Finite Group Databasebeta

← Group #256997

Character table — Group #256997

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444448888888888888888888888161616161616161616161616161616161616
order12222222444444444444442444444444444488888888224444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-11-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-111-1-1-1-11111
χ511111111111111111111111-1-11-1-11111-1-1-1-111111111-11-1-1-11-1-1-1-1-1-1-1-11111
χ611111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1111111-1-1-1-1
χ711111111111111111111111-1-11-1-1-1-1-1-1111111111111-1-111-1-11111-1-1-1-1-1-1-1-1
χ811111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111
χ911111111111111111-1-1-1-11-111-1-1-111-1-111111111-1-1-1-1-11111-1-1-1-1-111-1-111-1-1
χ1011111111111111111-1-1-1-11-111-1-1-111-1-11111-1-1-1-11111-11-1-11-1-1-111-1-111-1-111
χ1111111111111111111-1-1-1-11-111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111
χ1211111111111111111-1-1-1-11-111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1
χ1411111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111
χ1511111111111111111-1-1-1-11-1-1-1-111-1-11111111111-1-1-1-11-111-11-1-1-1-1-1-111-1-111
χ1611111111111111111-1-1-1-11-1-1-1-111-1-1111111-1-1-1-111111-1-1-1-11-1-11111-1-111-1-1
χ172222222222-2-222-2-2-22222-2-222-2220000000000000000-2000-20000000000000
χ182222222222-2-222-2-2-22222-2-2-2-2-2-2-20000000000000000200020000000000000
χ192222222222-2-222-2-2-2-2-2-2-2-22222-2-200000000000000002000-20000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-22-2-22220000000000000000-200020000000000000
χ2122222222-2-222-2-222-222-2-2-2-20020022220000000000000-2000-2000000000000
χ2222222222-2-222-2-222-222-2-2-2-200200-2-2-2-2000000000000020002000000000000
χ2322222222-2-222-2-222-2-2-222-2200-20022-2-20000000000000-20002000000000000
χ2422222222-2-222-2-222-2-2-222-2200-200-2-22200000000000002000-2000000000000
χ2522222222-2-2-2-2-2-2-2-2222-2-22200-200000022-2-2000000000000002-20000000000
χ2622222222-2-2-2-2-2-2-2-2222-2-22200-2000000-2-22200000000000000-220000000000
χ2722222222-2-2-2-2-2-2-2-22-2-2222-200200000022-2-200000000000000-220000000000
χ2822222222-2-2-2-2-2-2-2-22-2-2222-2002000000-2-222000000000000002-20000000000
χ2922-222-2-2-22-22-22-22-2-20000200000000002i−2i2i−2i000022-2-2000000002i−2i00000000
χ3022-222-2-2-22-22-22-22-2-20000200000000002i−2i2i−2i0000-2-22200000000−2i2i00000000
χ3122-222-2-2-22-22-22-22-2-2000020000000000−2i2i−2i2i000022-2-200000000−2i2i00000000
χ3222-222-2-2-22-22-22-22-2-2000020000000000−2i2i−2i2i0000-2-222000000002i−2i00000000
χ3322-222-2-2-2-22-22-22-22-20000200000000002i−2i−2i2i22-2-20000002i−2i00000000000000
χ3422-222-2-2-2-22-22-22-22-20000200000000002i−2i−2i2i-2-222000000−2i2i00000000000000
χ3522-222-2-2-2-22-22-22-22-2000020000000000−2i2i2i−2i22-2-2000000−2i2i00000000000000
χ3622-222-2-2-2-22-22-22-22-2000020000000000−2i2i2i−2i-2-2220000002i−2i00000000000000
χ372-222-2-22-2-22002-20002i−2i2i−2i002-202i−2i00000000i2−i2i2−i22−22−20000000000i2−i22−20000
χ382-222-2-22-2-22002-20002i−2i2i−2i002-202i−2i00000000−i2i2−i2i2−22−220000000000−i2i2−220000
χ392-222-2-22-2-22002-20002i−2i2i−2i00-220−2i2i00000000i2−i2i2−i22−22−20000000000−i2i2−220000
χ402-222-2-22-2-22002-20002i−2i2i−2i00-220−2i2i00000000−i2i2−i2i2−22−220000000000i2−i22−20000
χ412-222-2-22-2-22002-2000−2i2i−2i2i002-20−2i2i00000000i2−i2i2−i2−22−220000000000i2−i2−220000
χ422-222-2-22-2-22002-2000−2i2i−2i2i002-20−2i2i00000000−i2i2−i2i22−22−20000000000−i2i22−20000
χ432-222-2-22-2-22002-2000−2i2i−2i2i00-2202i−2i00000000i2−i2i2−i2−22−220000000000−i2i22−20000
χ442-222-2-22-2-22002-2000−2i2i−2i2i00-2202i−2i00000000−i2i2−i2i22−22−20000000000i2−i2−220000
χ4544-444-4-4-44-4-444-4-4440000-40000000000000000000000000000000000000000
χ4644-444-4-4-4-444-4-444-440000-40000000000000000000000000000000000000000
χ474-444-4-44-44-400-440004i−4i−4i4i00000000000000000000000000000000000000000
χ484-444-4-44-44-400-44000−4i4i4i−4i00000000000000000000000000000000000000000
χ494-44-44-4-44004-400-44000000000000000000000000000000000000000000002i2−2i2
χ504-44-44-4-44004-400-4400000000000000000000000000000000000000000000−2i22i2
χ514-44-44-4-4400-44004-40000000000000000000000000000000000000000002i2−2i200
χ524-44-44-4-4400-44004-4000000000000000000000000000000000000000000−2i22i200
χ534-4-44-44-444400-4-400000000000000000000002i2−2i2−2i22i20000000000000000000000
χ544-4-44-44-444400-4-40000000000000000000000−2i22i22i2−2i20000000000000000000000
χ554-4-44-44-44-4-400440000000000000000000000000022−22−2222000000000000000000
χ564-4-44-44-44-4-4004400000000000000000000000000−222222−22000000000000000000
χ574-4-4-4444-4004400-4-40000000000004i−4i00000000000000000000000000000000
χ584-4-4-4444-4004400-4-4000000000000−4i4i00000000000000000000000000000000
χ594-4-4-4444-400-4-40044000000000000004-4000000000000000000000000000000
χ604-4-4-4444-400-4-4004400000000000000-44000000000000000000000000000000
χ61888-8-88-8-8000000000000000000000000000000000000000000000000000000
χ6288-8-8-8-888000000000000000000000000000000000000000000000000000000

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