Finite Group Databasebeta

← Group #97392

Character table — Group #97392

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12222222222222224444444444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-111111111-1-1-1-111-1-11111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-1-1-111111111-1-1-1-111-1-11111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111−i−iiiii−i−iii−i−i−i−iii
χ172222222222222222-2-2-2-22222-2-2-2-2-2-2220000-2-2000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2000022000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2000022000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222220000-2-2000000000000000000000000
χ2122222222-2-2-2-22-22-222-2-2000022-2-2000000000022-2-22-2000000000000000000
χ2222222222-2-2-2-22-22-222-2-2000022-2-20000000000-2-222-22000000000000000000
χ2322222222-2-2-2-22-22-2-2-2220000-2-222000022-2-2000000002-20000000000000000
χ2422222222-2-2-2-22-22-2-2-2220000-2-2220000-2-22200000000-220000000000000000
χ2522222222-2-2-2-2-22-2222-2-20000-2-222000000000022-2-2-22000000000000000000
χ2622222222-2-2-2-2-22-2222-2-20000-2-2220000000000-2-2222-2000000000000000000
χ2722222222-2-2-2-2-22-22-2-222000022-2-2000022-2-200000000-220000000000000000
χ2822222222-2-2-2-2-22-22-2-222000022-2-20000-2-222000000002-20000000000000000
χ2922-22-2-22-222-2-20000000022-2-22i−2i2i−2i000000002i−2i000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ3022-22-2-22-222-2-20000000022-2-22i−2i2i−2i000000002i−2i00000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ3122-22-2-22-222-2-20000000022-2-2−2i2i−2i2i00000000−2i2i000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ3222-22-2-22-222-2-20000000022-2-2−2i2i−2i2i00000000−2i2i00000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ3322-22-2-22-222-2-200000000-2-2222i−2i2i−2i00000000−2i2i000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ3422-22-2-22-222-2-200000000-2-2222i−2i2i−2i00000000−2i2i00000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ3522-22-2-22-222-2-200000000-2-222−2i2i−2i2i000000002i−2i000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ3622-22-2-22-222-2-200000000-2-222−2i2i−2i2i000000002i−2i00000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ372-222-2-2-222-22-22-2-2200002i−2i2i−2i0000002i−2i00000000000000000000002−22−2i2−i2i2−i2
χ382-222-2-2-222-22-22-2-2200002i−2i2i−2i0000002i−2i0000000000000000000000−22−22−i2i2−i2i2
χ392-222-2-2-222-22-22-2-220000−2i2i−2i2i000000−2i2i00000000000000000000002−22−2−i2i2−i2i2
χ402-222-2-2-222-22-22-2-220000−2i2i−2i2i000000−2i2i0000000000000000000000−22−22i2−i2i2−i2
χ412-222-2-2-222-22-2-222-200002i−2i2i−2i000000−2i2i0000000000000000000000i2−i2−i2i2−222−2
χ422-222-2-2-222-22-2-222-200002i−2i2i−2i000000−2i2i0000000000000000000000−i2i2i2−i22−2−22
χ432-222-2-2-222-22-2-222-20000−2i2i−2i2i0000002i−2i0000000000000000000000i2−i2−i2i22−2−22
χ442-222-2-2-222-22-2-222-20000−2i2i−2i2i0000002i−2i0000000000000000000000−i2i2i2−i2−222−2
χ4544-44-4-44-4-4-4440000000000004i−4i−4i4i0000000000000000000000000000000000
χ4644-44-4-44-4-4-444000000000000−4i4i4i−4i0000000000000000000000000000000000
χ4744-4-44-4-4400000000004-4000000000000004i−4i00000000000000000000000000
χ4844-4-44-4-4400000000004-400000000000000−4i4i00000000000000000000000000
χ4944-4-44-4-440000000000-440000000000004i−4i0000000000000000000000000000
χ5044-4-44-4-440000000000-44000000000000−4i4i0000000000000000000000000000
χ514-444-4-4-44-44-4444-4-40000000000000000000000000000000000000000000000
χ524-444-4-4-44-44-44-4-4440000000000000000000000000000000000000000000000
χ534-44-44-44-4000000004-400000000000000000000004i−4i00000000000000000000
χ544-44-44-44-4000000004-40000000000000000000000−4i4i00000000000000000000
χ554-44-44-44-400000000-44000000000000000000004i−4i0000000000000000000000
χ564-44-44-44-400000000-4400000000000000000000−4i4i0000000000000000000000
χ574-4-4444-4-44-4-44000000004i−4i−4i4i00000000000000000000000000000000000000
χ584-4-4444-4-44-4-4400000000−4i4i4i−4i00000000000000000000000000000000000000
χ594-4-4444-4-4-444-400000000000000004i−4i00000000000000000000000000000000
χ604-4-4444-4-4-444-40000000000000000−4i4i00000000000000000000000000000000
χ61888-8-88-8-8000000000000000000000000000000000000000000000000000000
χ628-8-8-8-8888000000000000000000000000000000000000000000000000000000

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