Finite Group Databasebeta

← Group #11921344

Character table — Group #11921344

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222224444444444444444666666668888888888881212121212121212121212121616161616161616161616161616161624242424242424243636363648484848
order12442346121233666881212121212242424242244444433666612121212121224668812122424242466121224242424242424242424242412121212121212122444661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111-1-111111-1-1-1-111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1
χ4111111111111111-1-111111-1-1-1-11111-1-1-1-11111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1+i32−1+i32111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1+i32−1−i32−1+i32
χ61111111111−1−i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1+i32−1+i3211111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-11+i321−i321+i321−i32
χ71111111111−1−i32−1+i321−1−i32−1+i32-1-11−1−i32−1−i32−1+i32−1+i32-1-1-1-111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111-1-111-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1111+i321−i321+i321−i32
χ81111111111−1−i32−1+i321−1−i32−1+i32-1-11−1−i32−1−i32−1+i32−1+i32-1-1-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111-1-111-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-1−1−i32−1+i32−1−i32−1+i32
χ91111111111−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1−i32−1−i32111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1−i32−1+i32−1−i32
χ101111111111−1+i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1−i32−1−i3211111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-11−i321+i321−i321+i32
χ111111111111−1+i32−1−i321−1+i32−1−i32-1-11−1+i32−1+i32−1−i32−1−i32-1-1-1-111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111-1-111-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1111−i321+i321−i321+i32
χ121111111111−1+i32−1−i321−1+i32−1−i32-1-11−1+i32−1+i32−1−i32−1−i32-1-1-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111-1-111-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-1−1+i32−1−i32−1+i32−1−i32
χ1311-1-1-1111-1-111-111i−i1-1-1-1-1ii−i−i1-11-1ii−i−i1111-1-111-1-1-1-11-11-1i−i1-1ii−i−i-1-111i−ii−iii−i−iii−i−iii−i−iii−i−i-11i−i11-1-1
χ1411-1-1-1111-1-111-111i−i1-1-1-1-1ii−i−i1-11-1−i−iii1111-1-111-1-1-1-1-111-1i−i1-1ii−i−i-1-111i−ii−iii−i−iii−i−i−i−iii−i−iii1-1−ii-1-111
χ1511-1-1-1111-1-111-111−ii1-1-1-1-1−i−iii1-11-1ii−i−i1111-1-111-1-1-1-1-111-1−ii1-1−i−iii-1-111−ii−ii−i−iii−i−iiiii−i−iii−i−i1-1i−i-1-111
χ1611-1-1-1111-1-111-111−ii1-1-1-1-1−i−iii1-11-1−i−iii1111-1-111-1-1-1-11-11-1−ii1-1−i−iii-1-111−ii−ii−i−iii−i−iii−i−iii−i−iii-11−ii11-1-1
χ1711-1-1-1111-1-1−1−i32−1+i32-1−1−i32−1+i32i−i11+i321+i321−i321−i32ii−i−i1-11-1ii−i−i−1−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321+i321−i321−i321-11-1i−i1-1ii−i−i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ7ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7-11i−i−1−i32−1+i321+i321−i32
χ1811-1-1-1111-1-1−1−i32−1+i32-1−1−i32−1+i32i−i11+i321+i321−i321−i32ii−i−i1-11-1−i−iii−1−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321+i321−i321−i32-111-1i−i1-1ii−i−i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ7ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ71-1−ii1+i321−i32−1−i32−1+i32
χ1911-1-1-1111-1-1−1−i32−1+i32-1−1−i32−1+i32−ii11+i321+i321−i321−i32−i−iii1-11-1ii−i−i−1−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321+i321−i321−i32-111-1−ii1-1−i−iii1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ7−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ7ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ71-1i−i1+i321−i32−1−i32−1+i32
χ2011-1-1-1111-1-1−1−i32−1+i32-1−1−i32−1+i32−ii11+i321+i321−i321−i32−i−iii1-11-1−i−iii−1−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321+i321−i321−i321-11-1−ii1-1−i−iii1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ7−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ7-11−ii−1−i32−1+i321+i321−i32
χ2111-1-1-1111-1-1−1+i32−1−i32-1−1+i32−1−i32i−i11−i321−i321+i321+i32ii−i−i1-11-1ii−i−i−1+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321−i321+i321+i321-11-1i−i1-1ii−i−i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ11ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11-11i−i−1+i32−1−i321−i321+i32
