Finite Group Databasebeta

← Group #308507

Character table — Group #308507

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-111-1-111-11-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-11-1-1-1-1-111-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111
χ71111111111111111111111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-11
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1111-1-111-1
χ911111111111111111-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111
χ1011111111111111111-1-1-1-111111-1-1111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-1-1-1111111111111-1-11-1-1-111-1-1-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1111
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-11-1-11111-1
χ172222222222-22-2-2-22-20000-222220022-2-2-2-200-2-2000000000000000000020000000
χ182222222222-22-2-2-22-20000-2222200-2-2222200-2-20000000000000000000-20000000
χ192222222222-22-2-2-22-20000-2-2-2-2-2002222-2-200220000000000000000000-20000000
χ202222222222-22-2-2-22-20000-2-2-2-2-200-2-2-2-2220022000000000000000000020000000
χ2122222222-2-22-2222-2-22222-20000-2-20000002200-2-22200000000000000-200000000
χ2222222222-2-22-2222-2-22222-20000-2-2000000-2-20022-2-200000000000000200000000
χ2322222222-2-22-2222-2-2-2-2-2-2-2000022000000220022-2-200000000000000-200000000
χ2422222222-2-22-2222-2-2-2-2-2-2-2000022000000-2-200-2-22200000000000000200000000
χ25222-2-22-2-2222-2-22-2-2222-2-2-200002-20000000000000000000000002-200002-200000
χ26222-2-22-2-2222-2-22-2-2222-2-2-200002-2000000000000000000000000-220000-2200000
χ27222-2-22-2-2222-2-22-2-22-2-222-20000-220000000000000000000000002-20000-2200000
χ28222-2-22-2-2222-2-22-2-22-2-222-20000-22000000000000000000000000-2200002-200000
χ29222-2-22-2-2-2-222-22-22-222-2-220000-222i−2i002i−2i000000000000000000002i−2i000000000
χ30222-2-22-2-2-2-222-22-22-222-2-220000-22−2i2i00−2i2i00000000000000000000−2i2i000000000
χ31222-2-22-2-2-2-222-22-22-2-2-222200002-22i−2i002i−2i00000000000000000000−2i2i000000000
χ32222-2-22-2-2-2-222-22-22-2-2-222200002-2−2i2i00−2i2i000000000000000000002i−2i000000000
χ33222-2-22-2-2-2-2-222-22220000-20000002i−2i00−2i2i0000000022-2-200002i−2i0000000000000
χ34222-2-22-2-2-2-2-222-22220000-20000002i−2i00−2i2i00000000-2-2220000−2i2i0000000000000
χ35222-2-22-2-2-2-2-222-22220000-2000000−2i2i002i−2i0000000022-2-20000−2i2i0000000000000
χ36222-2-22-2-2-2-2-222-22220000-2000000−2i2i002i−2i00000000-2-22200002i−2i0000000000000
χ372-2-22-22-2200202-2-2002i−2i2i−2i022−2−2000000002-22−2002i−2ii2−i2i2−i2i2i2−i2−i20000000000002−20
χ382-2-22-22-2200202-2-2002i−2i2i−2i022−2−200000000-222−200−2i2ii2−i2i2−i2−i2−i2i2i2000000000000−220
χ392-2-22-22-2200202-2-2002i−2i2i−2i0−2−222000000002-2−22002i−2i−i2i2−i2i2−i2−i2i2i2000000000000−220
χ402-2-22-22-2200202-2-2002i−2i2i−2i0−2−22200000000-22−2200−2i2i−i2i2−i2i2i2i2−i2−i20000000000002−20
χ412-2-22-22-2200202-2-200−2i2i−2i2i022−2−2000000002-22−200−2i2i−i2i2−i2i2−i2−i2i2i20000000000002−20
χ422-2-22-22-2200202-2-200−2i2i−2i2i022−2−200000000-222−2002i−2i−i2i2−i2i2i2i2−i2−i2000000000000−220
χ432-2-22-22-2200202-2-200−2i2i−2i2i0−2−222000000002-2−2200−2i2ii2−i2i2−i2i2i2−i2−i2000000000000−220
χ442-2-22-22-2200202-2-200−2i2i−2i2i0−2−22200000000-22−22002i−2ii2−i2i2−i2−i2−i2i2i20000000000002−20
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-44-4-444-4-44-44-4-4000040000000000000000000000000000000000000000000
χ4744-4-44-4-44000000000000002i2−2i22i2−2i200000000000022−220000002i−2i2i−2i000000000000000
χ4844-4-44-4-44000000000000002i2−2i22i2−2i2000000000000−2222000000−2i2i−2i2i000000000000000
χ4944-4-44-4-4400000000000000−2i22i2−2i22i200000000000022−22000000−2i2i−2i2i000000000000000
χ5044-4-44-4-4400000000000000−2i22i2−2i22i2000000000000−22220000002i−2i2i−2i000000000000000
χ514-4444-4-4-44-404000-4000000000000004-4000000000000000000000000000000000
χ524-4444-4-4-44-404000-400000000000000-44000000000000000000000000000000000
χ534-4444-4-4-4-440-40004000000000000000000000000000000000000000000002i2−2i2000
χ544-4444-4-4-4-440-4000400000000000000000000000000000000000000000000−2i22i2000
χ554-44-4-4-4444-40-4000400000000000000000000000000000022−22−2222000000000000000
χ564-44-4-4-4444-40-40004000000000000000000000000000000−222222−22000000000000000
χ574-44-4-4-444-4404000-40000004i−4i−4i4i000000000000000000000000000000000000000
χ584-44-4-4-444-4404000-4000000−4i4i4i−4i000000000000000000000000000000000000000
χ594-4-44-44-4400-40-44400000002222−22−220000000000−2222000000000000000000000000000
χ604-4-44-44-4400-40-4440000000−22−222222000000000022−22000000000000000000000000000
χ614-4-4-4444-40040-4-44004i−4i−4i4i00000000000000000000000000000000000000000000
χ624-4-4-4444-40040-4-4400−4i4i4i−4i00000000000000000000000000000000000000000000
χ634-4-4-4444-400-4044-40000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ644-4-4-4444-400-4044-4000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ6588-88-8-88-8000000000000000000000000000000000000000000000000000000000

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