Finite Group Databasebeta

← Group #147802

Character table — Group #147802

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222244444444444488888888888816161616161616161616161616161616161616161616
order12442224442222224444448888888888882244444488888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11-11-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-11-11-1-111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-11111-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111111111-1-1-1-1
χ911-1-1-1-11-111111-1-1-1111-1-1-1iiii−i−i−i−i11-1-111-1-11-11-11-1ii−i−iii−i−iii−i−i
χ1011-1-1-1-11-111111-1-1-1111-1-1-1iiii−i−i−i−i11-1-1-1-111-11-111-1ii−i−i−i−iii−i−iii
χ1111-1-1-1-11-111111-1-1-1111-1-1-1iiii−i−i−i−i-1-1111-1-111-1-11-11−i−iiiii−i−i−i−iii
χ1211-1-1-1-11-111111-1-1-1111-1-1-1iiii−i−i−i−i-1-111-111-1-111-1-11−i−iii−i−iiiii−i−i
χ1311-1-1-1-11-111111-1-1-1111-1-1-1−i−i−i−iiiii11-1-111-1-11-11-11-1−i−iii−i−iii−i−iii
χ1411-1-1-1-11-111111-1-1-1111-1-1-1−i−i−i−iiiii11-1-1-1-111-11-111-1−i−iiiii−i−iii−i−i
χ1511-1-1-1-11-111111-1-1-1111-1-1-1−i−i−i−iiiii-1-1111-1-111-1-11-11ii−i−i−i−iiiii−i−i
χ1611-1-1-1-11-111111-1-1-1111-1-1-1−i−i−i−iiiii-1-111-111-1-111-1-11ii−i−iii−i−i−i−iii
χ1722222222222-2-22-2-22-2-22-2-2000000000000020200-2-200000000000000
χ1822222222222-2-22-2-22-2-22-2-20000000000000-20-2002200000000000000
χ192222222222-22-2-22-2-22-2-22-20000000000002020-2-20000000000000000
χ202222222222-22-2-22-2-22-2-22-2000000000000-20-20220000000000000000
χ212222222222-2-22-2-22-2-22-2-2200000000222200000000-2-2000000000000
χ222222222222-2-22-2-22-2-22-2-2200000000-2-2-2-20000000022000000000000
χ232222-2-222-2-222-2-2-22-2-2222-222-2-222-2-200000000000000000000000000
χ242222-2-222-2-222-2-2-22-2-2222-2-2-222-2-22200000000000000000000000000
χ252222-2-222-2-22-22-22-2-22-22-220000000000000000000000000000002-22-2
χ262222-2-222-2-22-22-22-2-22-22-22000000000000000000000000000000-22-22
χ272222-2-222-2-2-2222-2-22-2-2-222000000000000000000000000002-22-20000
χ282222-2-222-2-2-2222-2-22-2-2-22200000000000000000000000000-22-220000
χ292222-2-222-2-2-2-2-2222222-2-2-200000000000000000000002i−2i2i−2i00000000
χ302222-2-222-2-2-2-2-2222222-2-2-20000000000000000000000−2i2i−2i2i00000000
χ3122-2-2222-2-2-222-222-2-2-22-2-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ3222-2-2222-2-2-222-222-2-2-22-2-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ3322-2-2222-2-2-22-222-22-22-2-22-20000000000000000000000000000002i−2i−2i2i
χ3422-2-2222-2-2-22-222-22-22-2-22-2000000000000000000000000000000−2i2i2i−2i
χ3522-2-2222-2-2-2-222-2222-2-22-2-2000000000000000000000000002i−2i−2i2i0000
χ3622-2-2222-2-2-2-222-2222-2-22-2-200000000000000000000000000−2i2i2i−2i0000
χ3722-2-2222-2-2-2-2-2-2-2-2-222222200000000000000000000002-2-2200000000
χ3822-2-2222-2-2-2-2-2-2-2-2-22222220000000000000000000000-222-200000000
χ3922-2-2-2-22-2222-2-2-2222-2-2-222000000000000020-200-2200000000000000
χ4022-2-2-2-22-2222-2-2-2222-2-2-2220000000000000-202002-200000000000000
χ4122-2-2-2-22-222-22-22-22-22-22-2200000000000020-20-220000000000000000
χ4222-2-2-2-22-222-22-22-22-22-22-22000000000000-20202-20000000000000000
χ4322-2-2-2-22-222-2-2222-2-2-2222-20000000022-2-200000000-22000000000000
χ4422-2-2-2-22-222-2-2222-2-2-2222-200000000-2-222000000002-2000000000000
χ4544444-4-4-44-40000000000002-22-22-22-200000000000000000000000000
χ4644444-4-4-44-4000000000000-22-22-22-2200000000000000000000000000
χ474444-44-4-4-440000000000002-2-222-2-2200000000000000000000000000
χ484444-44-4-4-44000000000000-222-2-222-200000000000000000000000000
χ4944-4-44-4-44-440000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ5044-4-44-4-44-44000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5144-4-4-44-444-40000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ5244-4-4-44-444-4000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ538-88i−8i0000000000000000000000000022−222i2−2i20000000000000000000000
χ548-88i−8i00000000000000000000000000−2222−2i22i20000000000000000000000
χ558-8−8i8i0000000000000000000000000022−22−2i22i20000000000000000000000
χ568-8−8i8i00000000000000000000000000−22222i2−2i20000000000000000000000

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