Finite Group Databasebeta

← Group #116298

Character table — Group #116298

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222222222222444444444444444444444444448888888888888888444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111
χ911-1-1-1-11111111-1-1-1-11-1-111-1-111-1-1-11ii−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-11-11-1ii−i−iii−i−i
χ1011-1-1-1-11111111-1-1-1-11-1-111-1-111-1-1-11ii−i−i1111-1-1-1-1ii−i−i−i−i−i−iiiii-1-1-1-11111-11-11−i−iiiii−i−i
χ1111-1-1-1-11111111-1-1-1-11-1-111-1-111-1-1-11ii−i−i-1-1-1-11111ii−i−iiiii−i−i−i−i1111-1-1-1-1-11-11−i−iii−i−iii
χ1211-1-1-1-11111111-1-1-1-11-1-111-1-111-1-1-11ii−i−i-1-1-1-11111ii−i−i−i−i−i−iiiii-1-1-1-111111-11-1ii−i−i−i−iii
χ1311-1-1-1-11111111-1-1-1-11-1-111-1-111-1-1-11−i−iii1111-1-1-1-1−i−iiiiiii−i−i−i−i-1-1-1-11111-11-11ii−i−i−i−iii
χ1411-1-1-1-11111111-1-1-1-11-1-111-1-111-1-1-11−i−iii1111-1-1-1-1−i−iii−i−i−i−iiiii1111-1-1-1-11-11-1−i−iii−i−iii
χ1511-1-1-1-11111111-1-1-1-11-1-111-1-111-1-1-11−i−iii-1-1-1-11111−i−iiiiiii−i−i−i−i-1-1-1-111111-11-1−i−iiiii−i−i
χ1611-1-1-1-11111111-1-1-1-11-1-111-1-111-1-1-11−i−iii-1-1-1-11111−i−iii−i−i−i−iiiii1111-1-1-1-1-11-11ii−i−iii−i−i
χ1722222222222222222222-2-2-2-2-2-2-2-2-2-2222200000000-2-2-2-20000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000000000000000000000000
χ192222222222-2-2-222-2-2-2-2-22222-2-22-2-220000000000000000000000000000000000002i−2i2i−2i0000
χ202222222222-2-2-222-2-2-2-2-22222-2-22-2-22000000000000000000000000000000000000−2i2i−2i2i0000
χ212222222222-2-2-222-2-2-2-2-2-2-2-2-222-222-20000000000000000000000000000000022-2-200000000
χ222222222222-2-2-222-2-2-2-2-2-2-2-2-222-222-200000000000000000000000000000000-2-22200000000
χ2322222222-2-222-2-2-22-2-22-222222-2-22-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2422222222-2-222-2-2-22-2-22-222222-2-22-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2522222222-2-222-2-2-22-2-22-2-2-2-2-2-222-22200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2622222222-2-222-2-2-22-2-22-2-2-2-2-2-222-2220000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2722222222-2-2-2-22-2-2-222-222222-22-2-22-200000000000000000000000000000000000000002-22-2
χ2822222222-2-2-2-22-2-2-222-222222-22-2-22-20000000000000000000000000000000000000000-22-22
χ2922222222-2-2-2-22-2-2-222-22-2-2-2-22-222-22000022-2-222-2-200000000000000000000000000000000
χ3022222222-2-2-2-22-2-2-222-22-2-2-2-22-222-220000-2-222-2-22200000000000000000000000000000000
χ312222-2-2-2-22-22-222-222-2-2-200000000002-22-20000000000002−22−22−22−22−22−22−22−2000000000000
χ322222-2-2-2-22-22-222-222-2-2-200000000002-22-2000000000000−22−22−22−22−22−22−22−22000000000000
χ332222-2-2-2-22-22-222-222-2-2-20000000000-22-220000000000002−22−22−22−2−22−22−22−22000000000000
χ342222-2-2-2-22-22-222-222-2-2-20000000000-22-22000000000000−22−22−22−222−22−22−22−2000000000000
χ352222-2-2-2-2-222-2-2-222-22-2200000000000000000000002-22-2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ362222-2-2-2-2-222-2-2-222-22-2200000000000000000000002-22-2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ372222-2-2-2-2-222-2-2-222-22-220000000000000000000000-22-22i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ382222-2-2-2-2-222-2-2-222-22-220000000000000000000000-22-22−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ3922-2-222-2-22-22-22-22-2-2-22200000000002i−2i−2i2i000000000000i2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000
