Finite Group Databasebeta

← Group #149774

Character table — Group #149774

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size1111224444444444888888888888881616161616163232323232323232
order12222222444444444444448888888822444488888888
χ111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-111111111-1-1-1-1-1-1ii−i−iii−i−i
χ6111111111111111111-1-1-1-111111111-1-1-1-1-1-1−i−iii−i−iii
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i
χ9111111-1-11-1-1-1-1-1-111111111111-1-1-1-111-1-1-1-11-11-11-11-1
χ10111111-1-11-1-1-1-1-1-111111111111-1-1-1-111-1-1-1-1-11-11-11-11
χ11111111-1-11-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1111-11-1-11-11
χ12111111-1-11-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-111-11-111-11-1
χ13111111-1-11-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-11111i−i−iii−i−ii
χ14111111-1-11-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-11111−iii−i−iii−i
χ15111111-1-11-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1i−i−ii−iii−i
χ16111111-1-11-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1−iii−ii−i−ii
χ1722222222222-2-2-2-22-2-222-2-200000000002-20000000000
χ1822222222222-2-2-2-22-2-2-2-2220000000000-220000000000
χ19222222-2-22-2-222222-2-222-2-20000000000-220000000000
χ20222222-2-22-2-222222-2-2-2-22200000000002-20000000000
χ212-2-22-22002000000-22-22i−2i2i−2i00002i2i−2i−2i00002-200000000
χ222-2-22-22002000000-22-22i−2i2i−2i0000−2i−2i2i2i0000-2200000000
χ232-2-22-22002000000-22-2−2i2i−2i2i00002i2i−2i−2i0000-2200000000
χ242-2-22-22002000000-22-2−2i2i−2i2i0000−2i−2i2i2i00002-200000000
χ252-2-22-22002000000-2-222i−2i−2i2i2i2i−2i−2i00002-2000000000000
χ262-2-22-22002000000-2-222i−2i−2i2i−2i−2i2i2i0000-22000000000000
χ272-2-22-22002000000-2-22−2i2i2i−2i2i2i−2i−2i0000-22000000000000
χ282-2-22-22002000000-2-22−2i2i2i−2i−2i−2i2i2i00002-2000000000000
χ2944444444-4-4-40000-40000000000000000000000000000
χ30444444-4-4-4440000-40000000000000000000000000000
χ314444-4-44-4000000000000002-22-22-22-200000000000000
χ324444-4-44-400000000000000-22-22-22-2200000000000000
χ334444-4-4-44000000000000002-22-2-22-2200000000000000
χ344444-4-4-4400000000000000-22-222-22-200000000000000
χ354-4-444-40004-4000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ364-4-444-40004-400000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ374-4-444-4000-44000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ384-4-444-4000-4400000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ394-4-44-4400-40044-4-440000000000000000000000000000
χ404-4-44-4400-400-4-44440000000000000000000000000000
χ4188-8-800000004i−4i4i−4i00000000000000000000000000000
χ4288-8-80000000−4i4i−4i4i00000000000000000000000000000
χ438-88-800000004i−4i−4i4i00000000000000000000000000000
χ448-88-80000000−4i4i4i−4i00000000000000000000000000000

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