Finite Group Databasebeta

← Group #12049

Character table — Group #12049

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size1111111111111111222222222222222244444444444444444444444444444444444488888888
order122244448888888844448888161616161616161622448888888888881616161616161616161616161616161616161616448816161616
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111ii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-111111111-1-1-1-1ii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-11111-1-1-1-11111ii−i−i−i−i−i−iiiii−i−i−i−iiiii11-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii
χ1411111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i
χ1511111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i
χ1611111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-11111-1-1-1-11111−i−iiiiiii−i−i−i−iiiii−i−i−i−i11-1-1−i−iii
χ171111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−iζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ611-1-1ii−i−i11-1-1ii−i−iζ2−ζ2ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ61-1i−iζ2−ζ2ζ6−ζ6
χ181111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−iζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ611-1-1ii−i−i-1-111−i−iiiζ2−ζ2ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6-11−ii−ζ2ζ2−ζ6ζ6
χ191111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−iζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6-1-111−i−iii11-1-1ii−i−iζ2−ζ2ζ6−ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6-11−ii−ζ2ζ2−ζ6ζ6
χ201111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−iζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6-1-111−i−iii-1-111−i−iiiζ2−ζ2ζ6−ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ61-1i−iζ2−ζ2ζ6−ζ6
χ211111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ611-1-1ii−i−i11-1-1ii−i−i−ζ2ζ2−ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ61-1i−i−ζ2ζ2−ζ6ζ6
χ221111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ611-1-1ii−i−i-1-111−i−iii−ζ2ζ2−ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6-11−iiζ2−ζ2ζ6−ζ6
χ231111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6-1-111−i−iii11-1-1ii−i−i−ζ2ζ2−ζ6ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6-11−iiζ2−ζ2ζ6−ζ6
χ241111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6-1-111−i−iii-1-111−i−iii−ζ2ζ2−ζ6ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ61-1i−i−ζ2ζ2−ζ6ζ6
χ251111-1-1-1-1−i−i−i−iiiii11-1-1−i−iiiζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ211-1-1−i−iii11-1-1−i−iiiζ6−ζ6ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ21-1−iiζ6−ζ6ζ2−ζ2
χ261111-1-1-1-1−i−i−i−iiiii11-1-1−i−iiiζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ211-1-1−i−iii-1-111ii−i−iζ6−ζ6ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2-11i−i−ζ6ζ6−ζ2ζ2
χ271111-1-1-1-1−i−i−i−iiiii11-1-1−i−iiiζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2-1-111ii−i−i11-1-1−i−iiiζ6−ζ6ζ2−ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2-11i−i−ζ6ζ6−ζ2ζ2
χ281111-1-1-1-1−i−i−i−iiiii11-1-1−i−iiiζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2-1-111ii−i−i-1-111ii−i−iζ6−ζ6ζ2−ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ21-1−iiζ6−ζ6ζ2−ζ2
