Finite Group Databasebeta

← Group #136421

Character table — Group #136421

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11222222222224444444488888888888888888161616161616161616161616161616163232
order1222244448888448888882244444448888888844448888161616161616161688
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-11111-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1
χ911-11-11-11-11111111-11-1-1-11-11-1-1ii−i−i1111-1-1-1-1ii−i−ii−i1-111-1-1ii−i−ii−i
χ1011-11-11-11-11111111-11-1-1-11-11-1-1ii−i−i-1-1-1-11111ii−i−ii−i1-1-1-111−i−iii−ii
χ1111-11-11-11-11111111-11-1-1-11-11-1-1−i−iii1111-1-1-1-1−i−iii−ii1-111-1-1−i−iii−ii
χ1211-11-11-11-11111111-11-1-1-11-11-1-1−i−iii-1-1-1-11111−i−iii−ii1-1-1-111ii−i−ii−i
χ1311-11-11-11-11111111-11-1-1-1-11-11-1ii−i−i1111-1-1-1-1−i−iiii−i-11-1-111ii−i−i−ii
χ1411-11-11-11-11111111-11-1-1-1-11-11-1ii−i−i-1-1-1-11111−i−iiii−i-1111-1-1−i−iiii−i
χ1511-11-11-11-11111111-11-1-1-1-11-11-1−i−iii1111-1-1-1-1ii−i−i−ii-11-1-111−i−iiii−i
χ1611-11-11-11-11111111-11-1-1-1-11-11-1−i−iii-1-1-1-11111ii−i−i−ii-1111-1-1ii−i−i−ii
χ1722222222222-2-2-2-222-2-2-222222-2000000000000000000-2-20000000000
χ1822222222222-2-2-2-222-2-2-22-2-2-2-2-2000000000000000000220000000000
χ19222222222-2-222-2-2-2-2222-20000-22222000000000000-2-2000000000000
χ20222222222-2-222-2-2-2-2222-20000-2-2-2-2-200000000000022000000000000
χ21222222222-2-2-2-222-2-2-2-2-2-2000020000000000002-22-200000000000000
χ22222222222-2-2-2-222-2-2-2-2-2-200002000000000000-22-2200000000000000
χ23222-2-22-2-22220000-2-200022-2-2200000i2i2−i2−i2i2i2−i2−i200000000i2−i2i2−i2000000
χ24222-2-22-2-22220000-2-200022-2-2200000−i2−i2i2i2−i2−i2i2i200000000−i2i2−i2i2000000
χ25222-2-22-2-22220000-2-20002-222-200000i2i2−i2−i2i2i2−i2−i200000000−i2i2−i2i2000000
χ26222-2-22-2-22220000-2-20002-222-200000−i2−i2i2i2−i2−i2i2i200000000i2−i2i2−i2000000
χ27222-2-2-222-200220000-22-20000002i−2i2i−2i2−22−22−22−2000000000000i2−i2i2−i200
χ28222-2-2-222-200220000-22-20000002i−2i2i−2i−22−22−22−22000000000000−i2i2−i2i200
χ29222-2-2-222-200220000-22-2000000−2i2i−2i2i2−22−22−22−2000000000000−i2i2−i2i200
χ30222-2-2-222-200220000-22-2000000−2i2i−2i2i−22−22−22−22000000000000i2−i2i2−i200
χ3122-22-22-22-222-2-2-2-22-2-222-22-22-22000000000000000000-220000000000
χ3222-22-22-22-222-2-2-2-22-2-222-2-22-2220000000000000000002-20000000000
χ3322-22-22-22-2-2-222-2-2-222-2-22000022i2i−2i−2i000000000000−2i2i000000000000
χ3422-22-22-22-2-2-222-2-2-222-2-2200002−2i−2i2i2i0000000000002i−2i000000000000
χ3522-22-22-22-2-2-2-2-222-22-22220000-20000000000002i−2i−2i2i00000000000000
χ3622-22-22-22-2-2-2-2-222-22-22220000-2000000000000−2i2i2i−2i00000000000000
χ3722-2-2222-2-2220000-22000-222-2-200000i2i2−i2−i2−i2−i2i2i200000000i2−i2−i2i2000000
χ3822-2-2222-2-2220000-22000-222-2-200000−i2−i2i2i2i2i2−i2−i200000000−i2i2i2−i2000000
χ3922-2-2222-2-2220000-22000-2-2-22200000i2i2−i2−i2−i2−i2i2i200000000−i2i2i2−i2000000
χ4022-2-2222-2-2220000-22000-2-2-22200000−i2−i2i2i2i2i2−i2−i200000000i2−i2−i2i2000000
χ4122-2-22-2-22200220000-2-220000002-2-222−22−2−22−220000000000002−2−2200
χ4222-2-22-2-22200220000-2-220000002-2-22−22−222−22−2000000000000−222−200
χ4322-2-22-2-22200220000-2-22000000-222-22−22−2−22−22000000000000−222−200
χ4422-2-22-2-22200220000-2-22000000-222-2−22−222−22−20000000000002−2−2200
χ4544444-4-4-4-40000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ4644444-4-4-4-4000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ47444-4-44-4-44-4-4000044000-400000000000000000000000000000000000
χ48444-4-4-444-400-4-400004-44000000000000000000000000000000000000
χ4944-44-4-44-440000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ5044-44-4-44-44000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ5144-4-4444-4-4-4-400004-4000400000000000000000000000000000000000
χ5244-4-44-4-44400-4-4000044-4000000000000000000000000000000000000
χ538-8000000042−424i2−4i24i−4i00000000000000000000000000000000000000000
χ548-8000000042−42−4i24i2−4i4i00000000000000000000000000000000000000000
χ558-80000000−42424i2−4i2−4i4i00000000000000000000000000000000000000000
χ568-80000000−4242−4i24i24i−4i00000000000000000000000000000000000000000

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