Finite Group Databasebeta

← Group #278721

Character table — Group #278721

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444444888888888888888888888881616161616161616161616163232
order12222222444444444444444488882244488888888888888888844444488888824
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-11-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1
χ41111111111111111111111111111-1-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ5111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111
χ7111111111111111111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111
χ8111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1
χ9111111111111111111-1-1-1-1-1-1111111-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-11
χ10111111111111111111-1-1-1-1-1-1111111-111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11-1
χ11111111111111111111-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111-1
χ12111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-111-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-11111-1-1-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1111-1
χ17222222222-2-2222-2-2-2-222-2-222000022-2-2-20000000000000000002-2000000000000
χ18222222222-2-2222-2-2-2-222-2-2220000-2-2-222000000000000000000-22000000000000
χ19222222222-2-2222-2-2-2-2-2-222-2-20000222-2-2000000000000000000-22000000000000
χ20222222222-2-2222-2-2-2-2-2-222-2-20000-2-22220000000000000000002-2000000000000
χ2122222222-222-2-2-222-2-222-2-2-2-22222002000000-2-222-2-20000000000000000000000
χ2222222222-222-2-2-222-2-222-2-2-2-2-2-2-2-200200000022-2-2220000000000000000000000
χ2322222222-222-2-2-222-2-2-2-22222222200-2000000-2-2-2-2220000000000000000000000
χ2422222222-222-2-2-222-2-2-2-22222-2-2-2-200-20000002222-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2222222-2-2000000-20000000000002i2i−2i−2i0000000000002i−2i0000
χ2622222222-2-2-2-2-2-2-2-2222222-2-2000000-2000000000000−2i−2i2i2i000000000000−2i2i0000
χ2722222222-2-2-2-2-2-2-2-222-2-2-2-22200000020000000000002i2i−2i−2i000000000000−2i2i0000
χ2822222222-2-2-2-2-2-2-2-222-2-2-2-2220000002000000000000−2i−2i2i2i0000000000002i−2i0000
χ29222-2-2-22-202-20002-200002i−2i2i−2i22-2-200000i2i2−i2−i200002i−2i000022−2−20000002−200i2−i200
χ30222-2-2-22-202-20002-200002i−2i2i−2i22-2-200000−i2−i2i2i200002i−2i0000−2−222000000−2200−i2i200
χ31222-2-2-22-202-20002-200002i−2i2i−2i-2-22200000i2i2−i2−i20000−2i2i000022−2−2000000−2200−i2i200
χ32222-2-2-22-202-20002-200002i−2i2i−2i-2-22200000−i2−i2i2i20000−2i2i0000−2−2220000002−200i2−i200
χ33222-2-2-22-202-20002-20000−2i2i−2i2i22-2-200000i2i2−i2−i20000−2i2i0000−2−222000000−2200i2−i200
χ34222-2-2-22-202-20002-20000−2i2i−2i2i22-2-200000−i2−i2i2i20000−2i2i000022−2−20000002−200−i2i200
χ35222-2-2-22-202-20002-20000−2i2i−2i2i-2-22200000i2i2−i2−i200002i−2i0000−2−2220000002−200−i2i200
χ36222-2-2-22-202-20002-20000−2i2i−2i2i-2-22200000−i2−i2i2i200002i−2i000022−2−2000000−2200i2−i200
χ372-2-22-222-2-2222-22-2-22-200000000002-202-22i−2i2i−2i00000000000000002i−2i0000000000
χ382-2-22-222-2-2222-22-2-22-200000000002-202-2−2i2i−2i2i0000000000000000−2i2i0000000000
χ392-2-22-222-2-2222-22-2-22-20000000000-220-222i−2i2i−2i0000000000000000−2i2i0000000000
χ402-2-22-222-2-2222-22-2-22-20000000000-220-22−2i2i−2i2i00000000000000002i−2i0000000000
χ412-2-22-222-2-2-2-22-2222-2200000000002-20-22000000000000002-22-200002-200000000
χ422-2-22-222-2-2-2-22-2222-2200000000002-20-2200000000000000-22-220000-2200000000
χ432-2-22-222-2-2-2-22-2222-220000000000-2202-2000000000000002-22-20000-2200000000
χ442-2-22-222-2-2-2-22-2222-220000000000-2202-200000000000000-22-2200002-200000000
χ45444-4-4-44-40-44000-4400004i−4i−4i4i00000000000000000000000000000000000000000
χ46444-4-4-44-40-44000-440000−4i4i4i−4i00000000000000000000000000000000000000000
χ4744-44-4-4-4400000000004i−4i00002i2−2i22i2−2i20000000000022−22000000000000000000000000
χ4844-44-4-4-4400000000004i−4i0000−2i22i2−2i22i200000000000−2222000000000000000000000000
χ4944-44-4-4-440000000000−4i4i00002i2−2i22i2−2i200000000000−2222000000000000000000000000
χ5044-44-4-4-440000000000−4i4i0000−2i22i2−2i22i20000000000022−22000000000000000000000000
χ5144-4-444-4-4400-4-4400000000002i2−2i2−2i22i20000000002i2−2i200000000000000000000000000
χ5244-4-444-4-4400-4-440000000000−2i22i22i2−2i2000000000−2i22i200000000000000000000000000
χ5344-4-444-4-4-40044-400000000002i2−2i2−2i22i2000000000−2i22i200000000000000000000000000
χ5444-4-444-4-4-40044-40000000000−2i22i22i2−2i20000000002i2−2i200000000000000000000000000
χ554-44-4-44-444004-4-4000000000000000000000000000002i2−2i22i2−2i2000000000000000000
χ564-44-4-44-444004-4-400000000000000000000000000000−2i22i2−2i22i2000000000000000000
χ574-44-4-44-44-400-4440000000000000000000000000000022−22−2222000000000000000000
χ584-44-4-44-44-400-44400000000000000000000000000000−222222−22000000000000000000
χ594-4-44-444-4444-44-4-4-4-4400000000000000000000000000000000000000000000000
χ604-4-44-444-44-4-4-44-4444-400000000000000000000000000000000000000000000000
χ614-4-4-44-44404-4000-440000000000000000022−22−22220000000000000000000000000000
χ624-4-4-44-44404-4000-4400000000000000000−222222−220000000000000000000000000000
χ634-4-4-44-4440-440004-4000000000000000000000000000000022−22−222200000000000000
χ644-4-4-44-4440-440004-40000000000000000000000000000000−222222−2200000000000000
χ658-8888-8-8-8000000000000000000000000000000000000000000000000000000000

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