Finite Group Databasebeta

← Group #12014

Character table — Group #12014

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size1111111111111111222222222222222244444444444444444444444444444444444488888888
order1222444488888888444444448888888824888888888888888888161616161616161616161616161616161616161616161616
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii
χ171111-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i1-1i−i11-1-1ii−i−i11-1-1ii−i−iζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2−ζ2ζ6−ζ6ζ2−ζ2ζ6−ζ6
χ181111-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i1-1i−i11-1-1ii−i−i11-1-1ii−i−i−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2ζ2−ζ6ζ6−ζ2ζ2−ζ6ζ6
χ191111-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i1-1i−i-1-111−i−iii-1-111−i−iiiζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−ζ2ζ2−ζ6ζ6−ζ2ζ2−ζ6ζ6
χ201111-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i1-1i−i-1-111−i−iii-1-111−i−iii−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6ζ2−ζ2ζ6−ζ6ζ2−ζ2ζ6−ζ6
χ211111-1-1-1-1iiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii-11−ii11-1-1ii−i−i-1-111−i−iiiζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6ζ2−ζ2ζ6−ζ6−ζ2ζ2−ζ6ζ6
χ221111-1-1-1-1iiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii-11−ii11-1-1ii−i−i-1-111−i−iii−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−ζ2ζ2−ζ6ζ6ζ2−ζ2ζ6−ζ6
χ231111-1-1-1-1iiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii-11−ii-1-111−i−iii11-1-1ii−i−iζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2ζ2−ζ6ζ6ζ2−ζ2ζ6−ζ6
χ241111-1-1-1-1iiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii-11−ii-1-111−i−iii11-1-1ii−i−i−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2−ζ2ζ6−ζ6−ζ2ζ2−ζ6ζ6
χ251111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii1-1−ii11-1-1−i−iii11-1-1−i−iiiζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6−ζ6ζ2−ζ2ζ6−ζ6ζ2−ζ2
χ261111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii1-1−ii11-1-1−i−iii11-1-1−i−iii−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6ζ6−ζ2ζ2−ζ6ζ6−ζ2ζ2
χ271111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii1-1−ii-1-111ii−i−i-1-111ii−i−iζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ζ6ζ6−ζ2ζ2−ζ6ζ6−ζ2ζ2
χ281111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii1-1−ii-1-111ii−i−i-1-111ii−i−i−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2ζ6−ζ6ζ2−ζ2ζ6−ζ6ζ2−ζ2
χ291111-1-1-1-1−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i-11i−i11-1-1−i−iii-1-111ii−i−iζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2ζ6−ζ6ζ2−ζ2−ζ6ζ6−ζ2ζ2
χ301111-1-1-1-1−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i-11i−i11-1-1−i−iii-1-111ii−i−i−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ζ6ζ6−ζ2ζ2ζ6−ζ6ζ2−ζ2