χ291111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ211-1-1−i−iii11-1-1−i−iii−ζ6ζ6−ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ21-1−ii−ζ6ζ6−ζ2ζ2
χ301111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ211-1-1−i−iii-1-111ii−i−i−ζ6ζ6−ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2-11i−iζ6−ζ6ζ2−ζ2
χ311111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2-1-111ii−i−i11-1-1−i−iii−ζ6ζ6−ζ2ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2-11i−iζ6−ζ6ζ2−ζ2
χ321111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2-1-111ii−i−i-1-111ii−i−i−ζ6ζ6−ζ2ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ21-1−ii−ζ6ζ6−ζ2ζ2
χ332222222222222222-2-2-2-2-2-2-2-2222222220000000000000000-2-2-2-2000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222000000000000000000000000
χ3522222222-2-2-2-2-2-2-2-2-2-2-2-222222i2i2i2i−2i−2i−2i−2i0000000000000000−2i−2i2i2i000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-2-2-2-2-22222−2i−2i−2i−2i2i2i2i2i00000000000000002i2i−2i−2i000000000000000000000000
χ372222-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-222−2i−2i2i2i2ζ22ζ2−2ζ2−2ζ22ζ62ζ6−2ζ6−2ζ60000000000000000−2ζ22ζ2−2ζ62ζ6000000000000000000000000
χ382222-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-222−2i−2i2i2i−2ζ2−2ζ22ζ22ζ2−2ζ6−2ζ62ζ62ζ600000000000000002ζ2−2ζ22ζ6−2ζ6000000000000000000000000
χ392222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-2222i2i−2i−2i2ζ62ζ6−2ζ6−2ζ62ζ22ζ2−2ζ2−2ζ20000000000000000−2ζ62ζ6−2ζ22ζ2000000000000000000000000
χ402222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-2222i2i−2i−2i−2ζ6−2ζ62ζ62ζ6−2ζ2−2ζ22ζ22ζ200000000000000002ζ6−2ζ62ζ2−2ζ2000000000000000000000000
χ4122-2-222-2-222-2-222-2-2000000002-22-22-22-200000000i2−i2i2−i2i2−i2i2−i2000000000000i2−i2i2−i2i2−i2i2−i200000000
χ4222-2-222-2-222-2-222-2-2000000002-22-22-22-200000000−i2i2−i2i2−i2i2−i2i2000000000000−i2i2−i2i2−i2i2−i2i200000000
χ4322-2-222-2-222-2-222-2-200000000-22-22-22-2200000000i2−i2i2−i2i2−i2i2−i2000000000000−i2i2−i2i2−i2i2−i2i200000000
χ4422-2-222-2-222-2-222-2-200000000-22-22-22-2200000000−i2i2−i2i2−i2i2−i2i2000000000000i2−i2i2−i2i2−i2i2−i200000000
χ4522-2-222-2-2-2-222-2-222000000002i−2i2i−2i−2i2i−2i2i00000000i2−i2i2−i2−i2i2−i2i2000000000000−22−222−22−200000000
χ4622-2-222-2-2-2-222-2-222000000002i−2i2i−2i−2i2i−2i2i00000000−i2i2−i2i2i2−i2i2−i20000000000002−22−2−22−2200000000
χ4722-2-222-2-2-2-222-2-22200000000−2i2i−2i2i2i−2i2i−2i00000000i2−i2i2−i2−i2i2−i2i20000000000002−22−2−22−2200000000
χ4822-2-222-2-2-2-222-2-22200000000−2i2i−2i2i2i−2i2i−2i00000000−i2i2−i2i2i2−i2i2−i2000000000000−22−222−22−200000000
χ4922-2-2-2-2222i2i−2i−2i−2i−2i2i2i000000002ζ2−2ζ2−2ζ22ζ22ζ6−2ζ6−2ζ62ζ600000000i2−i2−i2i2−222−2000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ5022-2-2-2-2222i2i−2i−2i−2i−2i2i2i000000002ζ2−2ζ2−2ζ22ζ22ζ6−2ζ6−2ζ62ζ600000000−i2i2i2−i22−2−220000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ5122-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000−2ζ22ζ22ζ2−2ζ2−2ζ62ζ62ζ6−2ζ600000000i2−i2−i2i2−222−20000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ5222-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000−2ζ22ζ22ζ2−2ζ2−2ζ62ζ62ζ6−2ζ600000000−i2i2i2−i22−2−22000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ5322-2-2-2-222−2i−2i2i2i2i2i−2i−2i000000002ζ6−2ζ6−2