Finite Group Databasebeta

← Group #170308

Character table — Group #170308

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444448888888888888888888888881616161616161616161616163232
order12222222444444444444444444444444888888888888888824444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-11-1-11111-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-11-1-1-1-1-1-111
χ5111111111111111111111111-1-1-1-111111111111111111111-1-11-1-1-11-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-111-1-11-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-111111-1-1
χ911111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-11111-111-1-11-1
χ1011111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-11111-1-1-111-11
χ1111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111-11-1-11-1111-1-1-11
χ1211111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111111111-1-1-1-11-11-1-11-11-1-1111-1
χ1311111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-11
χ1411111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-11-1
χ1511111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1111111-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1111-1
χ1611111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111111111-1-1-1-1-11111-1-1-111-1-1-11
χ1722222222222222-2-2-2-222-2-2-2-200002222000000000000000000-2000-20000000
χ1822222222222222-2-2-2-222-2-2-2-20000-2-2-2-2000000000000000000200020000000
χ19222222222222-2-222-2-2-2-222-2-20000000000000000000000002002-200-2000000
χ20222222222222-2-222-2-2-2-222-2-2000000000000000000000000-200-22002000000
χ21222222222222-2-2-2-222-2-2-2-2222222000000000000000000000-2000-200000000
χ22222222222222-2-2-2-222-2-2-2-222-2-2-2-20000000000000000000002000200000000
χ2322222222-2-2-2-22222-2-2-2-2-2-22222-2-20000000000000000000002000-200000000
χ2422222222-2-2-2-22222-2-2-2-2-2-222-2-222000000000000000000000-2000200000000
χ2522222222-2-2-2-222-2-222-2-222-2-2000000000000000000000000200-2200-2000000
χ2622222222-2-2-2-222-2-222-2-222-2-2000000000000000000000000-2002-2002000000
χ2722222222-2-2-2-2-2-2222222-2-2-2-2000022-2-20000000000000000002000-20000000
χ2822222222-2-2-2-2-2-2222222-2-2-2-20000-2-222000000000000000000-200020000000
χ2922-2-2-2-2222i2i−2i−2i2i−2i00002-2000000002i−2i2-222−2−2i2i2−i2−i2i2i2−i2−i222−2−200000000000000
χ3022-2-2-2-2222i2i−2i−2i2i−2i00002-2000000002i−2i2-2−2−222−i2−i2i2i2−i2−i2i2i2−2−22200000000000000
χ3122-2-2-2-2222i2i−2i−2i2i−2i00002-200000000−2i2i-2222−2−2i2i2−i2−i2−i2−i2i2i2−2−22200000000000000
χ3222-2-2-2-2222i2i−2i−2i2i−2i00002-200000000−2i2i-22−2−222−i2−i2i2i2i2i2−i2−i222−2−200000000000000
χ3322-2-2-2-222−2i−2i2i2i−2i2i00002-2000000002i−2i-2222−2−2−i2−i2i2i2i2i2−i2−i2−2−22200000000000000
χ3422-2-2-2-222−2i−2i2i2i−2i2i00002-2000000002i−2i-22−2−222i2i2−i2−i2−i2−i2i2i222−2−200000000000000
χ3522-2-2-2-222−2i−2i2i2i−2i2i00002-200000000−2i2i2-222−2−2−i2−i2i2i2−i2−i2i2i222−2−200000000000000
χ3622-2-2-2-222−2i−2i2i2i−2i2i00002-200000000−2i2i2-2−2−222i2i2−i2−i2i2i2−i2−i2−2−22200000000000000
χ372-222-2-22-22i−2i2i−2i00002i−2i00002-22i−2i2-20000i2−i2i2−i22−22−200000000000000002−2i2−i200
χ382-222-2-22-22i−2i2i−2i00002i−2i00002-22i−2i2-20000−i2i2−i2i2−22−220000000000000000−22−i2i200
χ392-222-2-22-22i−2i2i−2i00002i−2i00002-2−2i2i-220000i2−i2i2−i22−22−20000000000000000−22−i2i200
χ402-222-2-22-22i−2i2i−2i00002i−2i00002-2−2i2i-220000−i2i2−i2i2−22−2200000000000000002−2i2−i200
χ412-222-2-22-2−2i2i−2i2i0000−2i2i00002-22i−2i-220000i2−i2i2−i2−22−2200000000000000002−2−i2i200
χ422-222-2-22-2−2i2i−2i2i0000−2i2i00002-22i−2i-220000−i2i2−i2i22−22−20000000000000000−22i2−i200
χ432-222-2-22-2−2i2i−2i2i0000−2i2i00002-2−2i2i2-20000i2−i2i2−i2−22−220000000000000000−22i2−i200
χ442-222-2-22-2−2i2i−2i2i0000−2i2i00002-2−2i2i2-20000−i2i2−i2i22−22−200000000000000002−2−i2i200
χ4544-4-4-4-4444i4i−4i−4i−4i4i0000-44000000000000000000000000000000000000000000
χ4644-4-4-4-444−4i−4i4i4i4i−4i0000-44000000000000000000000000000000000000000000
χ474-444-4-44-44i−4i4i−4i0000−4i4i0000-4400000000000000000000000000000000000000
χ484-444-4-44-4−4i4i−4i4i00004i−4i0000-4400000000000000000000000000000000000000
χ494-44-44-4-440000004i−4i0000000000000000000000002-22-22i−2i2i−2i00000000000000
χ504-44-44-4-440000004i−4i000000000000000000000000-22-22−2i2i−2i2i00000000000000
χ514-44-44-4-44000000−4i4i0000000000000000000000002-22-2−2i2i−2i2i00000000000000
χ524-44-44-4-44000000−4i4i000000000000000000000000-22-222i−2i2i−2i00000000000000
χ534-4-44-44-440000000000004-40000000000000000002i2−2i2−2i22i2000000000000000000
χ544-4-44-44-440000000000004-4000000000000000000−2i22i22i2−2i2000000000000000000
χ554-4-44-44-44000000000000-4400000000000000000000002i2−2i2−2i22i200000000000000
χ564-4-44-44-44000000000000-440000000000000000000000−2i22i22i2−2i200000000000000
χ574-4-4-4444-44-4-44000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ584-4-4-4444-44-4-4400000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ594-4-4-4444-4-444-4000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ604-4-4-4444-4-444-400000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ61888-8-88-8-8000000000000000000000000000000000000000000000000000000
χ6288-888-8-8-8000000000000000000000000000000000000000000000000000000

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