Finite Group Databasebeta

← Group #309725

Character table — Group #309725

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888222444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-11-1-1-1-111-1-1-1-1-1
χ311111111111111111111111111-1-11111111111-1-1-1-11111-1-1-1-1111-111-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-11
χ61111111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-111-1
χ71111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1111111-1-111-1
χ81111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-11111-1-11
χ911111111111111111-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-11
χ1011111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-11111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-111-11111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-111111-1-111-1-1-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1111-1-1-1111111-1-1-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1111
χ1722222222222-2-2-2-22-22222-2000022-2-20000000022-2-200000000000-200000000000
χ1822222222222-2-2-2-22-22222-20000-2-2-2-200000000-2-22200000000000200000000000
χ1922222222222-2-2-2-22-2-2-2-2-2-20000222200000000-2-22200000000000-200000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-20000-2-2220000000022-2-200000000000200000000000
χ2122222222-2-2-22222-2-20000-2222200002222-2-2-2-2000000000000-200000000000000
χ2222222222-2-2-22222-2-20000-222220000-2-2-2-222-2-2000000000000200000000000000
χ2322222222-2-2-22222-2-20000-2-2-2-2-2000022-2-22222000000000000-200000000000000
χ2422222222-2-2-22222-2-20000-2-2-2-2-20000-2-222-2-222000000000000200000000000000
χ252-22-222-2-22-2-222-2-22-22i2i−2i−2i20000002i−2i000000000000000000000000002i−2i00002-20
χ262-22-222-2-22-2-222-2-22-22i2i−2i−2i20000002i−2i00000000000000000000000000−2i2i0000-220
χ272-22-222-2-22-2-222-2-22-2−2i−2i2i2i2000000−2i2i000000000000000000000000002i−2i0000-220
χ282-22-222-2-22-2-222-2-22-2−2i−2i2i2i2000000−2i2i00000000000000000000000000−2i2i00002-20
χ292-22-222-2-22-2-2-2-222222i2i−2i−2i-2000000−2i2i002i−2i2i−2i0000000000000002-2000000000000
χ302-22-222-2-22-2-2-2-222222i2i−2i−2i-2000000−2i2i00−2i2i−2i2i000000000000000-22000000000000
χ312-22-222-2-22-2-2-2-22222−2i−2i2i2i-20000002i−2i002i−2i2i−2i000000000000000-22000000000000
χ322-22-222-2-22-2-2-2-22222−2i−2i2i2i-20000002i−2i00−2i2i−2i2i0000000000000002-2000000000000
χ332-22-222-2-2-222-2-222-2-20000200000000002i−2i−2i2i00000022-2-2000000002i−2i000000000
χ342-22-222-2-2-222-2-222-2-20000200000000002i−2i−2i2i000000-2-22200000000−2i2i000000000
χ352-22-222-2-2-222-2-222-2-2000020000000000−2i2i2i−2i00000022-2-200000000−2i2i000000000
χ362-22-222-2-2-222-2-222-2-2000020000000000−2i2i2i−2i000000-2-222000000002i−2i000000000
χ372-2-2-22-222-22-20000202-22-2022−2−22-2000000002−22-2002−22−222−2−2000000002−200000
χ382-2-2-22-222-22-20000202-22-2022−2−2-22000000002−2-22002−22−2−2−22200000000−2200000
χ392-2-2-22-222-22-20000202-22-20−2−2222-200000000−222-200−22−22−2−22200000000−2200000
χ402-2-2-22-222-22-20000202-22-20−2−222-2200000000−22-2200−22−2222−2−2000000002−200000
χ412-2-2-22-222-22-2000020-22-22022−2−22-2000000002−2-2200−22−22−2−222000000002−200000
χ422-2-2-22-222-22-2000020-22-22022−2−2-22000000002−22-200−22−2222−2−200000000−2200000
χ432-2-2-22-222-22-2000020-22-220−2−2222-200000000−22-22002−22−222−2−200000000−2200000
χ442-2-2-22-222-22-2000020-22-220−2−222-2200000000−222-2002−22−2−2−222000000002−200000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ4644-444-4-4-444-40000-40000000000000000000000000022−22−22220000000000000000000
χ4744-444-4-4-444-40000-400000000000000000000000000−222222−220000000000000000000
χ4844-444-4-4-4-4-440000404i−4i−4i4i00000000000000000000000000000000000000000000
χ4944-444-4-4-4-4-44000040−4i4i4i−4i00000000000000000000000000000000000000000000
χ5044-4-4-44-440004-44-4000000000000000000000000000000022−2222−22000000000000000
χ5144-4-4-44-440004-44-40000000000000000000000000000000−2222−2222000000000000000
χ5244-4-4-44-44000-44-4400000004-44-4000000000000000000000000000000000000000
χ5344-4-4-44-44000-44-440000000-44-44000000000000000000000000000000000000000
χ544-444-4-4-440000000000000022−22−22220000000000000022−2200002-2-22000000000000000
χ554-444-4-4-440000000000000022−22−222200000000000000−22220000-222-2000000000000000
χ564-444-4-4-4400000000000000−222222−220000000000000022−220000-222-2000000000000000
χ574-444-4-4-4400000000000000−222222−2200000000000000−222200002-2-22000000000000000
χ584-44-444-4-4-44444-4-4-440000-40000000000000000000000000000000000000000000
χ594-4-44-444-40004-4-440000000000000004i−4i000000000000000000000000000000000
χ604-4-44-444-40004-4-44000000000000000−4i4i000000000000000000000000000000000
χ614-4-44-444-4000-444-40000000000000000000000000000000000000000000002i2−2i2000
χ624-4-44-444-4000-444-4000000000000000000000000000000000000000000000−2i22i2000
χ634-4-4-44-4444-440000-40000002222−22−220000000000−2222000000000000000000000000000
χ644-4-4-44-4444-440000-4000000−22−222222000000000022−22000000000000000000000000000
χ65888-8-8-88-8000000000000000000000000000000000000000000000000000000000

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