Finite Group Databasebeta

← Group #101014

Character table — Group #101014

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444422444488888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ172222222222222222-2-22222222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-2222222-2-2-2-2-2-222-2-2-2-22200000000000000000000000000000000
χ20222222222222-2-2-2-222-2-2-2-22222-2-22222-2-2-2-200000000000000000000000000000000
χ2122222222-2-2-2-222222-200000000-2-22-2002-2000000000022-2-222-2-20000000000000000
χ2222222222-2-2-2-222222-200000000-2-22-2002-20000000000-2-222-2-2220000000000000000
χ2322222222-2-2-2-22222-2200000000-2-2-2200-220022-2-222-2-2000000000000000000000000
χ2422222222-2-2-2-22222-2200000000-2-2-2200-2200-2-222-2-222000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22-200000000222-200-22002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-22-200000000222-200-2200−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-220000000022-22002-200000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-220000000022-22002-20000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ292222-2-2-2-222-2-2000022000022-2-200-2-22-200002−22−22−22−22−22−22−22−20000000000000000
χ302222-2-2-2-222-2-2000022000022-2-200-2-22-20000−22−22−22−22−22−22−22−220000000000000000
χ312222-2-2-2-222-2-20000220000-2-22200-2-2-2200002−22−22−22−2−22−22−22−220000000000000000
χ322222-2-2-2-222-2-20000220000-2-22200-2-2-220000−22−22−22−222−22−22−22−20000000000000000
χ332222-2-2-2-222-2-20000-2-2000022-2-20022-220000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ342222-2-2-2-222-2-20000-2-2000022-2-20022-220000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ352222-2-2-2-222-2-20000-2-20000-2-22200222-20000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ362222-2-2-2-222-2-20000-2-20000-2-22200222-20000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ372222-2-2-2-2-2-22200002-22i2i−2i−2i000000-2200002i−2ii2−i2−i2i2−i2i2i2−i22−2−222−2−220000000000000000
χ382222-2-2-2-2-2-22200002-22i2i−2i−2i000000-2200002i−2i−i2i2i2−i2i2−i2−i2i2−222−2−222−20000000000000000
χ392222-2-2-2-2-2-22200002-2−2i−2i2i2i000000-220000−2i2ii2−i2−i2i2−i2i2i2−i2−222−2−222−20000000000000000
χ402222-2-2-2-2-2-22200002-2−2i−2i2i2i000000-220000−2i2i−i2i2i2−i2i2−i2−i2i22−2−222−2−220000000000000000
χ412222-2-2-2-2-2-2220000-222i2i−2i−2i0000002-20000−2i2i2−2−222−2−22−i2i2i2−i2i2−i2−i2i20000000000000000
χ422222-2-2-2-2-2-2220000-222i2i−2i−2i0000002-20000−2i2i−222−2−222−2i2−i2−i2i2−i2i2i2−i20000000000000000
χ432222-2-2-2-2-2-2220000-22−2i−2i2i2i0000002-200002i−2i2−2−222−2−22i2−i2−i2i2−i2i2i2−i20000000000000000
χ442222-2-2-2-2-2-2220000-22−2i−2i2i2i0000002-200002i−2i−222−2−222−2−i2i2i2−i2i2−i2−i2i20000000000000000
χ4522-2-2-2-2222-22-222-2-2002i−2i2i−2i2i−2i2i−2i2-2000000000000000000000000000000002−22−2i2−i2i2−i2
χ4622-2-2-2-2222-22-222-2-2002i−2i2i−2i2i−2i2i−2i2-200000000000000000000000000000000−22−22−i2i2−i2i2
χ4722-2-2-2-2222-22-222-2-200−2i2i−2i2i−2i2i−2i2i2-2000000000000000000000000000000002−22−2−i2i2−i2i2
χ4822-2-2-2-2222-22-222-2-200−2i2i−2i2i−2i2i−2i2i2-200000000000000000000000000000000−22−22i2−i2i2−i2
χ4922-2-2-2-2222-22-2-2-222002i−2i2i−2i−2i2i−2i2i-2200000000000000000000000000000000i2−i2−i2i2−222−2
χ5022-2-2-2-2222-22-2-2-222002i−2i2i−2i−2i2i−2i2i-2200000000000000000000000000000000−i2i2i2−i22−2−22
χ5122-2-2-2-2222-22-2-2-22200−2i2i−2i2i2i−2i2i−2i-2200000000000000000000000000000000i2−i2−i2i22−2−22
χ5222-2-2-2-2222-22-2-2-22200−2i2i−2i2i2i−2i2i−2i-2200000000000000000000000000000000−i2i2i2−i2−222−2
χ5344-4-444-4-44-4-4400000000004i−4i−4i4i000000000000000000000000000000000000000000
χ5444-4-444-4-44-4-440000000000−4i4i4i−4i000000000000000000000000000000000000000000
χ5544-4-444-4-4-444-40000004-4-440000000000000000000000000000000000000000000000
χ5644-4-444-4-4-444-4000000-444-40000000000000000000000000000000000000000000000
χ5744-4-4-4-444-44-4444-4-40000000000-440000000000000000000000000000000000000000
χ5844-4-4-4-444-44-44-4-44400000000004-40000000000000000000000000000000000000000
χ594-44-44-44-400004-44-40000000000000000000000000000000000002i−2i2i−2i000000000000
χ604-44-44-44-400004-44-4000000000000000000000000000000000000−2i2i−2i2i000000000000
χ614-44-44-44-40000-44-440000000000000000000000000000000000002i−2i−2i2i000000000000
χ624-44-44-44-40000-44-44000000000000000000000000000000000000−2i2i2i−2i000000000000
χ634-4-44-444-400004-4-4400000000000000000000000000000000000000002i−2i2i−2i00000000
χ644-4-44-444-400004-4-440000000000000000000000000000000000000000−2i2i−2i2i00000000
χ654-4-44-444-40000-444-400000000000000000000000000000000000000002i−2i−2i2i00000000
χ664-4-44-444-40000-444-40000000000000000000000000000000000000000−2i2i2i−2i00000000
χ678-88-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-8-888-8-88000000000000000000000000000000000000000000000000000000000000

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