Finite Group Databasebeta

← Group #167682

Character table — Group #167682

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444422444444488888888888888882444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ3111111111111111111111111111-1-111-1-11111111111111111-11-1-1-1-1-1-11-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1111111
χ5111111111111111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1111-1-1-1-1
χ6111111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-11-1-11111
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-11-1-1-1-1-1-11111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1111-1-111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11-1-11111111-111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-111-1111-1-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-11-1-11111111-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-111-1-1-11-111-1-111
χ1111111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11-1-11-1-11111-1-111
χ1211111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11-1-111111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-11-1-111111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-111-11111-1-1-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-11-1-111111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-111-111-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-11-1-1-1-1-111111-1-1
χ1611111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-11-1-111-11-1-1-1-111
χ172222222222222222-2-2-222-2-2-200-222002200000000000000000000-20000-2000000
χ182222222222222222-2-2-222-2-2-200-2-2-200-2-200000000000000000000200002000000
χ19222222222222-2-2-2-2222-2-2-2-2200-20000000000000000000000202-20-20000000000
χ20222222222222-2-2-2-2222-2-2-2-2200-20000000000000000000000-20-22020000000000
χ21222222222222-2-2-2-2-2-2-2-2-222-222200-2-200000000000000000002000000-20000000
χ22222222222222-2-2-2-2-2-2-2-2-222-2-2-2200220000000000000000000-200000020000000
χ2322222222-2-2-2-222222-2-2-2-2-2-22002000000000000000000000020-2-2020000000000
χ2422222222-2-2-2-222222-2-2-2-2-2-220020000000000000000000000-20220-20000000000
χ2522222222-2-2-2-22222-222-2-222-222-200220000000000000000000-2000000-20000000
χ2622222222-2-2-2-22222-222-2-222-2-2-2-200-2-20000000000000000000200000020000000
χ2722222222-2-2-2-2-2-2-2-2-22222-2-2-20022200-2-200000000000000000000-200002000000
χ2822222222-2-2-2-2-2-2-2-2-22222-2-2-2002-2-200220000000000000000000020000-2000000
χ2922-2-22-2-222i2i−2i−2i2i2i−2i−2i0002-20000002-2002i−2i00000000i2i2−i2−i222−2−2000000000000i2−i22−2
χ3022-2-22-2-222i2i−2i−2i2i2i−2i−2i0002-20000002-2002i−2i00000000−i2−i2i2i2−2−222000000000000−i2i2−22
χ3122-2-22-2-222i2i−2i−2i2i2i−2i−2i0002-2000000-2200−2i2i00000000i2i2−i2−i222−2−2000000000000−i2i2−22
χ3222-2-22-2-222i2i−2i−2i2i2i−2i−2i0002-2000000-2200−2i2i00000000−i2−i2i2i2−2−222000000000000i2−i22−2
χ3322-2-22-2-22−2i−2i2i2i−2i−2i2i2i0002-20000002-200−2i2i00000000i2i2−i2−i2−2−222000000000000i2−i2−22
χ3422-2-22-2-22−2i−2i2i2i−2i−2i2i2i0002-20000002-200−2i2i00000000−i2−i2i2i222−2−2000000000000−i2i22−2
χ3522-2-22-2-22−2i−2i2i2i−2i−2i2i2i0002-2000000-22002i−2i00000000i2i2−i2−i2−2−222000000000000−i2i22−2
χ3622-2-22-2-22−2i−2i2i2i−2i−2i2i2i0002-2000000-22002i−2i00000000−i2−i2i2i222−2−2000000000000i2−i2−22
χ372-22-222-2-200002i−2i2i−2i02i−2i002-202-20002i−2i0022−2−2i2i2−i2−i22−22−2i2−i2i2−i20000000000000000
χ382-22-222-2-200002i−2i2i−2i02i−2i002-202-20002i−2i00−2−222−i2−i2i2i2−22−22−i2i2−i2i20000000000000000
χ392-22-222-2-200002i−2i2i−2i02i−2i002-20-22000−2i2i0022−2−2i2i2−i2−i2−22−22−i2i2−i2i20000000000000000
χ402-22-222-2-200002i−2i2i−2i02i−2i002-20-22000−2i2i00−2−222−i2−i2i2i22−22−2i2−i2i2−i20000000000000000
χ412-22-222-2-20000−2i2i−2i2i0−2i2i002-202-2000−2i2i0022−2−2−i2−i2i2i22−22−2−i2i2−i2i20000000000000000
χ422-22-222-2-20000−2i2i−2i2i0−2i2i002-202-2000−2i2i00−2−222i2i2−i2−i2−22−22i2−i2i2−i20000000000000000
χ432-22-222-2-20000−2i2i−2i2i0−2i2i002-20-220002i−2i0022−2−2−i2−i2i2i2−22−22i2−i2i2−i20000000000000000
χ442-22-222-2-20000−2i2i−2i2i0−2i2i002-20-220002i−2i00−2−222i2i2−i2−i22−22−2−i2i2−i2i20000000000000000
χ454444-4-4-4-44-44-40000000000000000000002-22-22-22-2000000000000000000000000
χ464444-4-4-4-44-44-4000000000000000000000-22-22-22-22000000000000000000000000
χ474444-4-4-4-4-44-440000000000000000000002-22-2-22-22000000000000000000000000
χ484444-4-4-4-4-44-44000000000000000000000-22-222-22-2000000000000000000000000
χ4944-4-44-4-444i4i−4i−4i−4i−4i4i4i000-4400000000000000000000000000000000000000000000
χ5044-4-44-4-44−4i−4i4i4i4i4i−4i−4i000-4400000000000000000000000000000000000000000000
χ5144-4-4-444-44i−4i−4i4i00000000000000000000000000000000000000000002-2002i−2i0000
χ5244-4-4-444-44i−4i−4i4i0000000000000000000000000000000000000000000-2200−2i2i0000
χ5344-4-4-444-4−4i4i4i−4i00000000000000000000000000000000000000000002-200−2i2i0000
χ5444-4-4-444-4−4i4i4i−4i0000000000000000000000000000000000000000000-22002i−2i0000
χ554-44-444-4-400004i−4i4i−4i0−4i4i00-44000000000000000000000000000000000000000000
χ564-44-444-4-40000−4i4i−4i4i04i−4i00-44000000000000000000000000000000000000000000
χ574-44-4-4-444000000004000000-400000000000002i2−2i2−2i22i2000000000000000000000000
χ584-44-4-4-444000000004000000-40000000000000−2i22i22i2−2i2000000000000000000000000
χ594-44-4-4-44400000000-4000000400000000022−22−22220000000000000000000000000000
χ604-44-4-4-44400000000-40000004000000000−222222−220000000000000000000000000000
χ614-4-444-44-400004-4-4400000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ624-4-444-44-400004-4-440000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ634-4-444-44-40000-444-400000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ644-4-444-44-40000-444-40000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ658-8-88-88-88000000000000000000000000000000000000000000000000000000000

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