χ311111-1-1-1-1−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i-11i−i-1-111ii−i−i11-1-1−i−iiiζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6ζ6−ζ2ζ2ζ6−ζ6ζ2−ζ2
χ321111-1-1-1-1−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i-11i−i-1-111ii−i−i11-1-1−i−iii−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6−ζ6ζ2−ζ2−ζ6ζ6−ζ2ζ2
χ3322222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ3522222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2220000000000000000000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-20000000000000000000000000000000000000000
χ372222-2-2-2-22i2i2i2i−2i−2i−2i−2i22-2-2-2-222−2i−2i2i2i2i2i−2i−2i-22−2i2i0000000000000000000000000000000000000000
χ382222-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-222-2-222−2i−2i2i2i−2i−2i2i2i2-22i−2i0000000000000000000000000000000000000000
χ392222-2-2-2-2−2i−2i−2i−2i2i2i2i2i22-2-2-2-2222i2i−2i−2i−2i−2i2i2i-222i−2i0000000000000000000000000000000000000000
χ402222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-222-2-2222i2i−2i−2i2i2i−2i−2i2-2−2i2i0000000000000000000000000000000000000000
χ4122-2-222-2-222-2-222-2-22i−2i2i−2i000000002i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000000000000000
χ4222-2-222-2-222-2-222-2-22i−2i2i−2i000000002i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000000000000000
χ4322-2-222-2-222-2-222-2-2−2i2i−2i2i00000000−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000000000000000
χ4422-2-222-2-222-2-222-2-2−2i2i−2i2i00000000−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000000000000000
χ4522-2-222-2-2-2-222-2-2222i−2i2i−2i00000000−2i2i−2i2i0000i2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000000000000000
χ4622-2-222-2-2-2-222-2-2222i−2i2i−2i00000000−2i2i−2i2i0000−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000000000000000
χ4722-2-222-2-2-2-222-2-222−2i2i−2i2i000000002i−2i2i−2i0000i2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000000000000000
χ4822-2-222-2-2-2-222-2-222−2i2i−2i2i000000002i−2i2i−2i0000−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000000000000000
χ4922-2-2-2-2222i2i−2i−2i−2i−2i2i2i2i−2i−2i2i00000000-222-20000i2−i2−i2i2−222−22−2−22i2−i2−i2i2000000000000000000000000
χ5022-2-2-2-2222i2i−2i−2i−2i−2i2i2i2i−2i−2i2i00000000-222-20000−i2i2i2−i22−2−22−222−2−i2i2i2−i2000000000000000000000000
χ5122-2-2-2-2222i2i−2i−2i−2i−2i2i2i−2i2i2i−2i000000002-2-220000i2−i2−i2i2−222−2−222−2−i2i2i2−i2000000000000000000000000
χ5222-2-2-2-2222i2i−2i−2i−2i−2i2i2i−2i2i2i−2i000000002-2-220000−i2i2i2−i22−2−222−2−22i2−i2−i2i2000000000000000000000000
χ5322-2-2-2-222−2i−2i2i2i2i2i−2i−2i2i−2i−2i2i000000002-2-220000i2−i2−i2i22−2−222−2−22−i2i2i2−i2000000000000000000000000
