Finite Group Databasebeta

← Group #311610

Character table — Group #311610

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488884444444444448888888888888844444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ51111111111111111111111-1-11111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-1-1-11-111-1-111-1-1-1-1-11
χ10111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-11111-11
χ11111111111111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1111111111-111-1-1-1-111-1-11-1
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-11111-1-1111-1
χ13111111111111111111-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-11-1-111-1-111-1-11-1
χ14111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-111-1-1111-1
χ15111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-11-1-11111-1-1-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1111-1-1-1-11111-11
χ17222222222-222-2-2-22-2-22222220000220000-2-2000000000000-2-2000000000000
χ18222222222-222-2-2-22-2-22222-2-20000-2-20000-2-200000000000022000000000000
χ19222222222-222-2-2-22-2-2-2-2-2-2220000-2-2000022000000000000-22000000000000
χ20222222222-222-2-2-22-2-2-2-2-2-2-2-20000220000220000000000002-2000000000000
χ2122222222-22-2-2222-2-2-2000000222200-2-2-2-20022-2-20000000000000000000000
χ2222222222-22-2-2222-2-2-200000022-2-200-2-22200-2-2220000000000000000000000
χ2322222222-22-2-2222-2-2-2000000-2-2220022-2-200-2-2220000000000000000000000
χ2422222222-22-2-2222-2-2-2000000-2-2-2-20022220022-2-20000000000000000000000
χ25222-2-2-2-2222-2-2-22-22-222i2i−2i−2i0000000000002i−2i000000000000002i−2i2-200000000
χ26222-2-2-2-2222-2-2-22-22-222i2i−2i−2i0000000000002i−2i00000000000000−2i2i-2200000000
χ27222-2-2-2-2222-2-2-22-22-22−2i−2i2i2i000000000000−2i2i000000000000002i−2i-2200000000
χ28222-2-2-2-2222-2-2-22-22-22−2i−2i2i2i000000000000−2i2i00000000000000−2i2i2-200000000
χ29222-2-2-2-222-2-2-22-2222-22i2i−2i−2i00002i−2i00002i−2i−2i2i00000000000000000000002-200
χ30222-2-2-2-222-2-2-22-2222-22i2i−2i−2i0000−2i2i0000−2i2i−2i2i0000000000000000000000-2200
χ31222-2-2-2-222-2-2-22-2222-2−2i−2i2i2i00002i−2i00002i−2i2i−2i0000000000000000000000-2200
χ32222-2-2-2-222-2-2-22-2222-2−2i−2i2i2i0000−2i2i0000−2i2i2i−2i00000000000000000000002-200
χ33222-2-2-2-22-2-2222-22-2-22000000002i−2i0000−2i2i0000002i2i−2i−2i22-2-200000000000000
χ34222-2-2-2-22-2-2222-22-2-22000000002i−2i0000−2i2i000000−2i−2i2i2i-2-22200000000000000
χ35222-2-2-2-22-2-2222-22-2-2200000000−2i2i00002i−2i0000002i2i−2i−2i-2-22200000000000000
χ36222-2-2-2-22-2-2222-22-2-2200000000−2i2i00002i−2i000000−2i−2i2i2i22-2-200000000000000
χ3722-22-22-2-2-202-20002002-22-22i−2i00002i−2i0000002−22−200002−22−2000000i2−i2i2−i20000
χ3822-22-22-2-2-202-20002002-22-22i−2i00002i−2i000000−22−220000−22−22000000−i2i2−i2i20000
χ3922-22-22-2-2-202-20002002-22-2−2i2i0000−2i2i0000002−22−200002−22−2000000−i2i2−i2i20000
χ4022-22-22-2-2-202-20002002-22-2−2i2i0000−2i2i000000−22−220000−22−22000000i2−i2i2−i20000
χ4122-22-22-2-2-202-2000200-22-222i−2i0000−2i2i0000002−22−20000−22−22000000i2−i2−i2i20000
χ4222-22-22-2-2-202-2000200-22-222i−2i0000−2i2i000000−22−2200002−22−2000000−i2i2i2−i20000
χ4322-22-22-2-2-202-2000200-22-22−2i2i00002i−2i0000002−22−20000−22−22000000−i2i2i2−i20000
χ4422-22-22-2-2-202-2000200-22-22−2i2i00002i−2i000000−22−2200002−22−2000000i2−i2−i2i20000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-4-4-4-44-4444-44-4-44-400000000000000000000000000000000000000000000
χ4744-44-44-4-440-44000-40000000000000000000022−22−22220000000000000000000000
χ4844-44-44-4-440-44000-400000000000000000000−222222−220000000000000000000000
χ4944-4-44-44-4404-4000-4000000000000000000000000000022−22−222200000000000000
χ5044-4-44-44-4404-4000-40000000000000000000000000000−222222−2200000000000000
χ5144-4-44-44-4-40-440004004i−4i−4i4i0000000000000000000000000000000000000000
χ5244-4-44-44-4-40-44000400−4i4i4i−4i0000000000000000000000000000000000000000
χ534-4-444-4-440400-4-4400000000000000000000000002i2−2i22i2−2i2000000000000000000
χ544-4-444-4-440400-4-440000000000000000000000000−2i22i2−2i22i2000000000000000000
χ554-4-444-4-440-40044-40000000000000004i−4i000000000000000000000000000000
χ564-4-444-4-440-40044-4000000000000000−4i4i000000000000000000000000000000
χ574-4-4-4-444404004-4-40000000004i−4i000000000000000000000000000000000000
χ584-4-4-4-444404004-4-4000000000−4i4i000000000000000000000000000000000000
χ594-4-4-4-44440-400-444000000000000000000000000022−22−2222000000000000000000
χ604-4-4-4-44440-400-4440000000000000000000000000−222222−22000000000000000000
χ618-888-8-88-8000000000000000000000000000000000000000000000000000000
χ628-88-888-8-8000000000000000000000000000000000000000000000000000000

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