Finite Group Databasebeta

← Group #167299

Character table — Group #167299

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444444444444488888888888888882244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-1-1-11-1-1-1-11111
χ51111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ61111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-111-1-11111
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11111-1-1-111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1111-1-1111-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-1
χ1011111111-1-1-1-1-1-1-1-1111-1-1111-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-111-11-11-1-1-111
χ1111111111-1-1-1-1-1-1-1-1111-1-1111-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111-11-1-1-1-11-11-1-111
χ1211111111-1-1-1-1-1-1-1-1111-1-1111-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11-1111-1-11-1111-1-1
χ1311111111-1-1-1-1-1-1-1-1111-1-1111-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11-1-111
χ1411111111-1-1-1-1-1-1-1-1111-1-1111-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-11-1-111-1-1111-1-1
χ1511111111-1-1-1-1-1-1-1-1111-1-1111-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-11-1111-111-111-1-1
χ1611111111-1-1-1-1-1-1-1-1111-1-1111-1-1-111-1-111-1-1-1-111111111-1-1-1-111-11-1-1-11-111-1-1-111
χ1722222222222222222-2-2-2-22-2-2-222220000000000000000000000-20000-200000000
χ1822222222222222222-2-2-2-22-2-2-2-2-2-2-2000000000000000000000020000200000000
χ19222222222222-2-2-2-2-22-2-2-2-22-22000022-2-2000000000000000000000000-22000000
χ20222222222222-2-2-2-2-22-2-2-2-22-220000-2-2220000000000000000000000002-2000000
χ21222222222222-2-2-2-2-2-2222-2-22-20000000000000000000000000002-200000-220000
χ22222222222222-2-2-2-2-2-2222-2-22-2000000000000000000000000000-22000002-20000
χ2322222222-2-2-2-22222-22-222-22-2-200002222000000000000000000000000-2-2000000
χ2422222222-2-2-2-22222-22-222-22-2-20000-2-2-2-200000000000000000000000022000000
χ2522222222-2-2-2-22222-2-22-2-2-2-2220000000000000000000000000002200000-2-20000
χ2622222222-2-2-2-22222-2-22-2-2-2-222000000000000000000000000000-2-200000220000
χ2722222222-2-2-2-2-2-2-2-22-2-2222-2-2222-2-20000000000000000000000-20000200000000
χ2822222222-2-2-2-2-2-2-2-22-2-2222-2-22-2-222000000000000000000000020000-200000000
χ29222-22-2-2-222-2-222-2-2-2000020002-22-2000000000000i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i2
χ30222-22-2-2-222-2-222-2-2-2000020002-22-2000000000000−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i2
χ31222-22-2-2-222-2-222-2-2-200002000-22-22000000000000i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i2
χ32222-22-2-2-222-2-222-2-2-200002000-22-22000000000000−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i2
χ33222-22-2-2-2-2-222-2-222-2000020002-2-22000000000000i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i2
χ34222-22-2-2-2-2-222-2-222-2000020002-2-22000000000000−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i2
χ35222-22-2-2-2-2-222-2-222-200002000-222-2000000000000i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2
χ36222-22-2-2-2-2-222-2-222-200002000-222-2000000000000−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2
χ372-2-2-222-2200002-22-20202-20-20000002i−2i2i−2ii2i2−i2−i2i2i2−i2−i22−22−22−22−20000000000000000
χ382-2-2-222-2200002-22-20202-20-20000002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2−22−22−22−220000000000000000
χ392-2-2-222-2200002-22-20202-20-2000000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2−22−22−22−220000000000000000
χ402-2-2-222-2200002-22-20202-20-2000000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i22−22−22−22−20000000000000000
χ412-2-2-222-220000-22-22020-220-20000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i22−22−2−22−220000000000000000
χ422-2-2-222-220000-22-22020-220-20000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i2−22−222−22−20000000000000000
χ432-2-2-222-220000-22-22020-220-2000000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2−22−222−22−20000000000000000
χ442-2-2-222-220000-22-22020-220-2000000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i22−22−2−22−220000000000000000
χ45444-44-4-4-444-4-4-4-44440000-40000000000000000000000000000000000000000000
χ46444-44-4-4-4-4-44444-4-440000-40000000000000000000000000000000000000000000
χ4744-44-4-4-444i−4i4i−4i0000000000000000000002-22-22i−2i2i−2i000000000000000000000000
χ4844-44-4-4-444i−4i4i−4i000000000000000000000-22-22−2i2i−2i2i000000000000000000000000
χ4944-44-4-4-44−4i4i−4i4i0000000000000000000002-22-2−2i2i−2i2i000000000000000000000000
χ5044-44-4-4-44−4i4i−4i4i000000000000000000000-22-222i−2i2i−2i000000000000000000000000
χ5144-4-4-444-44i−4i−4i4i00000000000000000000000000000000000002-20002i−2i000000000
χ5244-4-4-444-44i−4i−4i4i0000000000000000000000000000000000000-22000−2i2i000000000
χ5344-4-4-444-4−4i4i4i−4i00000000000000000000000000000000000002-2000−2i2i000000000
χ5444-4-4-444-4−4i4i4i−4i0000000000000000000000000000000000000-220002i−2i000000000
χ554-44-4-4-444000000000040000-40000000002i2−2i2−2i22i20000000000000000000000000000
χ564-44-4-4-444000000000040000-4000000000−2i22i22i2−2i20000000000000000000000000000
χ574-44-4-4-4440000000000-400004000000000000022−22−2222000000000000000000000000
χ584-44-4-4-4440000000000-4000040000000000000−222222−22000000000000000000000000
χ594-4-444-44-400004-4-4400000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ604-4-444-44-400004-4-440000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ614-4-444-44-40000-444-400000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ624-4-444-44-40000-444-40000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ634-4-4-444-4400004-44-40-40-4404000000000000000000000000000000000000000000
χ644-4-4-444-440000-44-440-404-404000000000000000000000000000000000000000000
χ658-888-88-8-8000000000000000000000000000000000000000000000000000000000

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