Finite Group Databasebeta

← Group #167652

Character table — Group #167652

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
χ311111111111111111111111111111-1-1-1-11111111111111111-1-1-11-1-1-1-11-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1111111
χ5111111111111111111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1
χ6111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-111-1-1-11-1-11111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-11111-1111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11-1-11111111-1-1-111-1-11111-1-1-1-11111-1-1-1-1-111-1-1-11111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-11-1-11111111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-111-1-1-1-1-11111-1-111
χ1111111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-1-111-1-11-111-1-111
χ1211111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-111-1-1-1-11111-1-1-1-111111-1-1-111111-1-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-11-1-111111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-11-111111-1-1-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-11-1-111111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-1111-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-11-1-111111-1-1-111-1-1111111-1-1-1-1-1-1-1-111111-111-1-1-1-1-111111-1-1
χ1611111111-1-1-1-1-1-1-1-11-1-111111-1-1-111-1-111-1-1-1-111111111-1-1-1-11-111-1-111-11-1-1-1-111
χ172222222222222222-2-2-222-2-2-200-20022220000000000000000-2-200000000000000
χ182222222222222222-2-2-222-2-2-200-200-2-2-2-200000000000000002200000000000000
χ19222222222222-2-2-2-22-2-2-2-2-2-22002000000000000000000000000202-2000-2000000
χ20222222222222-2-2-2-22-2-2-2-2-2-22002000000000000000000000000-20-220002000000
χ21222222222222-2-2-2-2-222-2-222-222-22200000000000000000000000-20000-20000000
χ22222222222222-2-2-2-2-222-2-222-2-2-2-2-2-2000000000000000000000002000020000000
χ2322222222-2-2-2-22222222-2-2-2-2200-200000000000000000000000020-22000-2000000
χ2422222222-2-2-2-22222222-2-2-2-2200-2000000000000000000000000-202-20002000000
χ2522222222-2-2-2-22222-2-2-2-2-222-2222-2-20000000000000000000000020000-20000000
χ2622222222-2-2-2-22222-2-2-2-2-222-2-2-222200000000000000000000000-2000020000000
χ2722222222-2-2-2-2-2-2-2-2-22222-2-2-20020022-2-200000000000000002-200000000000000
χ2822222222-2-2-2-2-2-2-2-2-22222-2-2-200200-2-2220000000000000000-2200000000000000
χ2922-2-22-2-222i2i−2i−2i2i2i−2i−2i0002-2000000002-22i−2i00000000i2i2−i2−i222−2−2000000000000i2−i22−2
χ3022-2-22-2-222i2i−2i−2i2i2i−2i−2i0002-2000000002-22i−2i00000000−i2−i2i2i2−2−222000000000000−i2i2−22
χ3122-2-22-2-222i2i−2i−2i2i2i−2i−2i0002-200000000-22−2i2i00000000i2i2−i2−i222−2−2000000000000−i2i2−22
χ3222-2-22-2-222i2i−2i−2i2i2i−2i−2i0002-200000000-22−2i2i00000000−i2−i2i2i2−2−222000000000000i2−i22−2
χ3322-2-22-2-22−2i−2i2i2i−2i−2i2i2i0002-2000000002-2−2i2i00000000i2i2−i2−i2−2−222000000000000i2−i2−22
χ3422-2-22-2-22−2i−2i2i2i−2i−2i2i2i0002-2000000002-2−2i2i00000000−i2−i2i2i222−2−2000000000000−i2i22−2
χ3522-2-22-2-22−2i−2i2i2i−2i−2i2i2i0002-200000000-222i−2i00000000i2i2−i2−i2−2−222000000000000−i2i22−2
χ3622-2-22-2-22−2i−2i2i2i−2i−2i2i2i0002-200000000-222i−2i00000000−i2−i2i2i222−2−2000000000000i2−i2−22
χ3722-2-2-222-22i−2i2i−2i000002i−2i002-202-202i−2i0000i2i2−i2−i222−2−2i2−i2i2−i22−22−20000000000000000
χ3822-2-2-222-22i−2i2i−2i000002i−2i002-202-202i−2i0000−i2−i2i2i2−2−222−i2i2−i2i2−22−220000000000000000
χ3922-2-2-222-22i−2i2i−2i000002i−2i002-20-220−2i2i0000i2i2−i2−i222−2−2−i2i2−i2i2−22−220000000000000000
χ4022-2-2-222-22i−2i2i−2i000002i−2i002-20-220−2i2i0000−i2−i2i2i2−2−222i2−i2i2−i22−22−20000000000000000
χ4122-2-2-222-2−2i2i−2i2i00000−2i2i002-202-20−2i2i0000i2i2−i2−i2−2−222i2−i2i2−i2−22−220000000000000000
χ4222-2-2-222-2−2i2i−2i2i00000−2i2i002-202-20−2i2i0000−i2−i2i2i222−2−2−i2i2−i2i22−22−20000000000000000
χ4322-2-2-222-2−2i2i−2i2i00000−2i2i002-20-2202i−2i0000i2i2−i2−i2−2−222−i2i2−i2i22−22−20000000000000000
χ4422-2-2-222-2−2i2i−2i2i00000−2i2i002-20-2202i−2i0000−i2−i2i2i222−2−2i2−i2i2−i2−22−220000000000000000
χ454444-4-4-4-44-4-44000000000000000000000000000002-2-222-2-220000000000000000
χ464444-4-4-4-44-4-4400000000000000000000000000000-222-2-222-20000000000000000
χ474444-4-4-4-4-444-4000000000000000000000000000002-2-22-222-20000000000000000
χ484444-4-4-4-4-444-400000000000000000000000000000-222-22-2-220000000000000000
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−4i4i−4i00000−4i4i00-44000000000000000000000000000000000000000000
χ5244-4-4-444-4−4i4i−4i4i000004i−4i00-44000000000000000000000000000000000000000000
χ534-44-444-4-400004-44-4000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ544-44-444-4-400004-44-400000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ554-44-444-4-40000-44-44000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ564-44-444-4-40000-44-4400000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ574-4-444-44-400004i−4i−4i4i0000000000000000000000000000000000000002-2002i−2i0000
χ584-4-444-44-400004i−4i−4i4i000000000000000000000000000000000000000-2200−2i2i0000
χ594-4-444-44-40000−4i4i4i−4i0000000000000000000000000000000000000002-200−2i2i0000
χ604-4-444-44-40000−4i4i4i−4i000000000000000000000000000000000000000-22002i−2i0000
χ614-4-44-44-44000000004000000-400000000000002i2−2i2−2i22i2000000000000000000000000
χ624-4-44-44-44000000004000000-40000000000000−2i22i22i2−2i2000000000000000000000000
χ634-4-44-44-4400000000-4000000400000000022−22−22220000000000000000000000000000
χ644-4-44-44-4400000000-40000004000000000−222222−220000000000000000000000000000
χ658-88-8-8-888000000000000000000000000000000000000000000000000000000000

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