Finite Group Databasebeta

← Group #287883

Character table — Group #287883

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444488888888888888888888888822224444888824
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ9111111111-1-1-1-1111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-11-111-1-1-11
χ10111111111-1-1-1-1111111111-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11111-11-1-1-11-1-1111-1
χ11111111111-1-1-1-1111111111-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11-1111-1-1-1111-1
χ12111111111-1-1-1-1111111111-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1111-1111-1-1-11
χ13111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1111-1111-1-11-1
χ14111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-11-1111-1-1-111-11
χ15111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-111-11-1-1-11-1-111-11
χ16111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111111-1-1-11-111-1-11-1
χ172222222222222-222-2-22-2-2-222-2-2-2000000000000000000000000002-200-22000000
χ182222222222222-222-2-22-2-2-222-2-2-200000000000000000000000000-22002-2000000
χ19222222222-2-2-2-2-222-2-22-2-2-2-2-2222000000000000000000000000002200-2-2000000
χ20222222222-2-2-2-2-222-2-22-2-2-2-2-222200000000000000000000000000-2-20022000000
χ2122222222-222222-2-222-22-2-2-2-222-200000000222200000000-2-2-2-200000000000000
χ2222222222-222222-2-222-22-2-2-2-222-200000000-2-2-2-200000000222200000000000000
χ2322222222-22222-2-2-2-2-2-2-222-2-2-2-222i2i−2i−2i000000002i2i−2i−2i0000000000000000000000
χ2422222222-22222-2-2-2-2-2-2-222-2-2-2-22−2i−2i2i2i00000000−2i−2i2i2i0000000000000000000000
χ2522222222-2-2-2-2-22-2-222-22-2-222-2-220000000022-2-200000000-2-22200000000000000
χ2622222222-2-2-2-2-22-2-222-22-2-222-2-2200000000-2-2220000000022-2-200000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-22i2i−2i−2i00000000−2i−2i2i2i0000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2−2i−2i2i2i000000002i2i−2i−2i0000000000000000000000
χ29222-2-2-2-222000022-22-2-2-22-200000000022-2-200002i−2i2i−2i0000000000002i−2i00000000
χ30222-2-2-2-222000022-22-2-2-22-200000000022-2-20000−2i2i−2i2i000000000000−2i2i00000000
χ31222-2-2-2-222000022-22-2-2-22-2000000000-2-22200002i−2i2i−2i000000000000−2i2i00000000
χ32222-2-2-2-222000022-22-2-2-22-2000000000-2-2220000−2i2i−2i2i0000000000002i−2i00000000
χ33222-2-2-2-22-20000-2-22-22222-2000000000000000002-2-2222-2-200002-2000000000000
χ34222-2-2-2-22-20000-2-22-22222-2000000000000000002-2-22-2-2220000-22000000000000
χ35222-2-2-2-22-20000-2-22-22222-200000000000000000-222-222-2-20000-22000000000000
χ36222-2-2-2-22-20000-2-22-22222-200000000000000000-222-2-2-22200002-2000000000000
χ372-2-22-2-222022-2-2-2002-20200002-2000002−22−2000000002−22−22-22-2000000002−22−200
χ382-2-22-2-222022-2-2-2002-20200002-2000002−22−2000000002−22−2-22-2200000000−22−2200
χ392-2-22-2-222022-2-2-2002-20200002-200000−22−2200000000−22−222-22-200000000−22−2200
χ402-2-22-2-222022-2-2-2002-20200002-200000−22−2200000000−22−22-22-22000000002−22−200
χ412-2-22-2-2220-2-222-2002-2020000-22000002−22−200000000−22−222-2-22000000002−2−2200
χ422-2-22-2-2220-2-222-2002-2020000-22000002−22−200000000−22−22-222-200000000−222−200
χ432-2-22-2-2220-2-222-2002-2020000-2200000−22−22000000002−22−22-2-2200000000−222−200
χ442-2-22-2-2220-2-222-2002-2020000-2200000−22−22000000002−22−2-222-2000000002−2−2200
χ45444-4-4-4-4440000-44-4-44-44-440000000000000000000000000000000000000000000
χ46444-4-4-4-44-400004-444-44-4-440000000000000000000000000000000000000000000
χ4744-444-4-4-404i−4i4i−4i00000000000000000000002i2−2i222−2200000000000000000000000000
χ4844-444-4-4-404i−4i4i−4i0000000000000000000000−2i22i2−222200000000000000000000000000
χ4944-444-4-4-40−4i4i−4i4i00000000000000000000002i2−2i2−222200000000000000000000000000
χ5044-444-4-4-40−4i4i−4i4i0000000000000000000000−2i22i222−2200000000000000000000000000
χ514-444-44-4-444i−4i−4i4i0-4-40040004i−4i00000000000000000000000000000000000000000
χ524-444-44-4-44−4i4i4i−4i0-4-4004000−4i4i00000000000000000000000000000000000000000
χ534-444-44-4-4-44i−4i−4i4i04400-4000−4i4i00000000000000000000000000000000000000000
χ544-444-44-4-4-4−4i4i4i−4i04400-40004i−4i00000000000000000000000000000000000000000
χ554-44-44-44-4400000-4400-4000000002i2−2i22i2−2i20000000000000000000000000000000000
χ564-44-44-44-4400000-4400-400000000−2i22i2−2i22i20000000000000000000000000000000000
χ574-44-44-44-4-4000004-40040000000022−22−22220000000000000000000000000000000000
χ584-44-44-44-4-4000004-400400000000−222222−220000000000000000000000000000000000
χ594-4-44-4-444044-4-4400-440-40000-44000000000000000000000000000000000000000
χ604-4-44-4-4440-4-444400-440-400004-4000000000000000000000000000000000000000
χ614-4-4-444-4400000400-4-4040000000000000000000000022−22−2222000000000000000000
χ624-4-4-444-4400000400-4-40400000000000000000000000−222222−22000000000000000000
χ634-4-4-444-4400000-400440-40000000000022−22−2222000000000000000000000000000000
χ644-4-4-444-4400000-400440-400000000000−222222−22000000000000000000000000000000
χ6588-8-8-888-8000000000000000000000000000000000000000000000000000000000

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