Finite Group Databasebeta

← Group #72317071

Character table — Group #72317071

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1111222222444488888888888888888888161616161616161616161616161616163232323232323232323264646464
order1222222222222222224444444444444444222444444444444444444444444488
χ11111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-11111-1-111111-1-1-1-111-1-11-1-111111111-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-11111-1-111111-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-11-111111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-11-11-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-1-111-1-11111-11111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1111111-1-1
χ9111111111111-1-11-1-1-11111111111111111-1-1-111-1-11111-1-1-1-1-1-1-1ii−i−iii−i−ii−ii−i
χ10111111111111-1-11-1-1-11111111111111111-1-1-111-1-11111-1-1-1-1-1-1-1−i−iii−i−iii−ii−ii
χ11111111111111-1-11-1-1-11111-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-1-1-111-111ii−i−iii−i−i−ii−ii
χ12111111111111-1-11-1-1-11111-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-1-1-111-111−i−iii−i−iiii−ii−i
χ13111111111111-1-11-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-11-1ii−i−i−i−iiii−i−ii
χ14111111111111-1-11-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-11-1−i−iiiii−i−i−iii−i
χ15111111111111-1-11-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-11111-1-1-1-11ii−i−i−i−iii−iii−i
χ16111111111111-1-11-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-11111-1-1-1-11−i−iiiii−i−ii−i−ii
χ17222222222222222222222200000000-2-2-2-200-2-2-2220000-2-200-200000000000000
χ18222222222222222222-2-2-2-200000000222200-2-2-2-2-200002200-200000000000000
χ19222222222222-2-22-2-2-2222200000000-2-2-2-2002-2-2-2-200002200200000000000000
χ20222222222222-2-22-2-2-2-2-2-2-2000000002222002-2-2220000-2-200200000000000000
χ212222222222-2-222-22-2-2000000002222000000-2-220000-2-200222-20000000000000
χ222222222222-2-222-22-2-200000000-2-2-2-2000000-2-2200002200-2-2220000000000000
χ232222222222-2-222-22-2-200002222000000002222-200-2-2000000-20-2000000000000
χ242222222222-2-222-22-2-20000-2-2-2-200000000-2-222-20022000000-202000000000000
χ252222222222-2-2-2-2-2-2220000000022220000002-220000-2-200-2-2-220000000000000
χ262222222222-2-2-2-2-2-22200000000-2-2-2-20000002-220000220022-2-20000000000000
χ272222222222-2-2-2-2-2-2220000222200000000-2-2-22-200-2-2000000202000000000000
χ282222222222-2-2-2-2-2-2220000-2-2-2-20000000022-22-2002200000020-2000000000000
χ29444444-4-4-4-40000004-4000000000000000000000000000000000000002i−2i2i−2i0000
χ30444444-4-4-4-40000004-400000000000000000000000000000000000000−2i2i−2i2i0000
χ31444444-4-4-4-4000000-44000000000000000000000000000000000000002-2-220000
χ32444444-4-4-4-4000000-4400000000000000000000000000000000000000-222-20000
χ334444-4-444-4-400440-40000000000000000000000000000000000002-22-200000000
χ344444-4-444-4-400440-4000000000000000000000000000000000000-22-2200000000
χ354444-4-444-4-400-4-4040000000000000000000000000000000000002i−2i−2i2i00000000
χ364444-4-444-4-400-4-404000000000000000000000000000000000000−2i2i2i−2i00000000
χ374444-4-4-4-4444400-400000000000000044-4-4000000000000000000000000000000
χ384444-4-4-4-4444400-4000000000000000-4-444000000000000000000000000000000
χ394444-4-4-4-444-4-400400044-4-4000000000000000000000000000000000000000000
χ404444-4-4-4-444-4-4004000-4-444000000000000000000000000000000000000000000
χ4144-4-4004-400004-400002i−2i2i−2i22-2-22i2i−2i−2i00002-20002i−2i0000002i−2i000000000000000
χ4244-4-4004-400004-400002i−2i2i−2i-2-222−2i−2i2i2i0000-220002i−2i000000−2i2i000000000000000
χ4344-4-4004-400004-40000−2i2i−2i2i22-2-2−2i−2i2i2i00002-2000−2i2i000000−2i2i000000000000000
χ4444-4-4004-400004-40000−2i2i−2i2i-2-2222i2i−2i−2i0000-22000−2i2i0000002i−2i000000000000000
χ4544-4-4004-40000-4400002i−2i2i−2i22-2-22i2i−2i−2i0000-22000−2i2i000000−2i2i000000000000000
χ4644-4-4004-40000-4400002i−2i2i−2i-2-222−2i−2i2i2i00002-2000−2i2i0000002i−2i000000000000000
χ4744-4-4004-40000-440000−2i2i−2i2i22-2-2−2i−2i2i2i0000-220002i−2i0000002i−2i000000000000000
χ4844-4-4004-40000-440000−2i2i−2i2i-2-2222i2i−2i−2i00002-20002i−2i000000−2i2i000000000000000
χ494-44-400004-44-400000000002-22-22i−2i2i−2i004i−4i00000002-22i−2i0000000000000000000
χ504-44-400004-44-400000000002-22-2−2i2i−2i2i00−4i4i00000002-2−2i2i0000000000000000000
χ514-44-400004-44-40000000000-22-222i−2i2i−2i00−4i4i0000000-222i−2i0000000000000000000
χ524-44-400004-44-40000000000-22-22−2i2i−2i2i004i−4i0000000-22−2i2i0000000000000000000
χ534-44-400004-4-4400000000002-22-22i−2i2i−2i4i−4i000000000-22−2i2i0000000000000000000
χ544-44-400004-4-4400000000002-22-2−2i2i−2i2i−4i4i000000000-222i−2i0000000000000000000
χ554-44-400004-4-440000000000-22-222i−2i2i−2i−4i4i0000000002-2−2i2i0000000000000000000
χ564-44-400004-4-440000000000-22-22−2i2i−2i2i4i−4i0000000002-22i−2i0000000000000000000
χ5788-8-800-8800000000004i−4i−4i4i000000000000000000000000000000000000000000
χ5888-8-800-880000000000−4i4i4i−4i000000000000000000000000000000000000000000
χ598-88-80000-88000000000000000000000000000000000004-400000000000000000
χ608-88-80000-8800000000000000000000000000000000000-4400000000000000000
χ618-8-888-8000000000000000000004-4-440000000000000000000000000000000000
χ628-8-888-800000000000000000000-444-40000000000000000000000000000000000
χ638-8-88-8800000000000000004-4-4400000000000000000000000000000000000000
χ648-8-88-880000000000000000-444-400000000000000000000000000000000000000

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