Finite Group Databasebeta

← Group #148573

Character table — Group #148573

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12222222222222222222444444442244444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111ii−i−iii−i−i−i−iii−i−iii
χ121111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−iii−i−iiiii−i−iii−i−i
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-22222-2-22222-2-2-2-200000000-2-22200000000000000000000
χ18222222222222-2-2-2-22222-2-2-2-2-2-2-2-2220000000022-2-200000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2222222222200000000-2-2-2-200000000000000000000
χ20222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-200000000222200000000000000000000
χ21222-2-2-2-2222-2-222-2-22-22-22-200002-20000002i2i−2i−2i0000002i−2i0000000000000000
χ22222-2-2-2-2222-2-222-2-22-22-22-200002-2000000−2i−2i2i2i000000−2i2i0000000000000000
χ23222-2-2-2-2222-2-222-2-2-22-22-220000-220000002i2i−2i−2i000000−2i2i0000000000000000
χ24222-2-2-2-2222-2-222-2-2-22-22-220000-22000000−2i−2i2i2i0000002i−2i0000000000000000
χ25222-2-2-2-2222-2-2-2-2222-22-2-220000-22002i2i−2i−2i000000002i−2i000000000000000000
χ26222-2-2-2-2222-2-2-2-2222-22-2-220000-2200−2i−2i2i2i00000000−2i2i000000000000000000
χ27222-2-2-2-2222-2-2-2-222-22-222-200002-2002i2i−2i−2i00000000−2i2i000000000000000000
χ28222-2-2-2-2222-2-2-2-222-22-222-200002-200−2i−2i2i2i000000002i−2i000000000000000000
χ292-2-22-22-222-22-22-22-222-2-22-20000-220000000000000000002i−2i2i−2i000000000000
χ302-2-22-22-222-22-22-22-222-2-22-20000-22000000000000000000−2i2i−2i2i000000000000
χ312-2-22-22-222-22-22-22-2-2-222-2200002-20000000000000000002-2-22000000000000
χ322-2-22-22-222-22-22-22-2-2-222-2200002-2000000000000000000-222-2000000000000
χ332-2-22-22-222-22-2-22-2222-2-2-2200002-200000000000000000000002i−2i2i−2i00000000
χ342-2-22-22-222-22-2-22-2222-2-2-2200002-20000000000000000000000−2i2i−2i2i00000000
χ352-2-22-22-222-22-2-22-22-2-2222-20000-2200000000000000000000002-2-2200000000
χ362-2-22-22-222-22-2-22-22-2-2222-20000-220000000000000000000000-222-200000000
χ372-2-2-22-2222-2-222-2-222-2-22220000-2-20000000000000000000000000000002i−2i2i−2i
χ382-2-2-22-2222-2-222-2-222-2-22220000-2-2000000000000000000000000000000−2i2i−2i2i
χ392-2-2-22-2222-2-222-2-22-222-2-2-20000220000000000000000000000000000002-2-22
χ402-2-2-22-2222-2-222-2-22-222-2-2-2000022000000000000000000000000000000-222-2
χ412-2-2-22-2222-2-22-222-22-2-22-2-2000022000000000000000000000000002-22-20000
χ422-2-2-22-2222-2-22-222-22-2-22-2-200002200000000000000000000000000-22-220000
χ432-2-2-22-2222-2-22-222-2-222-2220000-2-2000000000000000000000000002i−2i−2i2i0000
χ442-2-2-22-2222-2-22-222-2-222-2220000-2-200000000000000000000000000−2i2i2i−2i0000
χ4544444444-4-4-4-4000000000044-4-4000000000000000000000000000000000000
χ4644444444-4-4-4-40000000000-4-444000000000000000000000000000000000000
χ47444-4-4-4-44-4-444000000000000000000000000004-40000000000000000000000
χ48444-4-4-4-44-4-44400000000000000000000000000-440000000000000000000000
χ4944-44-4-44-400000000000000004i−4i00002i−2i2i−2i2-22-2000000000000000000000000
χ5044-44-4-44-400000000000000004i−4i0000−2i2i−2i2i-22-22000000000000000000000000
χ5144-44-4-44-40000000000000000−4i4i00002i−2i2i−2i-22-22000000000000000000000000
χ5244-44-4-44-40000000000000000−4i4i0000−2i2i−2i2i2-22-2000000000000000000000000
χ5344-4-444-4-4000000000000004i−4i0000002-2-222i−2i−2i2i000000000000000000000000
χ5444-4-444-4-4000000000000004i−4i000000-222-2−2i2i2i−2i000000000000000000000000
χ5544-4-444-4-400000000000000−4i4i0000002-2-22−2i2i2i−2i000000000000000000000000
χ5644-4-444-4-400000000000000−4i4i000000-222-22i−2i−2i2i000000000000000000000000
χ574-4-44-44-44-44-4400000000000000000000000000004-400000000000000000000
χ584-4-44-44-44-44-440000000000000000000000000000-4400000000000000000000
χ594-4-4-44-444-444-400000000000000004-400000000000000000000000000000000
χ604-4-4-44-444-444-40000000000000000-4400000000000000000000000000000000
χ618-8888-8-8-8000000000000000000000000000000000000000000000000000000
χ628-88-8-888-8000000000000000000000000000000000000000000000000000000

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