Finite Group Databasebeta

← Group #289485

Character table — Group #289485

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444444888888888888888888888881616161616161616161616163232
order12222222444444444444444488882244488888888888888888822444488888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-11-1-1111-1-1-1-1-1-1
χ31111111111111111111111111111-1-11-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111-1-11-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-111
χ5111111111111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11111-1-11-1-11-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1
χ7111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-11111111111-111-111-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111
χ91111111111111111-1-1-1-1-1-111111111-11111-1-11111-1-11111-1-1-1-1-1-1-111-1-1-1-1-1111-1
χ101111111111111111-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-11
χ111111111111111111-1-1-1-1-1-1111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1111-1-111-11
χ121111111111111111-1-1-1-1-1-1111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-11-1
χ131111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11-1
χ141111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-111-1-1-1-111-1-1-1-11111-1-1-111-111-1-111-11
χ151111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-1-1-11
χ161111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111111-1-11-1-1-1-1111-1
χ17222222222-222-2-22-22222-2-2-2-2000022-2-2-200000000000000000000200-200000000
χ18222222222-222-2-22-22222-2-2-2-20000-2-2-22200000000000000000000-200200000000
χ19222222222-222-2-22-2-2-2-2-222-2-20000222-2-200000000000000000000-200200000000
χ20222222222-222-2-22-2-2-2-2-222-2-20000-2-222200000000000000000000200-200000000
χ2122222222-22-2-222-2222-2-222-2-2222200-200-2-2220000-2-20000000000000000000000
χ2222222222-22-2-222-2222-2-222-2-2-2-2-2-200-20022-2-20000220000000000000000000000
χ2322222222-22-2-222-22-2-222-2-2-2-2222200200-2-2-2-20000220000000000000000000000
χ2422222222-22-2-222-22-2-222-2-2-2-2-2-2-2-20020022220000-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-22200000020000000000002i2i−2i−2i00000000002i−2i000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-2220000002000000000000−2i−2i2i2i0000000000−2i2i000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222222000000-20000000000002i2i−2i−2i0000000000−2i2i000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222222000000-2000000000000−2i−2i2i2i00000000002i−2i000000
χ29222-2-2-22-20200-2-2022i−2i002i−2i0022-2-200000002i−2ii2i2−i2−i200000022−2−2000000002−2i2−i200
χ30222-2-2-22-20200-2-2022i−2i002i−2i0022-2-200000002i−2i−i2−i2i2i2000000−2−22200000000−22−i2i200
χ31222-2-2-22-20200-2-2022i−2i002i−2i00-2-2220000000−2i2ii2i2−i2−i200000022−2−200000000−22−i2i200
χ32222-2-2-22-20200-2-2022i−2i002i−2i00-2-2220000000−2i2i−i2−i2i2i2000000−2−222000000002−2i2−i200
χ33222-2-2-22-20200-2-202−2i2i00−2i2i0022-2-20000000−2i2ii2i2−i2−i2000000−2−22200000000−22i2−i200
χ34222-2-2-22-20200-2-202−2i2i00−2i2i0022-2-20000000−2i2i−i2−i2i2i200000022−2−2000000002−2−i2i200
χ35222-2-2-22-20200-2-202−2i2i00−2i2i00-2-22200000002i−2ii2i2−i2−i2000000−2−222000000002−2−i2i200
χ36222-2-2-22-20200-2-202−2i2i00−2i2i00-2-22200000002i−2i−i2−i2i2i200000022−2−200000000−22i2−i200
χ372-2-2-22-222222-22-2-2-20000002-200000000000002-22-2002i−2i2i−2i00000002i−2i000000000
χ382-2-2-22-222222-22-2-2-20000002-200000000000002-22-200−2i2i−2i2i0000000−2i2i000000000
χ392-2-2-22-222222-22-2-2-20000002-20000000000000-22-22002i−2i2i−2i0000000−2i2i000000000
χ402-2-2-22-222222-22-2-2-20000002-20000000000000-22-2200−2i2i−2i2i00000002i−2i000000000
χ412-2-2-22-222-2-2-22-22220000002-200000000000000000002-2-222-22-22-2000000000000
χ422-2-2-22-222-2-2-22-22220000002-200000000000000000002-2-22-22-22-22000000000000
χ432-2-2-22-222-2-2-22-22220000002-20000000000000000000-222-22-22-2-22000000000000
χ442-2-2-22-222-2-2-22-22220000002-20000000000000000000-222-2-22-222-2000000000000
χ45444-4-4-44-40-400440-44i−4i00−4i4i0000000000000000000000000000000000000000000
χ46444-4-4-44-40-400440-4−4i4i004i−4i0000000000000000000000000000000000000000000
χ4744-444-4-4-440-4400-400000000000004-400000000000000000000000000000000000
χ4844-444-4-4-440-4400-40000000000000-4400000000000000000000000000000000000
χ4944-444-4-4-4-404-400400000000000000004i−4i00000000000000000000000000000000
χ5044-444-4-4-4-404-40040000000000000000−4i4i00000000000000000000000000000000
χ514-444-4-4-4400000000004i−4i00002i2−2i22i2−2i2000000000000022−220000000000000000000000
χ524-444-4-4-4400000000004i−4i0000−2i22i2−2i22i20000000000000−22220000000000000000000000
χ534-444-4-4-440000000000−4i4i00002i2−2i22i2−2i20000000000000−22220000000000000000000000
χ544-444-4-4-440000000000−4i4i0000−2i22i2−2i22i2000000000000022−220000000000000000000000
χ554-44-444-4-440-4-40040000000002i2−2i2−2i22i2000002i2−2i2000000000000000000000000000000
χ564-44-444-4-440-4-4004000000000−2i22i22i2−2i200000−2i22i2000000000000000000000000000000
χ574-44-444-4-4-404400-40000000002i2−2i2−2i22i200000−2i22i2000000000000000000000000000000
χ584-44-444-4-4-404400-4000000000−2i22i22i2−2i2000002i2−2i2000000000000000000000000000000
χ594-4-44-444-40400-440-40000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ604-4-44-444-40400-440-4000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ614-4-44-444-40-4004-404000000000000000000000000000000022−22−222200000000000000
χ624-4-44-444-40-4004-4040000000000000000000000000000000−222222−2200000000000000
χ634-4-4-44-4444-44-4-44-44000000-4400000000000000000000000000000000000000000
χ644-4-4-44-444-44-444-44-4000000-4400000000000000000000000000000000000000000
χ6588-8-8-88-88000000000000000000000000000000000000000000000000000000000

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