2i2i−2i0000000000000000000000000000000−2i2i−2i2i002-2000000
χ61444-4-4-4-444i4i−4i−4i0-4400-440000000−4i4i0000000000000000000000000000000000000000000000000
χ62444-4-4-4-44−4i−4i4i4i0-4400-4400000004i−4i0000000000000000000000000000000000000000000000000
χ6344-444-4-4-44-4-44000000000000000000000022−22−222222−22−222200000000000000000000000000000000000
χ6444-444-4-4-44-4-440000000000000000000000−222222−22−222222−2200000000000000000000000000000000000
χ6544-444-4-4-4-444-4000000000000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ6644-444-4-4-4-444-40000000000000000000000−222222−2222−22−222200000000000000000000000000000000000
χ674-44-444-4-40000400-4400-4004-4-44000000000000000000000000000000000000000000000000000
χ684-44-444-4-40000400-4400-400-444-4000000000000000000000000000000000000000000000000000
χ694-44-444-4-40000-4004-4004000000004i−4i−4i4i000000000000000000000000000000000000000000000
χ704-44-444-4-40000-4004-400400000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ714-4-44-44-440000-44-4-44-444-440000000000000000000000000000000000000000000000000000000
χ724-4-44-44-440000-4-44-444-444-40000000000000000000000000000000000000000000000000000000
χ734-4-4-44-444000004400-4-4000000000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ744-4-4-44-444000004400-4-400000000000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ754-4-4-44-44400000-4-400440000000000000000000000000000000000000000000022−22−22220000000000
χ764-4-4-44-44400000-4-4004400000000000000000000000000000000000000000000−222222−220000000000
χ778-888-8-88-8000000000000000000000000000000000000000000000000000000000000000000000

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