Finite Group Databasebeta

← Group #167363

Character table — Group #167363

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444444444444488888888888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ61111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1111-1-1111-111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-1111-11-1-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1111-1-1111-111-1-111-1-1-1-1-1-11111-1-1-1-111111-11-1-1-11-11-111-1-111
χ1111111111-1-1-1-1-1-1-1-1111-1-1111-111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1111-11-11-1-1-1-111
χ1211111111-1-1-1-1-1-1-1-1111-1-1111-111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-11-1-1-11-111111-1-1
χ1311111111-1-1-1-1-1-1-1-1111-1-1111-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-11-11-1-11-1-1111-1-111
χ1411111111-1-1-1-1-1-1-1-1111-1-1111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-11-11111-1-11-1-111-1-1
χ1511111111-1-1-1-1-1-1-1-1111-1-1111-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-111-1-1-1-111-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1111-1-1111-1-1-111-1-111-1-1-1-111111111-1-1-1-1-111-111-111-1-1-1-1-111
χ1722222222222222222-2-2-2-22-2-2-2222200000000000000000000-2-200000000000000
χ1822222222222222222-2-2-2-22-2-2-2-2-2-2-2000000000000000000002200000000000000
χ19222222222222-2-2-2-2-22-2-2-2-22-2200000000000000000000000000220000-2-2000000
χ20222222222222-2-2-2-2-22-2-2-2-22-2200000000000000000000000000-2-2000022000000
χ21222222222222-2-2-2-2-2-2222-2-22-2000022220000000000000000000000-2-200000000
χ22222222222222-2-2-2-2-2-2222-2-22-20000-2-2-2-200000000000000000000002200000000
χ2322222222-2-2-2-22222-22-222-22-2-2000000000000000000000000002-20000-22000000
χ2422222222-2-2-2-22222-22-222-22-2-200000000000000000000000000-2200002-2000000
χ2522222222-2-2-2-22222-2-22-2-2-2-222000022-2-20000000000000000000000-2200000000
χ2622222222-2-2-2-22222-2-22-2-2-2-2220000-2-22200000000000000000000002-200000000
χ2722222222-2-2-2-2-2-2-2-22-2-2222-2-2222-2-200000000000000000000-2200000000000000
χ2822222222-2-2-2-2-2-2-2-22-2-2222-2-22-2-222000000000000000000002-200000000000000
χ292222-2-2-2-222-2-222-2-220000-20002-22-200000000000022−2−222−2−20000000000002−22−2
χ302222-2-2-2-222-2-222-2-220000-20002-22-2000000000000−2−222−2−222000000000000−22−22
χ312222-2-2-2-222-2-222-2-220000-2000-22-2200000000000022−2−222−2−2000000000000−22−22
χ322222-2-2-2-222-2-222-2-220000-2000-22-22000000000000−2−222−2−2220000000000002−22−2
χ332222-2-2-2-2-2-222-2-22220000-20002-2-2200000000000022−2−2−2−2220000000000002−2−22
χ342222-2-2-2-2-2-222-2-22220000-20002-2-22000000000000−2−22222−2−2000000000000−222−2
χ352222-2-2-2-2-2-222-2-22220000-2000-222-200000000000022−2−2−2−222000000000000−222−2
χ362222-2-2-2-2-2-222-2-22220000-2000-222-2000000000000−2−22222−2−20000000000002−2−22
χ3722-2-2-2-2222-22-200000022-200-2000002i−2i2i−2ii2i2−i2−i2i2i2−i2−i22−22−22−22−20000000000000000
χ3822-2-2-2-2222-22-200000022-200-2000002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2−22−22−22−220000000000000000
χ3922-2-2-2-2222-22-200000022-200-200000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2−22−22−22−220000000000000000
χ4022-2-2-2-2222-22-200000022-200-200000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i22−22−22−22−20000000000000000
χ4122-2-2-2-222-22-220000002-2200-2000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i22−22−2−22−220000000000000000
χ4222-2-2-2-222-22-220000002-2200-2000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i2−22−222−22−20000000000000000
χ4322-2-2-2-222-22-220000002-2200-200000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2−22−222−22−20000000000000000
χ4422-2-2-2-222-22-220000002-2200-200000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i22−22−2−22−220000000000000000
χ454444-4-4-4-444-4-4-4-444-4000040000000000000000000000000000000000000000000
χ464444-4-4-4-4-4-44444-4-4-4000040000000000000000000000000000000000000000000
χ4744-4-444-4-44-4-44000000000000000000000000000002-2-222-2-220000000000000000
χ4844-4-444-4-44-4-4400000000000000000000000000000-222-2-222-20000000000000000
χ4944-4-444-4-4-444-4000000000000000000000000000002-2-22-222-20000000000000000
χ5044-4-444-4-4-444-400000000000000000000000000000-222-22-2-220000000000000000
χ5144-4-4-4-4444-44-4000000-4-4400400000000000000000000000000000000000000000
χ5244-4-4-4-444-44-44000000-44-400400000000000000000000000000000000000000000
χ534-44-44-4-4400004i−4i4i−4i000000000000000002i−2i2i−2i2-22-2000000000000000000000000
χ544-44-44-4-4400004i−4i4i−4i00000000000000000−2i2i−2i2i-22-22000000000000000000000000
χ554-44-44-4-440000−4i4i−4i4i000000000000000002i−2i2i−2i-22-22000000000000000000000000
χ564-44-44-4-440000−4i4i−4i4i00000000000000000−2i2i−2i2i2-22-2000000000000000000000000
χ574-44-4-444-400004i−4i−4i4i00000000000000000000000000000000000002-200002i−2i0000
χ584-44-4-444-400004i−4i−4i4i0000000000000000000000000000000000000-220000−2i2i0000
χ594-44-4-444-40000−4i4i4i−4i00000000000000000000000000000000000002-20000−2i2i0000
χ604-44-4-444-40000−4i4i4i−4i0000000000000000000000000000000000000-2200002i−2i0000
χ614-4-44-44-4400000000040000-4000000000000002i2−2i2−2i22i2000000000000000000000000
χ624-4-44-44-4400000000040000-400000000000000−2i22i22i2−2i2000000000000000000000000
χ634-4-44-44-44000000000-400004000000000022−22−22220000000000000000000000000000
χ644-4-44-44-44000000000-4000040000000000−222222−220000000000000000000000000000
χ658-8-888-88-8000000000000000000000000000000000000000000000000000000000

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