Finite Group Databasebeta

← Group #147804

Character table — Group #147804

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222244444444444488888888888816161616161616161616161616161616161616161616
order12222244442222224444444444444488882222444444448888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1
χ911-1-1-11-1-111111-1-1-1111-1-1-1iiii−i−i−i−i11-1-11-11-11-11-1ii−i−i1-1ii−i−iii−i−i
χ1011-1-1-11-1-111111-1-1-1111-1-1-1iiii−i−i−i−i11-1-1-11-11-11-11ii−i−i1-1−i−iii−i−iii
χ1111-1-1-11-1-111111-1-1-1111-1-1-1iiii−i−i−i−i-1-1111-1-111-1-11−i−iii-11ii−i−i−i−iii
χ1211-1-1-11-1-111111-1-1-1111-1-1-1iiii−i−i−i−i-1-111-111-1-111-1−i−iii-11−i−iiiii−i−i
χ1311-1-1-11-1-111111-1-1-1111-1-1-1−i−i−i−iiiii11-1-11-11-11-11-1−i−iii1-1−i−iii−i−iii
χ1411-1-1-11-1-111111-1-1-1111-1-1-1−i−i−i−iiiii11-1-1-11-11-11-11−i−iii1-1ii−i−iii−i−i
χ1511-1-1-11-1-111111-1-1-1111-1-1-1−i−i−i−iiiii-1-1111-1-111-1-11ii−i−i-11−i−iiiii−i−i
χ1611-1-1-11-1-111111-1-1-1111-1-1-1−i−i−i−iiiii-1-111-111-1-111-1ii−i−i-11ii−i−i−i−iii
χ1722222222222-2-22-2-22-2-2-22-2000000000000002200-2-200000000000000
χ1822222222222-2-22-2-22-2-2-22-200000000000000-2-2002200000000000000
χ192222222222-22-2-22-2-22-2-2-220000000000002200-2-20000000000000000
χ202222222222-22-2-22-2-22-2-2-22000000000000-2-200220000000000000000
χ212222222222-2-22-2-22-2-222-2-2000000002222000000000000-2-200000000
χ222222222222-2-22-2-22-2-222-2-200000000-2-2-2-20000000000002200000000
χ23222222-2-2-2-222-222-2-2-222-2-2000000000000000000002i−2i2i−2i0000000000
χ24222222-2-2-2-222-222-2-2-222-2-200000000000000000000−2i2i−2i2i0000000000
χ25222222-2-2-2-22-222-22-22-2-2-22000000000000000000000000002-22-20000
χ26222222-2-2-2-22-222-22-22-2-2-2200000000000000000000000000-22-220000
χ27222222-2-2-2-2-222-2222-2-2-22-20000000000000000000000000000002-22-2
χ28222222-2-2-2-2-222-2222-2-2-22-2000000000000000000000000000000-22-22
χ29222222-2-2-2-2-2-2-2-2-2-222222222-2-222-2-200000000000000000000000000
χ30222222-2-2-2-2-2-2-2-2-2-2222222-2-222-2-22200000000000000000000000000
χ3122-2-2-2222-2-222-2-2-22-2-22-222000000000000000000002-2-220000000000
χ3222-2-2-2222-2-222-2-2-22-2-22-22200000000000000000000-222-20000000000
χ3322-2-2-2222-2-22-22-22-2-22-222-2000000000000000000000000002i−2i−2i2i0000
χ3422-2-2-2222-2-22-22-22-2-22-222-200000000000000000000000000−2i2i2i−2i0000
χ3522-2-2-2222-2-2-2222-2-22-2-22-220000000000000000000000000000002i−2i−2i2i
χ3622-2-2-2222-2-2-2222-2-22-2-22-22000000000000000000000000000000−2i2i2i−2i
χ3722-2-2-2222-2-2-2-2-2222222-2-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ3822-2-2-2222-2-2-2-2-2222222-2-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ3922-2-2-22-2-2222-2-2-2222-2-22-22000000000000002-200-2200000000000000
χ4022-2-2-22-2-2222-2-2-2222-2-22-2200000000000000-22002-200000000000000
χ4122-2-2-22-2-222-22-22-22-22-222-20000000000002-200-220000000000000000
χ4222-2-2-22-2-222-22-22-22-22-222-2000000000000-22002-20000000000000000
χ4322-2-2-22-2-222-2-2222-2-2-22-2220000000022-2-2000000000000-2200000000
χ4422-2-2-22-2-222-2-2222-2-2-22-22200000000-2-2220000000000002-200000000
χ454444-4-44-44-40000000000002-22-22-22-200000000000000000000000000
χ464444-4-44-44-4000000000000-22-22-22-2200000000000000000000000000
χ474444-4-4-44-440000000000002-2-222-2-2200000000000000000000000000
χ484444-4-4-44-44000000000000-222-2-222-200000000000000000000000000
χ4944-4-44-44-4-440000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ5044-4-44-44-4-44000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5144-4-44-4-444-40000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ5244-4-44-4-444-4000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ538-88-80000000000000000000000000022−2222−220000000000000000000000
χ548-88-800000000000000000000000000−2222−22220000000000000000000000
χ558-8-880000000000000000000000000022−22−22220000000000000000000000
χ568-8-8800000000000000000000000000−222222−220000000000000000000000

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