Finite Group Databasebeta

← Group #281291

Character table — Group #281291

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488882222444444448888888888888844444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111-1-111-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-1-1-111
χ3111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-111111-1-11-1-1-1-11111-1-1
χ51111111111111111111111-1-11111-1-1111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-111-111-1-11111-1-1
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
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-111-111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-1-1-11-1-1-111-1-111-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-111-1-1111-1
χ11111111111111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1111111111-1-1-111-1-1-1-111-11
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-11111-1-1-11
χ13111111111111111111-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-11
χ14111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111111-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1111-1-1-1-111-1-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-111111-1-1111-1
χ17222222222-222-2-2-22-2-2000000222200-2-2-2-20022-2-20000000000000000000000
χ18222222222-222-2-2-22-2-200000022-2-200-2-22200-2-2220000000000000000000000
χ19222222222-222-2-2-22-2-2000000-2-2220022-2-200-2-2220000000000000000000000
χ20222222222-222-2-2-22-2-2000000-2-2-2-20022220022-2-20000000000000000000000
χ2122222222-22-2-2222-2-2-22222220000220000-2-2000000000000-200-20000000000
χ2222222222-22-2-2222-2-2-22222-2-20000-2-20000-2-200000000000020020000000000
χ2322222222-22-2-2222-2-2-2-2-2-2-2220000-2-2000022000000000000-20020000000000
χ2422222222-22-2-2222-2-2-2-2-2-2-2-2-2000022000022000000000000200-20000000000
χ252-222-2-22-222-2-2-22-22-22000000002i−2i00002i−2i0000002i2i−2i−2i22-2-200000000000000
χ262-222-2-22-222-2-2-22-22-22000000002i−2i00002i−2i000000−2i−2i2i2i-2-22200000000000000
χ272-222-2-22-222-2-2-22-22-2200000000−2i2i0000−2i2i0000002i2i−2i−2i-2-22200000000000000
χ282-222-2-22-222-2-2-22-22-2200000000−2i2i0000−2i2i000000−2i−2i2i2i22-2-200000000000000
χ292-222-2-22-22-2-2-22-2222-222-2-200002i−2i0000−2i2i2-20000000000000000002i−2i000000
χ302-222-2-22-22-2-2-22-2222-222-2-20000−2i2i00002i−2i2-2000000000000000000−2i2i000000
χ312-222-2-22-22-2-2-22-2222-2-2-22200002i−2i0000−2i2i-22000000000000000000−2i2i000000
χ322-222-2-22-22-2-2-22-2222-2-2-2220000−2i2i00002i−2i-220000000000000000002i−2i000000
χ332-222-2-22-2-2-2222-22-2-2222-2-2000000000000-2200000000000002i−2i02i−2i00000000
χ342-222-2-22-2-2-2222-22-2-2222-2-2000000000000-220000000000000−2i2i0−2i2i00000000
χ352-222-2-22-2-2-2222-22-2-22-2-2220000000000002-200000000000002i−2i0−2i2i00000000
χ362-222-2-22-2-2-2222-22-2-22-2-2220000000000002-20000000000000−2i2i02i−2i00000000
χ372-2-2-2222-20-20022-20002i−2i2i−2i2-200002i−2i000000i2−i2i2−i200002−22−200000000i2−i22−200
χ382-2-2-2222-20-20022-20002i−2i2i−2i2-200002i−2i000000−i2i2−i2i20000−22−2200000000−i2i2−2200
χ392-2-2-2222-20-20022-20002i−2i2i−2i-220000−2i2i000000i2−i2i2−i200002−22−200000000−i2i2−2200
χ402-2-2-2222-20-20022-20002i−2i2i−2i-220000−2i2i000000−i2i2−i2i20000−22−2200000000i2−i22−200
χ412-2-2-2222-20-20022-2000−2i2i−2i2i2-20000−2i2i000000i2−i2i2−i20000−22−2200000000i2−i2−2200
χ422-2-2-2222-20-20022-2000−2i2i−2i2i2-20000−2i2i000000−i2i2−i2i200002−22−200000000−i2i22−200
χ432-2-2-2222-20-20022-2000−2i2i−2i2i-2200002i−2i000000i2−i2i2−i20000−22−2200000000−i2i22−200
χ442-2-2-2222-20-20022-2000−2i2i−2i2i-2200002i−2i000000−i2i2−i2i200002−22−200000000i2−i2−2200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-44-4-4-4404-4000-4000000004-4000000000000000000000000000000000000
χ47444-44-4-4-4404-4000-400000000-44000000000000000000000000000000000000
χ48444-44-4-4-4-40-4400040000000000000000000000002i2−2i22i2−2i2000000000000000000
χ49444-44-4-4-4-40-440004000000000000000000000000−2i22i2−2i22i2000000000000000000
χ5044-4-4-4-44404004-4-40004i−4i−4i4i0000000000000000000000000000000000000000
χ5144-4-4-4-44404004-4-4000−4i4i4i−4i0000000000000000000000000000000000000000
χ5244-4-4-4-4440-400-4440000000000000000000000000000022−22−222200000000000000
χ5344-4-4-4-4440-400-44400000000000000000000000000000−222222−2200000000000000
χ544-444-4-44-4-4444-44-4-44-400000000000000000000000000000000000000000000
χ554-44-4-44-4440-44000-4000000000000004i−4i000000000000000000000000000000
χ564-44-4-44-4440-44000-400000000000000−4i4i000000000000000000000000000000
χ574-44-4-44-44-404-4000400000000000000000000000022−22−2222000000000000000000
χ584-44-4-44-44-404-40004000000000000000000000000−222222−22000000000000000000
χ594-4-4-4444-40400-4-440000000000000000000002i2−2i2−2i22i20000000000000000000000
χ604-4-4-4444-40400-4-44000000000000000000000−2i22i22i2−2i20000000000000000000000
χ6188-88-88-8-8000000000000000000000000000000000000000000000000000000
χ628-8-888-8-88000000000000000000000000000000000000000000000000000000

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