Finite Group Databasebeta

← Group #329403

Character table — Group #329403

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222222244444444444444444488888888888888882222444488888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ911111111-1-1-1-11-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-1-111
χ1111111111-1-1-1-11-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-111-1-1-1-111
χ1211111111-1-1-1-11-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111-1-11111-1-1
χ1311111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ1411111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-11111-1-1-111-1
χ1511111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-111-1-1-1-111-111-1
χ1611111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ1722222222222222222-2-2222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ1822222222222222222-2-2222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ19222222222222-2-2-2-2-222-2-2-222-2-2-2-22200000000000000002222-2-2-2-200000000000000000000
χ20222222222222-2-2-2-2-222-2-2-222-2-2-2-2220000000000000000-2-2-2-2222200000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2322222222-2-2-2-22-2-2-2-2-2-2222-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2422222222-2-2-2-22-2-2-2-2-2-2222-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2222222-2-2-222-2-222-2-2000000000000000022-2-2-2-22200000000000000000000
χ2622222222-2-2-2-2-2222222-2-2-222-2-222-2-20000000000000000-2-22222-2-200000000000000000000
χ2722222222-2-2-2-2-22222-2-2-2-2-2-2-222-2-2220000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-22222-2-2-2-2-2-2-222-2-222000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ29222-2-22-2-222-2-2-222-2-2002-2200000000000022-2-2000022-2-20000000000000000i2−i2i2−i2i2−i2i2−i20000
χ30222-2-22-2-222-2-2-222-2-2002-2200000000000022-2-2000022-2-20000000000000000−i2i2−i2i2−i2i2−i2i20000
χ31222-2-22-2-222-2-2-222-2-2002-22000000000000-2-2220000-2-2220000000000000000i2−i2i2−i2−i2i2−i2i20000
χ32222-2-22-2-222-2-2-222-2-2002-22000000000000-2-2220000-2-2220000000000000000−i2i2−i2i2i2−i2i2−i20000
χ33222-2-22-2-2-2-222-2-2-222002-2200000000000022-2-20000-2-2220000000000000000i2−i2−i2i2i2−i2−i2i20000
χ34222-2-22-2-2-2-222-2-2-222002-2200000000000022-2-20000-2-2220000000000000000−i2i2i2−i2−i2i2i2−i20000
χ35222-2-22-2-2-2-222-2-2-222002-22000000000000-2-222000022-2-20000000000000000i2−i2−i2i2−i2i2i2−i20000
χ36222-2-22-2-2-2-222-2-2-222002-22000000000000-2-222000022-2-20000000000000000−i2i2i2−i2i2−i2−i2i20000
χ3722-2-2-2-2222-22-20000022000-2-200002-222−2−22−22−222−2−22−22−200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000000000000
χ3822-2-2-2-2222-22-20000022000-2-200002-222−2−22−22−222−2−22−22−20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000000000000
χ3922-2-2-2-2222-22-20000022000-2-200002-2−2−222−22−22−2−222−22−2200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000000000000
χ4022-2-2-2-2222-22-20000022000-2-200002-2−2−222−22−22−2−222−22−220000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000000000000
χ4122-2-2-2-2222-22-200000-2-2000220000-2222−2−2−22−2222−2−2−22−222-22-200002−2−222−2−22000000000000
χ4222-2-2-2-2222-22-200000-2-2000220000-2222−2−2−22−2222−2−2−22−22-22-220000−222−2−222−2000000000000
χ4322-2-2-2-2222-22-200000-2-2000220000-22−2−2222−22−2−2−2222−22−22-22-20000−222−2−222−2000000000000
χ4422-2-2-2-2222-22-200000-2-2000220000-22−2−2222−22−2−2−2222−22−2-22-2200002−2−222−2−22000000000000
χ4522-2-2-2-222-22-220000022000-2-20000-2222−2−22−22−2−2−222−22−2200002i−2i−2i2ii2−i2i2−i2−i2i2−i2i2000000000000
χ4622-2-2-2-222-22-220000022000-2-20000-2222−2−22−22−2−2−222−22−220000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i2000000000000
χ4722-2-2-2-222-22-220000022000-2-20000-22−2−222−22−2222−2−22−22−200002i−2i−2i2i−i2i2−i2i2i2−i2i2−i2000000000000
χ4822-2-2-2-222-22-220000022000-2-20000-22−2−222−22−2222−2−22−22−20000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i2000000000000
χ4922-2-2-2-222-22-2200000-2-20002200002-222−2−2−22−22−2−2222−22−22-2-2200002−2−22−222−2000000000000
χ5022-2-2-2-222-22-2200000-2-20002200002-222−2−2−22−22−2−2222−22−2-222-20000−222−22−2−22000000000000
χ5122-2-2-2-222-22-2200000-2-20002200002-2−2−2222−22−222−2−2−22−222-2-220000−222−22−2−22000000000000
χ5222-2-2-2-222-22-2200000-2-20002200002-2−2−2222−22−222−2−2−22−22-222-200002−2−22−222−2000000000000
χ53444-4-44-4-444-4-44-4-44400-44-40000000000000000000000000000000000000000000000000000
χ54444-4-44-4-4-4-444444-4-400-44-40000000000000000000000000000000000000000000000000000
χ5544-444-4-4-44-4-44000000000000000000000022−22−2222000022−22−22220000000000000000000000000000
χ5644-444-4-4-44-4-440000000000000000000000−222222−220000−222222−220000000000000000000000000000
χ5744-444-4-4-4-444-4000000000000000000000022−22−22220000−222222−220000000000000000000000000000
χ5844-444-4-4-4-444-40000000000000000000000−222222−22000022−22−22220000000000000000000000000000
χ594-444-4-4-44000004i−4i4i−4i4-40004-4004i−4i0000000000000000000000000000000000000000000000
χ604-444-4-4-44000004i−4i4i−4i-44000-4400−4i4i0000000000000000000000000000000000000000000000
χ614-444-4-4-4400000−4i4i−4i4i4-40004-400−4i4i0000000000000000000000000000000000000000000000
χ624-444-4-4-4400000−4i4i−4i4i-44000-44004i−4i0000000000000000000000000000000000000000000000
χ634-44-44-44-4000004i−4i−4i4i000000000000022−2222−2200002i2−2i22i2−2i200000000000000000000000000000000
χ644-44-44-44-4000004i−4i−4i4i0000000000000−2222−22220000−2i22i2−2i22i200000000000000000000000000000000
χ654-44-44-44-400000−4i4i4i−4i000000000000022−2222−220000−2i22i2−2i22i200000000000000000000000000000000
χ664-44-44-44-400000−4i4i4i−4i0000000000000−2222−222200002i2−2i22i2−2i200000000000000000000000000000000
χ674-4-44-444-4000040000004-4-400000000000000004i−4i−4i4i00000000000000000000000000000000
χ684-4-44-444-4000040000004-4-40000000000000000−4i4i4i−4i00000000000000000000000000000000
χ694-4-44-444-40000-4000000-444000000004-4-440000000000000000000000000000000000000000
χ704-4-44-444-40000-4000000-44400000000-444-40000000000000000000000000000000000000000
χ714-4-4-444-440000400004-4-4-44-444-4000000000000000000000000000000000000000000000000
χ724-4-4-444-44000040000-44-4-444-4-44000000000000000000000000000000000000000000000000
χ734-4-4-444-440000-400004-444-4-44-44000000000000000000000000000000000000000000000000
χ744-4-4-444-440000-40000-4444-44-44-4000000000000000000000000000000000000000000000000

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