Finite Group Databasebeta

← Group #8235

Character table — Group #8235

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1111111122222222222222222222444444444444444444448888888888888888
order1222222244444444444444444444444488888888888888884444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ6111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ7111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ8111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ911111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ17111-1-1-11-1ii−i−i11-1-1ii−i−iii−i−i11-1-1i−i1-111-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i1-1i−i1-1i−i
χ18111-1-1-11-1ii−i−i11-1-1ii−i−iii−i−i11-1-1i−i1-111-1-1ii−i−i11-1-1ii−i−i-11−ii-11−ii-11−ii-11−ii
χ19111-1-1-11-1ii−i−i11-1-1ii−i−iii−i−i11-1-1i−i1-1-1-111−i−iii-1-111−i−iii1-1i−i1-1i−i-11−ii-11−ii
χ20111-1-1-11-1ii−i−i11-1-1ii−i−iii−i−i11-1-1i−i1-1-1-111−i−iii-1-111−i−iii-11−ii-11−ii1-1i−i1-1i−i
χ21111-1-1-11-1ii−i−i-1-111−i−iiiii−i−i-1-111−ii1-1ii−i−i-1-111−i−iii11-1-11-1i−i-11−iii−i-11−ii1-1
χ22111-1-1-11-1ii−i−i-1-111−i−iiiii−i−i-1-111−ii1-1ii−i−i-1-111−i−iii11-1-1-11−ii1-1i−i−ii1-1i−i-11
χ23111-1-1-11-1ii−i−i-1-111−i−iiiii−i−i-1-111−ii1-1−i−iii11-1-1ii−i−i-1-1111-1i−i-11−ii−ii1-1i−i-11
χ24111-1-1-11-1ii−i−i-1-111−i−iiiii−i−i-1-111−ii1-1−i−iii11-1-1ii−i−i-1-111-11−ii1-1i−ii−i-11−ii1-1
χ25111-1-1-11-1−i−iii11-1-1−i−iii−i−iii11-1-1−ii1-111-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii1-1−ii1-1−ii
χ26111-1-1-11-1−i−iii11-1-1−i−iii−i−iii11-1-1−ii1-111-1-1−i−iii11-1-1−i−iii-11i−i-11i−i-11i−i-11i−i
χ27111-1-1-11-1−i−iii11-1-1−i−iii−i−iii11-1-1−ii1-1-1-111ii−i−i-1-111ii−i−i1-1−ii1-1−ii-11i−i-11i−i
χ28111-1-1-11-1−i−iii11-1-1−i−iii−i−iii11-1-1−ii1-1-1-111ii−i−i-1-111ii−i−i-11i−i-11i−i1-1−ii1-1−ii
χ29111-1-1-11-1−i−iii-1-111ii−i−i−i−iii-1-111i−i1-1ii−i−i11-1-1−i−iii-1-1111-1−ii-11i−ii−i1-1−ii-11
χ30111-1-1-11-1−i−iii-1-111ii−i−i−i−iii-1-111i−i1-1ii−i−i11-1-1−i−iii-1-111-11i−i1-1−ii−ii-11i−i1-1
χ31111-1-1-11-1−i−iii-1-111ii−i−i−i−iii-1-111i−i1-1−i−iii-1-111ii−i−i11-1-11-1−ii-11i−i−ii-11i−i1-1
χ32111-1-1-11-1−i−iii-1-111ii−i−i−i−iii-1-111i−i1-1−i−iii-1-111ii−i−i11-1-1-11i−i1-1−iii−i1-1−ii-11
χ332222222222222-22-22222-2-2-2-22-22-2-2-2-2-200000000000000000000000000000000
χ34222222222222-22-22-2-2-2-2-2-2-2-2-22-2222-2-200000000000000000000000000000000
χ3522222222-2-2-2-22-22-2-2-2-2-222222-22-222-2-200000000000000000000000000000000
χ3622222222-2-2-2-2-22-2222222222-22-22-2-2-2-200000000000000000000000000000000
χ37222-2-2-22-22i2i−2i−2i2-2-222i2i−2i−2i−2i−2i2i2i2-2-22−2i2i-2200000000000000000000000000000000
χ38222-2-2-22-22i2i−2i−2i-222-2−2i−2i2i2i−2i−2i2i2i-222-22i−2i-2200000000000000000000000000000000
χ39222-2-2-22-2−2i−2i2i2i2-2-22−2i−2i2i2i2i2i−2i−2i2-2-222i−2i-2200000000000000000000000000000000
χ40222-2-2-22-2−2i−2i2i2i-222-22i2i−2i−2i2i2i−2i−2i-222-2−2i2i-2200000000000000000000000000000000
χ4122-222-2-2-22-22-220202-22-20000-20-2000002−22−22−22−22−22−22−22−20000000000000000
χ4222-222-2-2-22-22-220202-22-20000-20-200000−22−22−22−22−22−22−22−220000000000000000
χ4322-222-2-2-22-22-2-20-20-22-22000020200000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ4422-222-2-2-22-22-2-20-20-22-22000020200000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ4522-222-2-2-2-22-222020-22-220000-20-2000002−22−2−22−222−22−2−22−220000000000000000
χ4622-222-2-2-2-22-222020-22-220000-20-200000−22−222−22−2−22−222−22−20000000000000000
χ4722-222-2-2-2-22-22-20-202-22-2000020200000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ4822-222-2-2-2-22-22-20-202-22-2000020200000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ4922-2-2-22-222i−2i−2i2i20-202i−2i−2i2i0000-202000002−2−22i2−i2−i2i22−2−22i2−i2−i2i20000000000000000
χ5022-2-2-22-222i−2i−2i2i20-202i−2i−2i2i0000-20200000−222−2−i2i2i2−i2−222−2−i2i2i2−i20000000000000000
χ5122-2-2-22-222i−2i−2i2i-2020−2i2i2i−2i000020-200000i2−i2−i2i2−222−2−i2i2i2−i22−2−220000000000000000
χ5222-2-2-22-222i−2i−2i2i-2020−2i2i2i−2i000020-200000−i2i2i2−i22−2−22i2−i2−i2i2−222−20000000000000000
χ5322-2-2-22-22−2i2i2i−2i20-20−2i2i2i−2i0000-202000002−2−22−i2i2i2−i22−2−22−i2i2i2−i20000000000000000
χ5422-2-2-22-22−2i2i2i−2i20-20−2i2i2i−2i0000-20200000−222−2i2−i2−i2i2−222−2i2−i2−i2i20000000000000000
χ5522-2-2-22-22−2i2i2i−2i-20202i−2i−2i2i000020-200000i2−i2−i2i22−2−22−i2i2i2−i2−222−20000000000000000
χ5622-2-2-22-22−2i2i2i−2i-20202i−2i−2i2i000020-200000−i2i2i2−i2−222−2i2−i2−i2i22−2−220000000000000000
χ574-444-44-4-40000040-4000000000-404000000000000000000000000000000000000
χ584-444-44-4-400000-40400000000040-4000000000000000000000000000000000000
χ594-44-44-4-4400000404000000000-40-4000000000000000000000000000000000000
χ604-44-44-4-4400000-40-4000000000404000000000000000000000000000000000000
χ614-4-44-4-4440000000000004-44-40000000000000000000000000000000000000000
χ624-4-44-4-444000000000000-44-440000000000000000000000000000000000000000
χ634-4-4-4444-40000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ644-4-4-4444-4000000000000−4i4i4i−4i0000000000000000000000000000000000000000

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