Finite Group Databasebeta

← Group #136388

Character table — Group #136388

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11222222222224444444488888888888888888161616161616161616161616161616163232
order1222244448888448888882244488888888888844888888161616161616161644
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911-11-1-111-11111111-11-1-1-11-11-1-1ii−i−i1111-1-1-1-1i−i1-1ii−i−i11-1-1ii−i−ii−i
χ1011-11-1-111-11111111-11-1-1-11-11-1-1ii−i−i-1-1-1-11111i−i1-1ii−i−i-1-111−i−iii−ii
χ1111-11-1-111-11111111-11-1-1-11-11-1-1−i−iii1111-1-1-1-1−ii1-1−i−iii11-1-1−i−iii−ii
χ1211-11-1-111-11111111-11-1-1-11-11-1-1−i−iii-1-1-1-11111−ii1-1−i−iii-1-111ii−i−ii−i
χ1311-11-1-111-11111111-11-1-1-1-11-11-1ii−i−i1111-1-1-1-1i−i-11−i−iii-1-111ii−i−i−ii
χ1411-11-1-111-11111111-11-1-1-1-11-11-1ii−i−i-1-1-1-11111i−i-11−i−iii11-1-1−i−iiii−i
χ1511-11-1-111-11111111-11-1-1-1-11-11-1−i−iii1111-1-1-1-1−ii-11ii−i−i-1-111−i−iiii−i
χ1611-11-1-111-11111111-11-1-1-1-11-11-1−i−iii-1-1-1-11111−ii-11ii−i−i11-1-1ii−i−i−ii
χ1722222222222-2-2-2-222-2-2-222222-200000000000000-2-200000000000000
χ1822222222222-2-2-2-222-2-2-22-2-2-2-2-2000000000000002200000000000000
χ19222222222-2-222-2-2-2-2222-20000-2222200000000-2-20000000000000000
χ20222222222-2-222-2-2-2-2222-20000-2-2-2-2-200000000220000000000000000
χ21222222222-2-2-2-222-2-2-2-2-2-20000200000000000000002-22-20000000000
χ22222222222-2-2-2-222-2-2-2-2-2-2000020000000000000000-22-220000000000
χ23222-2-222-2-2-2-2000022000-222-2-20000022−2−222−2−2000000002−22−2000000
χ24222-2-222-2-2-2-2000022000-222-2-200000−2−222−2−22200000000−22−22000000
χ25222-2-222-2-2-2-2000022000-2-2-2220000022−2−222−2−200000000−22−22000000
χ26222-2-222-2-2-2-2000022000-2-2-22200000−2−222−2−222000000002−22−2000000
χ27222-2-2-2-22200-2-2000022-20000002-22-2i2−i2i2−i2i2−i2i2−i2000000000000i2−i2i2−i200
χ28222-2-2-2-22200-2-2000022-20000002-22-2−i2i2−i2i2−i2i2−i2i2000000000000−i2i2−i2i200
χ29222-2-2-2-22200-2-2000022-2000000-22-22i2−i2i2−i2i2−i2i2−i2000000000000−i2i2−i2i200
χ30222-2-2-2-22200-2-2000022-2000000-22-22−i2i2−i2i2−i2i2−i2i2000000000000i2−i2i2−i200
χ3122-22-2-222-222-2-2-2-22-2-222-22-22-2200000000000000-2200000000000000
χ3222-22-2-222-222-2-2-2-22-2-222-2-22-222000000000000002-200000000000000
χ3322-22-2-222-2-2-222-2-2-222-2-22000022i2i−2i−2i00000000−2i2i0000000000000000
χ3422-22-2-222-2-2-222-2-2-222-2-2200002−2i−2i2i2i000000002i−2i0000000000000000
χ3522-22-2-222-2-2-2-2-222-22-22220000-200000000000000002i−2i−2i2i0000000000
χ3622-22-2-222-2-2-2-2-222-22-22220000-20000000000000000−2i2i2i−2i0000000000
χ3722-2-222-22-200-2-200002-220000002i−2i−2i2ii2−i2i2−i2−i2i2−i2i2000000000000−222−200
χ3822-2-222-22-200-2-200002-220000002i−2i−2i2i−i2i2−i2i2i2−i2i2−i20000000000002−2−2200
χ3922-2-222-22-200-2-200002-22000000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i20000000000002−2−2200
χ4022-2-222-22-200-2-200002-22000000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i2000000000000−222−200
χ4122-2-22-22-22-2-200002-200022-2-220000022−2−2−2−222000000002−2−22000000
χ4222-2-22-22-22-2-200002-200022-2-2200000−2−22222−2−200000000−222−2000000
χ4322-2-22-22-22-2-200002-20002-222-20000022−2−2−2−22200000000−222−2000000
χ4422-2-22-22-22-2-200002-20002-222-200000−2−22222−2−2000000002−2−22000000
χ4544444-4-4-4-40000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ4644444-4-4-4-4000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ47444-4-444-4-4440000-4-4000400000000000000000000000000000000000
χ48444-4-4-4-44400440000-4-44000000000000000000000000000000000000
χ4944-44-44-4-440000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ5044-44-44-4-44000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ5144-4-444-44-400440000-44-4000000000000000000000000000000000000
χ5244-4-44-44-44440000-44000-400000000000000000000000000000000000
χ538-800000004i2−4i242−424i−4i00000000000000000000000000000000000000000
χ548-800000004i2−4i2−4242−4i4i00000000000000000000000000000000000000000
χ558-80000000−4i24i242−42−4i4i00000000000000000000000000000000000000000
χ568-80000000−4i24i2−42424i−4i00000000000000000000000000000000000000000

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