Finite Group Databasebeta

← Group #167635

Character table — Group #167635

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444422444444488888888888888882224444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-11111111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-11-1-1111111
χ5111111111111111111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-111-1-1-1-1
χ6111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-11-1-1-11111
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11-111-1-11-1-11111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-111-1-1111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11-1-11111111-1-1-111-1-11111-1-1-1-11111-1-1-1-1-111-1111-11-1-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-11-1-11111111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-11-111-1-111
χ1111111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-111-1-1-1-1111-1-111
χ1211111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111-1-1-1-11-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-11-1-111111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-1111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-11-1-111111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-11-1-1-11111111-1-1
χ1511111111-1-1-1-1-1-1-1-11-1-111111-1-1-111-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-1111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-11-1-111111-1-1-111-1-111-1-1-1-111111111-1-1-1-1111-1-1111-1-1-1-1-1-111
χ172222222222222222-2-2-2-2-222-200-20022220000000000000000-20000000-20000000
χ182222222222222222-2-2-2-2-222-200-200-2-2-2-200000000000000002000000020000000
χ19222222222222-2-2-2-2222-2-2-2-2200-20000000000000000000000000202-200-2000000
χ20222222222222-2-2-2-2222-2-2-2-2200-20000000000000000000000000-20-22002000000
χ21222222222222-2-2-2-2-2-2-222-2-2-2222-2-2000000000000000000000000-200200000000
χ22222222222222-2-2-2-2-2-2-222-2-2-2-2-2222000000000000000000000000200-200000000
χ2322222222-2-2-2-222222-2-2-2-2-2-22002000000000000000000000000020-2200-2000000
χ2422222222-2-2-2-222222-2-2-2-2-2-220020000000000000000000000000-202-2002000000
χ2522222222-2-2-2-22222-22222-2-2-222-222000000000000000000000000-200-200000000
χ2622222222-2-2-2-22222-22222-2-2-2-2-2-2-2-2000000000000000000000000200200000000
χ2722222222-2-2-2-2-2-2-2-2-222-2-222-20020022-2-2000000000000000020000000-20000000
χ2822222222-2-2-2-2-2-2-2-2-222-2-222-200200-2-2220000000000000000-2000000020000000
χ29222-2-2-22-200002i2i−2i−2i02i−2i2-20002-202i−2i0000i2i2−i2−i222−2−2i2i2−i2−i222−2−20000000000000000
χ30222-2-2-22-200002i2i−2i−2i02i−2i2-20002-202i−2i0000−i2−i2i2i2−2−222−i2−i2i2i2−2−2220000000000000000
χ31222-2-2-22-200002i2i−2i−2i02i−2i2-2000-220−2i2i0000i2i2−i2−i222−2−2−i2−i2i2i2−2−2220000000000000000
χ32222-2-2-22-200002i2i−2i−2i02i−2i2-2000-220−2i2i0000−i2−i2i2i2−2−222i2i2−i2−i222−2−20000000000000000
χ33222-2-2-22-20000−2i−2i2i2i0−2i2i2-20002-20−2i2i0000i2i2−i2−i2−2−222i2i2−i2−i2−2−2220000000000000000
χ34222-2-2-22-20000−2i−2i2i2i0−2i2i2-20002-20−2i2i0000−i2−i2i2i222−2−2−i2−i2i2i222−2−20000000000000000
χ35222-2-2-22-20000−2i−2i2i2i0−2i2i2-2000-2202i−2i0000i2i2−i2−i2−2−222−i2−i2i2i222−2−20000000000000000
χ36222-2-2-22-20000−2i−2i2i2i0−2i2i2-2000-2202i−2i0000−i2−i2i2i222−2−2i2i2−i2−i2−2−2220000000000000000
χ3722-2-222-2-22i2i−2i−2i2i−2i2i−2i000002-20000002-22i−2i000000002−22−2i2−i2i2−i20000000000002−2i2−i2
χ3822-2-222-2-22i2i−2i−2i2i−2i2i−2i000002-20000002-22i−2i00000000−22−22−i2i2−i2i2000000000000−22−i2i2
χ3922-2-222-2-22i2i−2i−2i2i−2i2i−2i000002-2000000-22−2i2i000000002−22−2i2−i2i2−i2000000000000−22−i2i2
χ4022-2-222-2-22i2i−2i−2i2i−2i2i−2i000002-2000000-22−2i2i00000000−22−22−i2i2−i2i20000000000002−2i2−i2
χ4122-2-222-2-2−2i−2i2i2i−2i2i−2i2i000002-20000002-2−2i2i000000002−22−2−i2i2−i2i20000000000002−2−i2i2
χ4222-2-222-2-2−2i−2i2i2i−2i2i−2i2i000002-20000002-2−2i2i00000000−22−22i2−i2i2−i2000000000000−22i2−i2
χ4322-2-222-2-2−2i−2i2i2i−2i2i−2i2i000002-2000000-222i−2i000000002−22−2−i2i2−i2i2000000000000−22i2−i2
χ4422-2-222-2-2−2i−2i2i2i−2i2i−2i2i000002-2000000-222i−2i00000000−22−22i2−i2i2−i20000000000002−2−i2i2
χ45444-4-4-44-400004i4i−4i−4i0−4i4i-4400000000000000000000000000000000000000000000
χ46444-4-4-44-40000−4i−4i4i4i04i−4i-4400000000000000000000000000000000000000000000
χ4744-44-4-4-4400004-4-4400000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ4844-44-4-4-4400004-4-440000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ4944-44-4-4-440000-444-400000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ5044-44-4-4-440000-444-40000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ5144-4-444-4-44i4i−4i−4i−4i4i−4i4i00000-44000000000000000000000000000000000000000000
χ5244-4-444-4-4−4i−4i4i4i4i−4i4i−4i00000-44000000000000000000000000000000000000000000
χ534-4444-4-4-44i−4i4i−4i000000000000000000000000000000000000002-200000002i−2i0000
χ544-4444-4-4-44i−4i4i−4i00000000000000000000000000000000000000-220000000−2i2i0000
χ554-4444-4-4-4−4i4i−4i4i000000000000000000000000000000000000002-20000000−2i2i0000
χ564-4444-4-4-4−4i4i−4i4i00000000000000000000000000000000000000-2200000002i−2i0000
χ574-4-44-444-4000000004000000-40000000002i2−2i22i2−2i20000000000000000000000000000
χ584-4-44-444-4000000004000000-4000000000−2i22i2−2i22i20000000000000000000000000000
χ594-4-44-444-400000000-40000004000000000000022−2222−22000000000000000000000000
χ604-4-44-444-400000000-400000040000000000000−2222−2222000000000000000000000000
χ614-4-4-44-4444-4-440000000000000000000002-2-222-2-22000000000000000000000000
χ624-4-4-44-4444-4-44000000000000000000000-222-2-222-2000000000000000000000000
χ634-4-4-44-444-444-40000000000000000000002-2-22-222-2000000000000000000000000
χ644-4-4-44-444-444-4000000000000000000000-222-22-2-22000000000000000000000000
χ658-88-8-88-88000000000000000000000000000000000000000000000000000000000

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