Finite Group Databasebeta

← Group #9711

Character table — Group #9711

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11111111222222222222222244444444444444444444448888888816161616
order1222222222224444444444444444444444444444444444888888884444
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ6111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ7111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ8111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ911111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-1
χ1011111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111
χ1111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111
χ1211111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-1
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ1722222222222222222222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000
χ1922222222-2-2-2-22222-2-2-2-22222-2-222-2-20000000000000000000000000000
χ2022222222-2-2-2-2-2-2-2-22222222222-2-2-2-20000000000000000000000000000
χ21222-22-2-2-222-2-222-2-222-2-2000000000000000000000000002−22−22−22−20000
χ22222-22-2-2-222-2-222-2-222-2-200000000000000000000000000−22−22−22−220000
χ23222-22-2-2-222-2-2-2-222-2-222000000000000000000000000002−22−2−22−220000
χ24222-22-2-2-222-2-2-2-222-2-22200000000000000000000000000−22−222−22−20000
χ25222-22-2-2-2-2-22222-2-2-2-22200000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ26222-22-2-2-2-2-22222-2-2-2-22200000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ27222-22-2-2-2-2-222-2-22222-2-200000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ28222-22-2-2-2-2-222-2-22222-2-200000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ2922-2-2-222-2000000002i−2i2i−2i2i−2i2i−2i2-200001+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ3022-2-2-222-2000000002i−2i2i−2i2i−2i2i−2i2-20000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ3122-2-2-222-2000000002i−2i2i−2i−2i2i−2i2i-2200001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ3222-2-2-222-2000000002i−2i2i−2i−2i2i−2i2i-220000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ3322-2-2-222-200000000−2i2i−2i2i2i−2i2i−2i-2200001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ3422-2-2-222-200000000−2i2i−2i2i2i−2i2i−2i-220000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ3522-2-2-222-200000000−2i2i−2i2i−2i2i−2i2i2-200001−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ3622-2-2-222-200000000−2i2i−2i2i−2i2i−2i2i2-20000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ372-22-2-2-2222-22-20000000022-2-200002-2000000002i−2i2i−2i2i−2i2i−2i000000000000
χ382-22-2-2-2222-22-20000000022-2-200002-200000000−2i2i−2i2i−2i2i−2i2i000000000000
χ392-22-2-2-2222-22-200000000-2-2220000-222-22-22-22-200000000000000000000
χ402-22-2-2-2222-22-200000000-2-2220000-22-22-22-22-2200000000000000000000
χ412-22-2-2-222-22-220000000022-2-20000-222i−2i2i−2i−2i2i−2i2i00000000000000000000
χ422-22-2-2-222-22-220000000022-2-20000-22−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ432-22-2-2-222-22-2200000000-2-22200002-2000000002-22-2-22-22000000000000
χ442-22-2-2-222-22-2200000000-2-22200002-200000000-22-222-22-2000000000000
χ452-2-222-22-200002-22-200002i−2i−2i2i002i−2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ462-2-222-22-200002-22-200002i−2i−2i2i002i−2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ472-2-222-22-200002-22-20000−2i2i2i−2i00−2i2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ482-2-222-22-200002-22-20000−2i2i2i−2i00−2i2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ492-2-222-22-20000-22-2200002i−2i−2i2i00−2i2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ502-2-222-22-20000-22-2200002i−2i−2i2i00−2i2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ512-2-222-22-20000-22-220000−2i2i2i−2i002i−2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ522-2-222-22-20000-22-220000−2i2i2i−2i002i−2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ5344-44-4-4-44000000004i−4i−4i4i00000000000000000000000000000000000000
χ5444-44-4-4-4400000000−4i4i4i−4i00000000000000000000000000000000000000
χ554-444-44-4-44-4-440000000000000000000000000000000000000000000000
χ564-444-44-4-4-444-40000000000000000000000000000000000000000000000
χ574-4-4-444-4400004-4-44000000000000000000000000000000000000000000
χ584-4-4-444-440000-444-4000000000000000000000000000000000000000000

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