χ5422-2-2-2-222−2i−2i2i2i2i2i−2i−2i2i−2i−2i2i000000002-2-220000−i2i2i2−i2−222−2−222−2i2−i2−i2i2000000000000000000000000
χ5522-2-2-2-222−2i−2i2i2i2i2i−2i−2i−2i2i2i−2i00000000-222-20000i2−i2−i2i22−2−22−222−2i2−i2−i2i2000000000000000000000000
χ5622-2-2-2-222−2i−2i2i2i2i2i−2i−2i−2i2i2i−2i00000000-222-20000−i2i2i2−i2−222−22−2−22−i2i2i2−i2000000000000000000000000
χ572-22-22i−2i2i−2i2ζ2−2ζ22ζ2−2ζ22ζ6−2ζ62ζ6−2ζ600002-22i−2i2ζ2−2ζ22ζ6−2ζ6000000000000000000000000000000002ζ−2ζ2ζ5−2ζ52ζ3−2ζ32ζ7−2ζ700000000
χ582-22-22i−2i2i−2i2ζ2−2ζ22ζ2−2ζ22ζ6−2ζ62ζ6−2ζ600002-22i−2i2ζ2−2ζ22ζ6−2ζ600000000000000000000000000000000−2ζ2ζ−2ζ52ζ5−2ζ32ζ3−2ζ72ζ700000000
χ592-22-22i−2i2i−2i2ζ2−2ζ22ζ2−2ζ22ζ6−2ζ62ζ6−2ζ60000-22−2i2i−2ζ22ζ2−2ζ62ζ60000000000000000000000002ζ−2ζ2ζ5−2ζ52ζ3−2ζ32ζ7−2ζ70000000000000000
χ602-22-22i−2i2i−2i2ζ2−2ζ22ζ2−2ζ22ζ6−2ζ62ζ6−2ζ60000-22−2i2i−2ζ22ζ2−2ζ62ζ6000000000000000000000000−2ζ2ζ−2ζ52ζ5−2ζ32ζ3−2ζ72ζ70000000000000000
χ612-22-22i−2i2i−2i−2ζ22ζ2−2ζ22ζ2−2ζ62ζ6−2ζ62ζ600002-22i−2i−2ζ22ζ2−2ζ62ζ6000000000000000000000000000000002ζ5−2ζ5−2ζ2ζ−2ζ72ζ72ζ3−2ζ300000000
χ622-22-22i−2i2i−2i−2ζ22ζ2−2ζ22ζ2−2ζ62ζ6−2ζ62ζ600002-22i−2i−2ζ22ζ2−2ζ62ζ600000000000000000000000000000000−2ζ52ζ52ζ−2ζ2ζ7−2ζ7−2ζ32ζ300000000
χ632-22-22i−2i2i−2i−2ζ22ζ2−2ζ22ζ2−2ζ62ζ6−2ζ62ζ60000-22−2i2i2ζ2−2ζ22ζ6−2ζ60000000000000000000000002ζ5−2ζ5−2ζ2ζ−2ζ72ζ72ζ3−2ζ30000000000000000
χ642-22-22i−2i2i−2i−2ζ22ζ2−2ζ22ζ2−2ζ62ζ6−2ζ62ζ60000-22−2i2i2ζ2−2ζ22ζ6−2ζ6000000000000000000000000−2ζ52ζ52ζ−2ζ2ζ7−2ζ7−2ζ32ζ30000000000000000
χ652-22-2−2i2i−2i2i2ζ6−2ζ62ζ6−2ζ62ζ2−2ζ22ζ2−2ζ200002-2−2i2i2ζ6−2ζ62ζ2−2ζ2000000000000000000000000000000002ζ3−2ζ3−2ζ72ζ7−2ζ2ζ2ζ5−2ζ500000000
χ662-22-2−2i2i−2i2i2ζ6−2ζ62ζ6−2ζ62ζ2−2ζ22ζ2−2ζ200002-2−2i2i2ζ6−2ζ62ζ2−2ζ200000000000000000000000000000000−2ζ32ζ32ζ7−2ζ72ζ−2ζ−2ζ52ζ500000000
χ672-22-2−2i2i−2i2i2ζ6−2ζ62ζ6−2ζ62ζ2−2ζ22ζ2−2ζ20000-222i−2i−2ζ62ζ6−2ζ22ζ20000000000000000000000002ζ3−2ζ3−2ζ72ζ7−2ζ2ζ2ζ5−2ζ50000000000000000
χ682-22-2−2i2i−2i2i2ζ6−2ζ62ζ6−2ζ62ζ2−2ζ22ζ2−2ζ20000-222i−2i−2ζ62ζ6−2ζ22ζ2000000000000000000000000−2ζ32ζ32ζ7−2ζ72ζ−2ζ−2ζ52ζ50000000000000000
χ692-22-2−2i2i−2i2i−2ζ62ζ6−2ζ62ζ6−2ζ22ζ2−2ζ22ζ200002-2−2i2i−2ζ62ζ6−2ζ22ζ2000000000000000000000000000000002ζ7−2ζ72ζ3−2ζ32ζ5−2ζ52ζ−2ζ00000000
χ702-22-2−2i2i−2i2i−2ζ62ζ6−2ζ62ζ6−2ζ22ζ2−2ζ22ζ200002-2−2i2i−2ζ62ζ6−2ζ22ζ200000000000000000000000000000000−2ζ72ζ7−2ζ32ζ3−2ζ52ζ5−2ζ2ζ00000000
χ712-22-2−2i2i−2i2i−2ζ62ζ6−2ζ62ζ6−2ζ22ζ2−2ζ22ζ20000-222i−2i2ζ6−2ζ62ζ2−2ζ20000000000000000000000002ζ7−2ζ72ζ3−2ζ32ζ5−2ζ52ζ−2ζ0000000000000000
χ722-22-2−2i2i−2i2i−2ζ62ζ6−2ζ62ζ6−2ζ22ζ2−2ζ22ζ20000-222i−2i2ζ6−2ζ62ζ2−2ζ2000000000000000000000000−2ζ72ζ7−2ζ32ζ3−2ζ52ζ5−2ζ2ζ0000000000000000
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.