Finite Group Databasebeta

← Group #310470

Character table — Group #310470

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ411111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-1-11111-1-11
χ51111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-111111
χ71111111111111111111111-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-1-111-1
χ91111111111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1111
χ101111111111111111-1-1-1-111111111-1-11111-1-1111111-1-1-1-11111-1-11-1-1-1-1-11111-1-1-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-11111-1-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111111111-111-1-11-1-111-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1111
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-11-1-111111-1-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111111-1-1-11111-1
χ17222222222-222-2-2-220000-2-222222200-2-22200-2-200000000000000-2000000000000
χ18222222222-222-2-2-220000-2-22222-2-20022-2-200-2-2000000000000002000000000000
χ19222222222-222-2-2-220000-2-2-2-2-2-22200-2-2-2-20022000000000000002000000000000
χ20222222222-222-2-2-220000-2-2-2-2-2-2-2-2002222002200000000000000-2000000000000
χ2122222222-22-2-2222-22222-2-2000000-2-200002200-2-222000000000000000-20000000
χ2222222222-22-2-2222-22222-2-2000000-2-20000-2-20022-2-200000000000000020000000
χ2322222222-22-2-2222-2-2-2-2-2-2-2000000220000220022-2-2000000000000000-20000000
χ2422222222-22-2-2222-2-2-2-2-2-2-2000000220000-2-200-2-22200000000000000020000000
χ252-22-2-222-20200-2-2202i2i−2i−2i00i2i2−i2−i2000000002i−2ii2−i2002-222−2−2i2i2−i2−i20000000000002−20
χ262-22-2-222-20200-2-2202i2i−2i−2i00i2i2−i2−i200000000−2i2ii2−i200-2222−2−2−i2−i2i2i2000000000000−220
χ272-22-2-222-20200-2-2202i2i−2i−2i00−i2−i2i2i2000000002i−2i−i2i2002-2−2−222−i2−i2i2i2000000000000−220
χ282-22-2-222-20200-2-2202i2i−2i−2i00−i2−i2i2i200000000−2i2i−i2i200-22−2−222i2i2−i2−i20000000000002−20
χ292-22-2-222-20200-2-220−2i−2i2i2i00i2i2−i2−i2000000002i−2ii2−i200-22−2−222−i2−i2i2i20000000000002−20
χ302-22-2-222-20200-2-220−2i−2i2i2i00i2i2−i2−i200000000−2i2ii2−i2002-2−2−222i2i2−i2−i2000000000000−220
χ312-22-2-222-20200-2-220−2i−2i2i2i00−i2−i2i2i2000000002i−2i−i2i200-2222−2−2i2i2−i2−i2000000000000−220
χ322-22-2-222-20200-2-220−2i−2i2i2i00−i2−i2i2i200000000−2i2i−i2i2002-222−2−2−i2−i2i2i20000000000002−20
χ332-2-2-22-22222-2-2-22-222i−2i2i−2i2-20000002i−2i000000000000000000000002i−2i0002-200000
χ342-2-2-22-22222-2-2-22-222i−2i2i−2i2-20000002i−2i00000000000000000000000−2i2i000-2200000
χ352-2-2-22-22222-2-2-22-22−2i2i−2i2i2-2000000−2i2i000000000000000000000002i−2i000-2200000
χ362-2-2-22-22222-2-2-22-22−2i2i−2i2i2-2000000−2i2i00000000000000000000000−2i2i0002-200000
χ372-2-2-22-222-2222-22-2-22i−2i2i−2i-2200002i−2i−2i2i2i−2i000000000000000000000002-200000000
χ382-2-2-22-222-2222-22-2-22i−2i2i−2i-220000−2i2i−2i2i−2i2i00000000000000000000000-2200000000
χ392-2-2-22-222-2222-22-2-2−2i2i−2i2i-2200002i−2i2i−2i2i−2i00000000000000000000000-2200000000
χ402-2-2-22-222-2222-22-2-2−2i2i−2i2i-220000−2i2i2i−2i−2i2i000000000000000000000002-200000000
χ412-2-2-22-222-2-2222-22-200002-200002i−2i00−2i2i00000000002i−2i2i−2i00002-20000000000000
χ422-2-2-22-222-2-2222-22-200002-200002i−2i00−2i2i0000000000−2i2i−2i2i0000-220000000000000
χ432-2-2-22-222-2-2222-22-200002-20000−2i2i002i−2i00000000002i−2i2i−2i0000-220000000000000
χ442-2-2-22-222-2-2222-22-200002-20000−2i2i002i−2i0000000000−2i2i−2i2i00002-20000000000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ4644-44-4-44-404004-4-404-4-44000000000000000000000000000000000000000000000
χ4744-44-4-44-404004-4-40-444-4000000000000000000000000000000000000000000000
χ4844-44-4-44-40-400-4440000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ4944-44-4-44-40-400-444000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ5044-4-444-4-4404-4000-400000000000000000000000000000022−2222−22000000000000000
χ5144-4-444-4-4404-4000-4000000000000000000000000000000−2222−2222000000000000000
χ5244-4-444-4-4-40-4400040000004i−4i4i−4i000000000000000000000000000000000000000
χ5344-4-444-4-4-40-440004000000−4i4i−4i4i000000000000000000000000000000000000000
χ544-4444-4-4-440-44000-400000000000000004-40000000000000000000000000000000
χ554-4444-4-4-440-44000-40000000000000000-440000000000000000000000000000000
χ564-4444-4-4-4-404-40004000000000000000000000000000000000000000000002i2−2i2000
χ574-4444-4-4-4-404-4000400000000000000000000000000000000000000000000−2i22i2000
χ584-44-4-444-40-40044-400000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ594-44-4-444-40-40044-40000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ604-4-44-44-440000000000000022−22−22220000000000002i2−2i20000002i−2i−2i2i000000000000000
χ614-4-44-44-440000000000000022−22−2222000000000000−2i22i2000000−2i2i2i−2i000000000000000
χ624-4-44-44-4400000000000000−222222−220000000000002i2−2i2000000−2i2i2i−2i000000000000000
χ634-4-44-44-4400000000000000−222222−22000000000000−2i22i20000002i−2i−2i2i000000000000000
χ644-4-4-44-4444-4-4-44-4440000-440000000000000000000000000000000000000000000
χ65888-8-8-8-88000000000000000000000000000000000000000000000000000000000

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