Finite Group Databasebeta

← Group #325849

Character table — Group #325849

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444488888888888844444444444488888888888888888844884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111-1-1-1-111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111
χ711111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ9111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-11
χ12111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1111-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111111111-1-11-1-11
χ1722222222222-2-2-2-22-2-200000000222222-2-200-2-22200-2-2000000000000000000000000
χ1822222222222-2-2-2-22-2-2000000002222-2-2220022-2-200-2-2000000000000000000000000
χ1922222222222-2-2-2-22-2-200000000-2-2-2-2222200-2-2-2-20022000000000000000000000000
χ2022222222222-2-2-2-22-2-200000000-2-2-2-2-2-2-2-20022220022000000000000000000000000
χ2122222222-2-2-22222-2-2-22222-2-2-2-200000000220000-2-20000000000000000002-2000000
χ2222222222-2-2-22222-2-2-22222-2-2-2-200000000-2-2000022000000000000000000-22000000
χ2322222222-2-2-22222-2-2-2-2-2-2-2222200000000220000-2-2000000000000000000-22000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2222200000000-2-20000220000000000000000002-2000000
χ252222-2-2-2-22-2-222-2-222-222-2-222-2-20000000000000000000000000022-2-20000002-20000
χ262222-2-2-2-22-2-222-2-222-222-2-222-2-200000000000000000000000000-2-222000000-220000
χ272222-2-2-2-22-2-222-2-222-2-2-222-2-2220000000000000000000000000022-2-2000000-220000
χ282222-2-2-2-22-2-222-2-222-2-2-222-2-22200000000000000000000000000-2-2220000002-20000
χ292222-2-2-2-2-22222-2-2-2-2222-2-2-2-22222-2-20000000000002-200000000000022-2-200000000
χ302222-2-2-2-2-22222-2-2-2-2222-2-2-2-222-2-222000000000000-22000000000000-2-22200000000
χ312222-2-2-2-2-22222-2-2-2-22-2-22222-2-222-2-20000000000002-2000000000000-2-22200000000
χ322222-2-2-2-2-22222-2-2-2-22-2-22222-2-2-2-222000000000000-2200000000000022-2-200000000
χ332222-2-2-2-2-222-2-222-22-20000000022-2-2000000000000-2222-2-222-2-20000000000000000
χ342222-2-2-2-2-222-2-222-22-20000000022-2-2000000000000-22-2-222-2-2220000000000000000
χ352222-2-2-2-2-222-2-222-22-200000000-2-2220000000000002-222-2-2-2-2220000000000000000
χ362222-2-2-2-2-222-2-222-22-200000000-2-2220000000000002-2-2-22222-2-20000000000000000
χ3722-2-222-2-2-22-200002002−22−22−22−22i−2i2i−2i002-2002i−2i000000i2−i2i2−i22−22−20000i2−i2i2−i200000000
χ3822-2-222-2-2-22-200002002−22−22−22−22i−2i2i−2i00-2200−2i2i000000−i2i2−i2i2−22−220000i2−i2i2−i200000000
χ3922-2-222-2-2-22-200002002−22−22−22−2−2i2i−2i2i002-200−2i2i000000−i2i2−i2i22−22−20000−i2i2−i2i200000000
χ4022-2-222-2-2-22-200002002−22−22−22−2−2i2i−2i2i00-22002i−2i000000i2−i2i2−i2−22−220000−i2i2−i2i200000000
χ4122-2-222-2-2-22-20000200−22−22−22−222i−2i2i−2i002-2002i−2i000000−i2i2−i2i2−22−220000−i2i2−i2i200000000
χ4222-2-222-2-2-22-20000200−22−22−22−222i−2i2i−2i00-2200−2i2i000000i2−i2i2−i22−22−20000−i2i2−i2i200000000
χ4322-2-222-2-2-22-20000200−22−22−22−22−2i2i−2i2i002-200−2i2i000000i2−i2i2−i2−22−220000i2−i2i2−i200000000
χ4422-2-222-2-2-22-20000200−22−22−22−22−2i2i−2i2i00-22002i−2i000000−i2i2−i2i22−22−20000i2−i2i2−i200000000
χ4522-2-2-2-22222-20000-2002−2−22−222−22i−2i−2i2i2i−2i0000002-20000i2−i2−i2i22−2−220000i2−i2−i2i200000000
χ4622-2-2-2-22222-20000-2002−2−22−222−22i−2i−2i2i−2i2i000000-220000−i2i2i2−i2−222−20000i2−i2−i2i200000000
χ4722-2-2-2-22222-20000-2002−2−22−222−2−2i2i2i−2i2i−2i000000-220000i2−i2−i2i2−222−20000−i2i2i2−i200000000
χ4822-2-2-2-22222-20000-2002−2−22−222−2−2i2i2i−2i−2i2i0000002-20000−i2i2i2−i22−2−220000−i2i2i2−i200000000
χ4922-2-2-2-22222-20000-200−222−22−2−222i−2i−2i2i2i−2i0000002-20000−i2i2i2−i2−222−20000−i2i2i2−i200000000
χ5022-2-2-2-22222-20000-200−222−22−2−222i−2i−2i2i−2i2i000000-220000i2−i2−i2i22−2−220000−i2i2i2−i200000000
χ5122-2-2-2-22222-20000-200−222−22−2−22−2i2i2i−2i2i−2i000000-220000−i2i2i2−i22−2−220000i2−i2−i2i200000000
χ5222-2-2-2-22222-20000-200−222−22−2−22−2i2i2i−2i−2i2i0000002-20000i2−i2−i2i2−222−20000i2−i2−i2i200000000
χ5344444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ544444-4-4-4-44-4-4-4-4444-4400000000000000000000000000000000000000000000000000
χ5544-4-444-4-44-440000-40022−2222−22−2222−2222000000000000000000000000000000000000000000
χ5644-4-444-4-44-440000-400−2222−222222−2222−22000000000000000000000000000000000000000000
χ5744-4-4-4-444-4-44000040022−22−222222−22−2222000000000000000000000000000000000000000000
χ5844-4-4-4-444-4-440000400−222222−22−222222−22000000000000000000000000000000000000000000
χ594-44-44-4-440004-44-400000000000000000004i−4i00000000000000000000000000000000
χ604-44-44-4-440004-44-40000000000000000000−4i4i00000000000000000000000000000000
χ614-44-44-4-44000-44-4400000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ624-44-44-4-44000-44-440000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ634-44-4-444-40004-4-4400000000000000000000000004i−4i00000000000000000000000000
χ644-44-4-444-40004-4-440000000000000000000000000−4i4i00000000000000000000000000
χ654-44-4-444-4000-444-400000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ664-44-4-444-4000-444-40000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ678-8-888-88-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-88-88000000000000000000000000000000000000000000000000000000000000

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