Finite Group Databasebeta

← Group #135339

Character table — Group #135339

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12222222222222224444444444442244444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-222-2-200000000-2-200000000000000000000
χ182222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2000000002200000000000000000000
χ19222222222222-2-2-2-22222-2-2-2-22222-2-2-2-2000000002200000000000000000000
χ20222222222222-2-2-2-2-2-2-2-22222222222-2-200000000-2-200000000000000000000
χ212222-2-2-2-222-2-222-2-222-2-2000000002-20000000000000000000000002−22−22−22−2
χ222222-2-2-2-222-2-222-2-222-2-2000000002-2000000000000000000000000−22−22−22−22
χ232222-2-2-2-222-2-222-2-2-2-22200000000-220000000000000000000000002−22−2−22−22
χ242222-2-2-2-222-2-222-2-2-2-22200000000-22000000000000000000000000−22−222−22−2
χ252222-2-2-2-222-2-2-2-22222-2-200000000-22000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ262222-2-2-2-222-2-2-2-22222-2-200000000-22000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ272222-2-2-2-222-2-2-2-222-2-222000000002-2000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ282222-2-2-2-222-2-2-2-222-2-222000000002-2000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ292-2-222-2-222-22-22-22-20000000022-2-2002-200002i2i−2i−2i00002i−2i0000000000000000
χ302-2-222-2-222-22-22-22-20000000022-2-2002-20000−2i−2i2i2i0000−2i2i0000000000000000
χ312-2-222-2-222-22-22-22-200000000-2-22200-222i2i−2i−2i0000002i−2i000000000000000000
χ322-2-222-2-222-22-22-22-200000000-2-22200-22−2i−2i2i2i000000−2i2i000000000000000000
χ332-2-222-2-222-22-2-22-220000000022-2-200-222i2i−2i−2i000000−2i2i000000000000000000
χ342-2-222-2-222-22-2-22-220000000022-2-200-22−2i−2i2i2i0000002i−2i000000000000000000
χ352-2-222-2-222-22-2-22-2200000000-2-222002-200002i2i−2i−2i0000−2i2i0000000000000000
χ362-2-222-2-222-22-2-22-2200000000-2-222002-20000−2i−2i2i2i00002i−2i0000000000000000
χ372-2-22-222-2-222-200002-22-200002i−2i2i−2i0000000000002i−2i00001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ382-2-22-222-2-222-200002-22-200002i−2i2i−2i0000000000002i−2i0000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ392-2-22-222-2-222-200002-22-20000−2i2i−2i2i000000000000−2i2i00001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ402-2-22-222-2-222-200002-22-20000−2i2i−2i2i000000000000−2i2i0000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ412-2-22-222-2-222-20000-22-2200002i−2i2i−2i000000000000−2i2i00001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ422-2-22-222-2-222-20000-22-2200002i−2i2i−2i000000000000−2i2i0000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ432-2-22-222-2-222-20000-22-220000−2i2i−2i2i0000000000002i−2i00001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ442-2-22-222-2-222-20000-22-220000−2i2i−2i2i0000000000002i−2i0000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ4544444444-4-4-4-40000000044-4-400000000000000000000000000000000000000
χ4644444444-4-4-4-400000000-4-44400000000000000000000000000000000000000
χ474444-4-4-4-4-4-4440000000000004i−4i−4i4i0000000000000000000000000000000000
χ484444-4-4-4-4-4-444000000000000−4i4i4i−4i0000000000000000000000000000000000
χ4944-4-444-4-4000000000000004i−4i000000002-22-22i−2i2i−2i0000000000000000000000
χ5044-4-444-4-4000000000000004i−4i00000000-22-22−2i2i−2i2i0000000000000000000000
χ5144-4-444-4-400000000000000−4i4i000000002-22-2−2i2i−2i2i0000000000000000000000
χ5244-4-444-4-400000000000000−4i4i00000000-22-222i−2i2i−2i0000000000000000000000
χ534-44-44-44-40000000000004i−4i00000000002i−2i−2i2i2-2-220000000000000000000000
χ544-44-44-44-40000000000004i−4i0000000000−2i2i2i−2i-222-20000000000000000000000
χ554-44-44-44-4000000000000−4i4i00000000002i−2i−2i2i-222-20000000000000000000000
χ564-44-44-44-4000000000000−4i4i0000000000−2i2i2i−2i2-2-220000000000000000000000
χ574-4-444-4-44-44-4400004-4-44000000000000000000000000000000000000000000
χ584-4-444-4-44-44-440000-444-4000000000000000000000000000000000000000000
χ594-4-44-444-44-4-444-4-440000000000000000000000000000000000000000000000
χ604-4-44-444-44-4-44-444-40000000000000000000000000000000000000000000000
χ6188-8-8-8-888000000000000000000000000000000000000000000000000000000
χ628-88-8-88-88000000000000000000000000000000000000000000000000000000

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