χ4022-2-222-2-22-22-22-22-2-2-22200000000002i−2i−2i2i000000000000−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000
χ4122-2-222-2-22-22-22-22-2-2-2220000000000−2i2i2i−2i000000000000i2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000
χ4222-2-222-2-22-22-22-22-2-2-2220000000000−2i2i2i−2i000000000000−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000
χ4322-2-222-2-2-222-2-22-2-2222-200000000000000000000002i−2i−2i2i2−2−22−222−2−i2i2i2−i2i2−i2−i2i2000000000000
χ4422-2-222-2-2-222-2-22-2-2222-200000000000000000000002i−2i−2i2i−222−22−2−22i2−i2−i2i2−i2i2i2−i2000000000000
χ4522-2-222-2-2-222-2-22-2-2222-20000000000000000000000−2i2i2i−2i2−2−22−222−2i2−i2−i2i2−i2i2i2−i2000000000000
χ4622-2-222-2-2-222-2-22-2-2222-20000000000000000000000−2i2i2i−2i−222−22−2−22−i2i2i2−i2i2−i2−i2i2000000000000
χ4722-2-2-2-22222222-2-2-2-22-2-2-2-222-2-2222-22i2i−2i−2i00000000−2i−2i2i2i0000000000000000000000000000
χ4822-2-2-2-22222222-2-2-2-22-2-2-2-222-2-2222-2−2i−2i2i2i000000002i2i−2i−2i0000000000000000000000000000
χ4922-2-2-2-22222-2-2-2-2-222-22222-2-2-2-2-22220000000000000000000000000000000000002-2-220000
χ5022-2-2-2-22222-2-2-2-2-222-22222-2-2-2-2-2222000000000000000000000000000000000000-222-20000
χ5122-2-2-2-22222-2-2-2-2-222-222-2-222222-2-2-2000000000000000000000000000000002-2-2200000000
χ5222-2-2-2-22222-2-2-2-2-222-222-2-222222-2-2-200000000000000000000000000000000-222-200000000
χ5322-2-2-2-222-2-222-222-22-2-2222-2-22-22-22-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ5422-2-2-2-222-2-222-222-22-2-2222-2-22-22-22-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ5522-2-2-2-222-2-222-222-22-2-22-2-222-22-22-22000000000000000022-2-2-2-22200000000000000000000
χ5622-2-2-2-222-2-222-222-22-2-22-2-222-22-22-220000000000000000-2-22222-2-200000000000000000000
χ5722-2-2-2-222-2-2-2-22222-222-222-2-2-2222-2-200000000000000000000000000000000000000002i−2i−2i2i
χ5822-2-2-2-222-2-2-2-22222-222-222-2-2-2222-2-20000000000000000000000000000000000000000−2i2i2i−2i
χ5922-2-2-2-222-2-2-2-22222-222-2-2-2222-2-2-222000022-2-2-2-22200000000000000000000000000000000
χ6022-2-2-2-222-2-2-2-22222-222-2-2-2222-2-2-2220000-2-22222-2-200000000000000000000000000000000
χ614444-4-4-4-44-4-44-44-4-4-4444000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-44-444-44-44-44-4000000000000000000000000000000000000000000000000000000
χ6344-4-444-4-44-4-44-4-44444-4-4000000000000000000000000000000000000000000000000000000
χ6444-4-444-4-4-44-4444-44-4-4-44000000000000000000000000000000000000000000000000000000
χ654-44-44-44-40000000000004i−4i4i−4i00000000002-22i−2i2-22i−2i00000000000000000000000000000000
χ664-44-44-44-40000000000004i−4i4i−4i0000000000-22−2i2i-22−2i2i00000000000000000000000000000000
χ674-44-44-44-4000000000000−4i4i−4i4i00000000002-2−2i2i2-2−2i2i00000000000000000000000000000000
χ684-44-44-44-4000000000000−4i4i−4i4i0000000000-222i−2i-222i−2i00000000000000000000000000000000
χ694-4-44-444-40000000000004i−4i−4i4i00000000002-22i−2i-22−2i2i00000000000000000000000000000000
χ704-4-44-444-40000000000004i−4i−4i4i0000000000-22−2i2i2-22i−2i00000000000000000000000000000000
χ714-4-44-444-4000000000000−4i4i4i−4i00000000002-2−2i2i-222i−2i00000000000000000000000000000000
χ724-4-44-444-4000000000000−4i4i4i−4i0000000000-222i−2i2-2−2i2i00000000000000000000000000000000
χ738-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000
χ748-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000

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