ζ62ζ62ζ2−2ζ2−2ζ22ζ200000000i2−i2−i2i22−2−22000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ5422-2-2-2-222−2i−2i2i2i2i2i−2i−2i000000002ζ6−2ζ6−2ζ62ζ62ζ2−2ζ2−2ζ22ζ200000000−i2i2i2−i2−222−20000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ5522-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000−2ζ62ζ62ζ6−2ζ6−2ζ22ζ22ζ2−2ζ200000000i2−i2−i2i22−2−220000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ5622-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000−2ζ62ζ62ζ6−2ζ6−2ζ22ζ22ζ2−2ζ200000000−i2i2i2−i2−222−2000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ572-22-22i−2i2i−2i2ζ2−2ζ22ζ2−2ζ22ζ6−2ζ62ζ6−2ζ62-22i−2i2ζ2−2ζ22ζ6−2ζ600000000000000000000000000002ζ−2ζ2ζ5−2ζ52ζ3−2ζ32ζ7−2ζ70000000000000000
χ582-22-22i−2i2i−2i2ζ2−2ζ22ζ2−2ζ22ζ6−2ζ62ζ6−2ζ62-22i−2i2ζ2−2ζ22ζ6−2ζ60000000000000000000000000000−2ζ2ζ−2ζ52ζ5−2ζ32ζ3−2ζ72ζ70000000000000000
χ592-22-22i−2i2i−2i2ζ2−2ζ22ζ2−2ζ22ζ6−2ζ62ζ6−2ζ6-22−2i2i−2ζ22ζ2−2ζ62ζ6000000002-22i−2i2ζ2−2ζ22ζ6−2ζ6000000000000000000000000000000000000
χ602-22-22i−2i2i−2i2ζ2−2ζ22ζ2−2ζ22ζ6−2ζ62ζ6−2ζ6-22−2i2i−2ζ22ζ2−2ζ62ζ600000000-22−2i2i−2ζ22ζ2−2ζ62ζ6000000000000000000000000000000000000
χ612-22-22i−2i2i−2i−2ζ22ζ2−2ζ22ζ2−2ζ62ζ6−2ζ62ζ62-22i−2i−2ζ22ζ2−2ζ62ζ600000000000000000000000000002ζ5−2ζ5−2ζ2ζ−2ζ72ζ72ζ3−2ζ30000000000000000
χ622-22-22i−2i2i−2i−2ζ22ζ2−2ζ22ζ2−2ζ62ζ6−2ζ62ζ62-22i−2i−2ζ22ζ2−2ζ62ζ60000000000000000000000000000−2ζ52ζ52ζ−2ζ2ζ7−2ζ7−2ζ32ζ30000000000000000
χ632-22-22i−2i2i−2i−2ζ22ζ2−2ζ22ζ2−2ζ62ζ6−2ζ62ζ6-22−2i2i2ζ2−2ζ22ζ6−2ζ6000000002-22i−2i−2ζ22ζ2−2ζ62ζ6000000000000000000000000000000000000
χ642-22-22i−2i2i−2i−2ζ22ζ2−2ζ22ζ2−2ζ62ζ6−2ζ62ζ6-22−2i2i2ζ2−2ζ22ζ6−2ζ600000000-22−2i2i2ζ2−2ζ22ζ6−2ζ6000000000000000000000000000000000000
χ652-22-2−2i2i−2i2i2ζ6−2ζ62ζ6−2ζ62ζ2−2ζ22ζ2−2ζ22-2−2i2i2ζ6−2ζ62ζ2−2ζ200000000000000000000000000002ζ3−2ζ3−2ζ72ζ7−2ζ2ζ2ζ5−2ζ50000000000000000
χ662-22-2−2i2i−2i2i2ζ6−2ζ62ζ6−2ζ62ζ2−2ζ22ζ2−2ζ22-2−2i2i2ζ6−2ζ62ζ2−2ζ20000000000000000000000000000−2ζ32ζ32ζ7−2ζ72ζ−2ζ−2ζ52ζ50000000000000000
χ672-22-2−2i2i−2i2i2ζ6−2ζ62ζ6−2ζ62ζ2−2ζ22ζ2−2ζ2-222i−2i−2ζ62ζ6−2ζ22ζ2000000002-2−2i2i2ζ6−2ζ62ζ2−2ζ2000000000000000000000000000000000000
χ682-22-2−2i2i−2i2i2ζ6−2ζ62ζ6−2ζ62ζ2−2ζ22ζ2−2ζ2-222i−2i−2ζ62ζ6−2ζ22ζ200000000-222i−2i−2ζ62ζ6−2ζ22ζ2000000000000000000000000000000000000
χ692-22-2−2i2i−2i2i−2ζ62ζ6−2ζ62ζ6−2ζ22ζ2−2ζ22ζ22-2−2i2i−2ζ62ζ6−2ζ22ζ200000000000000000000000000002ζ7−2ζ72ζ3−2ζ32ζ5−2ζ52ζ−2ζ0000000000000000
χ702-22-2−2i2i−2i2i−2ζ62ζ6−2ζ62ζ6−2ζ22ζ2−2ζ22ζ22-2−2i2i−2ζ62ζ6−2ζ22ζ20000000000000000000000000000−2ζ72ζ7−2ζ32ζ3−2ζ52ζ5−2ζ2ζ0000000000000000
χ712-22-2−2i2i−2i2i−2ζ62ζ6−2ζ62ζ6−2ζ22ζ2−2ζ22ζ2-222i−2i2ζ6−2ζ62ζ2−2ζ2000000002-2−2i2i−2ζ62ζ6−2ζ22ζ2000000000000000000000000000000000000
χ722-22-2−2i2i−2i2i−2ζ62ζ6−2ζ62ζ6−2ζ22ζ2−2ζ22ζ2-222i−2i2ζ6−2ζ62ζ2−2ζ200000000-222i−2i2ζ6−2ζ62ζ2−2ζ2000000000000000000000000000000000000
χ734-4-444i−4i−4i4i4ζ2−4ζ2−4ζ24ζ24ζ6−4ζ6−4ζ64ζ6000000000000000000000000000000000000000000000000000000000000
χ744-4-444i−4i−4i4i−4ζ24ζ24ζ2−4ζ2−4ζ64ζ64ζ6−4ζ6000000000000000000000000000000000000000000000000000000000000
χ754-4-44−4i4i4i−4i4ζ6−4ζ6−4ζ64ζ64ζ2−4ζ2−4ζ24ζ2000000000000000000000000000000000000000000000000000000000000
χ764-4-44−4i4i4i−4i−4ζ64ζ64ζ6−4ζ6−4ζ24ζ24ζ2−4ζ2000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.