Finite Group Databasebeta

← Group #306105

Character table — Group #306105

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488884444444444448888888888888844444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-111
χ4111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111111-1-11-1-1-1-11111-1-1
χ51111111111111111111111-1-11111-1-1111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ61111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-111-111-1-11111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-111-111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1111-1
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11-1-1-1111111-1-1-11
χ13111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-1-1-111-11
χ14111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1111-1-111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1111-1-11111-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1111-1-111-1-1111-1
χ17222222222-2-22-222-2-2-22222220000220000000000-2-2000000-200-20000000000
χ18222222222-2-22-222-2-2-22222-2-20000-2-20000000000-2-200000020020000000000
χ19222222222-2-22-222-2-2-2-2-2-2-2220000-2-2000000000022000000-20020000000000
χ20222222222-2-22-222-2-2-2-2-2-2-2-2-2000022000000000022000000200-20000000000
χ2122222222-222-22-2-22-2-200000022-2-20022-2-222000000-2-2000000000000000000
χ2222222222-222-22-2-22-2-200000022-2-200-2-222-2-200000022000000000000000000
χ2322222222-222-22-2-22-2-2000000-2-2220022-2-2-2-200000022000000000000000000
χ2422222222-222-22-2-22-2-2000000-2-22200-2-22222000000-2-2000000000000000000
χ25222-2-2-2-22-200-20220002i2i−2i−2i2-200002i−2i00002−20000002−2i2i2−i2−i2000000002−2i2−i200
χ26222-2-2-2-22-200-20220002i2i−2i−2i2-200002i−2i0000−22000000−22−i2−i2i2i200000000−22−i2i200
χ27222-2-2-2-22-200-20220002i2i−2i−2i-220000−2i2i00002−20000002−2i2i2−i2−i200000000−22−i2i200
χ28222-2-2-2-22-200-20220002i2i−2i−2i-220000−2i2i0000−22000000−22−i2−i2i2i2000000002−2i2−i200
χ29222-2-2-2-22-200-2022000−2i−2i2i2i2-20000−2i2i00002−20000002−2−i2−i2i2i2000000002−2−i2i200
χ30222-2-2-2-22-200-2022000−2i−2i2i2i2-20000−2i2i0000−22000000−22i2i2−i2−i200000000−22i2−i200
χ31222-2-2-2-22-200-2022000−2i−2i2i2i-2200002i−2i00002−20000002−2−i2−i2i2i200000000−22i2−i200
χ32222-2-2-2-22-200-2022000−2i−2i2i2i-2200002i−2i0000−22000000−22i2i2−i2−i2000000002−2−i2i200
χ3322-222-2-2-2222-2-22-2-2-220000002-22-20000000022-2-200002-22-200000000000000
χ3422-222-2-2-2222-2-22-2-2-220000002-22-200000000-2-2220000-22-2200000000000000
χ3522-222-2-2-2222-2-22-2-2-22000000-22-220000000022-2-20000-22-2200000000000000
χ3622-222-2-2-2222-2-22-2-2-22000000-22-2200000000-2-22200002-22-200000000000000
χ3722-222-2-2-2-2222-2-22-22-22-22-2002-2-220000000000002-20000000000002-2000000
χ3822-222-2-2-2-2222-2-22-22-22-22-200-222-20000000000002-2000000000000-22000000
χ3922-222-2-2-2-2222-2-22-22-2-22-22002-2-22000000000000-22000000000000-22000000
χ4022-222-2-2-2-2222-2-22-22-2-22-2200-222-2000000000000-220000000000002-2000000
χ4122-222-2-2-2-2-2-222-222-222-22-2000000000000000000-2200000002i−2i02i−2i00000000
χ4222-222-2-2-2-2-2-222-222-222-22-2000000000000000000-220000000−2i2i0−2i2i00000000
χ4322-222-2-2-2-2-2-222-222-22-22-220000000000000000002-200000002i−2i0−2i2i00000000
χ4422-222-2-2-2-2-2-222-222-22-22-220000000000000000002-20000000−2i2i02i−2i00000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-4-4-4-4440040-4-4000000000000000000022−22000000−2222000000000000000000
χ47444-4-4-4-4440040-4-40000000000000000000−222200000022−22000000000000000000
χ4844-444-4-4-44-4-4-444-444-400000000000000000000000000000000000000000000
χ4944-4-4-444-4400-40-440004i−4i−4i4i0000000000000000000000000000000000000000
χ5044-4-4-444-4400-40-44000−4i4i4i−4i0000000000000000000000000000000000000000
χ5144-4-4-444-4-400404-4000000000000000000000000000002i2−2i2−2i22i200000000000000
χ5244-4-4-444-4-400404-400000000000000000000000000000−2i22i22i2−2i200000000000000
χ534-444-44-4-404-40400-4000000000000004-4000000000000000000000000000000
χ544-444-44-4-404-40400-400000000000000-44000000000000000000000000000000
χ554-444-44-4-40-440-4004000000000000000000002i2−2i22i2−2i20000000000000000000000
χ564-444-44-4-40-440-400400000000000000000000−2i22i2−2i22i20000000000000000000000
χ574-4-44-4-44404-40-400400000000000000004-40000000000000000000000000000
χ584-4-44-4-44404-40-40040000000000000000-440000000000000000000000000000
χ594-4-44-4-4440-440400-4000000000000000000002i2−2i2−2i22i20000000000000000000000
χ604-4-44-4-4440-440400-400000000000000000000−2i22i22i2−2i20000000000000000000000
χ618-88-88-88-8000000000000000000000000000000000000000000000000000000
χ628-8-8-888-88000000000000000000000000000000000000000000000000000000

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