χ2211-1-1-1111-1-1−1+i32−1−i32-1−1+i32−1−i32i−i11−i321−i321+i321+i32ii−i−i1-11-1−i−iii−1+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321−i321+i321+i32-111-1i−i1-1ii−i−i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ11ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ111-1−ii1−i321+i32−1+i32−1−i32
χ2311-1-1-1111-1-1−1+i32−1−i32-1−1+i32−1−i32−ii11−i321−i321+i321+i32−i−iii1-11-1ii−i−i−1+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321−i321+i321+i32-111-1−ii1-1−i−iii1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ11−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ11ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ111-1i−i1−i321+i32−1+i32−1−i32
χ2411-1-1-1111-1-1−1+i32−1−i32-1−1+i32−1−i32−ii11−i321−i321+i321+i32−i−iii1-11-1−i−iii−1+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321−i321+i321+i321-11-1−ii1-1−i−iii1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ11−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ11-11−ii−1+i32−1−i321−i321+i32
χ2522222-12-1-1-122-12222-12222-1-1-1-122220000-1-1-1-12222-1-1-1-100-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ2622222-12-1-1-122-122-2-2-12222111122220000-1-1-1-12222-1-1-1-100-1-1-2-2-1-11111-1-1-1-1-2-2-2-2111111110000000000000000
χ2722222-12-1-1-1−1−i3−1+i3-1−1−i3−1+i322-1−1−i3−1−i3−1+i3−1+i3-1-1-1-1222200001+i321−i321+i321−i32−1−i3−1+i3−1−i3−1+i31+i321+i321−i321−i3200-1-122-1-1-1-1-1-11+i321−i321+i321−i32−1−i3−1−i3−1+i3−1+i31+i321+i321+i321+i321−i321−i321−i321−i320000000000000000
χ2822222-12-1-1-1−1−i3−1+i3-1−1−i3−1+i3-2-2-1−1−i3−1−i3−1+i3−1+i31111222200001+i321−i321+i321−i32−1−i3−1+i3−1−i3−1+i31+i321+i321−i321−i3200-1-1-2-2-1-111111+i321−i321+i321−i321+i31+i31−i31−i3−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i320000000000000000
χ2922222-12-1-1-1−1+i3−1−i3-1−1+i3−1−i322-1−1+i3−1+i3−1−i3−1−i3-1-1-1-1222200001−i321+i321−i321+i32−1+i3−1−i3−1+i3−1−i31−i321−i321+i321+i3200-1-122-1-1-1-1-1-11−i321+i321−i321+i32−1+i3−1+i3−1−i3−1−i31−i321−i321−i321−i321+i321+i321+i321+i320000000000000000
χ3022222-12-1-1-1−1+i3−1−i3-1−1+i3−1−i3-2-2-1−1+i3−1+i3−1−i3−1−i31111222200001−i321+i321−i321+i32−1+i3−1−i3−1+i3−1−i31−i321−i321+i321+i3200-1-1-2-2-1-111111−i321+i321−i321+i321−i31−i31+i31+i3−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i320000000000000000
χ312222-22-222222-22200-222220000-222-200002222-2-2-2-2222200-22002-20000-2-2-2-20000000000000000000000000000
χ322222-22-2222−1−i3−1+i3-2−1−i3−1+i300-2−1−i3−1−i3−1+i3−1+i30000-222-20000−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3−1−i3−1−i3−1+i3−1+i300-22002-200001+i31−i31+i31−i30000000000000000000000000000
χ332222-22-2222−1+i3−1−i3-2−1+i3−1−i300-2−1+i3−1+i3−1−i3−1−i30000-222-20000−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3−1+i3−1+i3−1−i3−1−i300-22002-200001−i31+i31−i31+i30000000000000000000000000000
χ342222-2-1-2-1-1-1221220012222−i3i3−i3i3-222-20000-1-1-1-1-2-2-2-2-1-1-1-1001-100-11−i3i3−i3i311110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ352222-2-1-2-1-1-1221220012222i3−i3i3−i3-222-20000-1-1-1-1-2-2-2-2-1-1-1-1001-100-11i3−i3i3−i311110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ362222-2-1-2-1-1-1−1−i3−1+i31−1−i3−1+i3001−1−i3−1−i3−1+i3−1+i3−i3i3−i3i3-222-200001+i321−i321+i321−i321+i31−i31+i31−i31+i321+i321−i321−i32001-100-11−i3i3−i3i3−1−i32−1+i32−1−i32−1+i320000−3+i323−i32−3+i323−i323+i32−3−i323+i32−3−i320000000000000000
χ372222-2-1-2-1-1-1−1−i3−1+i31−1−i3−1+i3001−1−i3−1−i3−1+i3−1+i3i3−i3i3−i3-222-200001+i321−i321+i321−i321+i31−i31+i31−i31+i321+i321−i321−i32001-100-11i3−i3i3−i3−1−i32−1+i32−1−i32−1+i3200003−i32−3+i323−i32−3+i32−3−i323+i32−3−i323+i320000000000000000
χ382222-2-1-2-1-1-1−1+i3−1−i31−1+i3−1−i3001−1+i3−1+i3−1−i3−1−i3−i3i3−i3i3-222-200001−i321+i321−i321+i321−i31+i31−i31+i31−i321−i321+i321+i32001-100-11−i3i3−i3i3−1+i32−1−i32−1+i32−1−i3200003+i32−3−i323+i32−3−i32−3+i323−i32−3+i323−i320000000000000000
χ392222-2-1-2-1-1-1−1+i3−1−i31−1+i3−1−i3001−1+i3−1+i3−1−i3−1−i3i3−i3i3−i3-222-200001−i321+i321−i321+i321−i31+i31−i31+i31−i321−i321+i321+i32001-100-11i3−i3i3−i3−1+i32−1−i32−1+i32−1−i320000−3−i323+i32−3−i323+i323−i32−3+i323−i32−3+i320000000000000000
χ4022-2-222-22-2-22222200-2-2-2-2-20000-2-2220000222222-2-2-2-2-2-200-2-20022000022-2-20000000000000000000000000000
χ4122-2-222-22-2-2−1−i3−1+i32−1−i3−1+i300-21+i31+i31−i31−i30000-2-2220000−1−i3−1+i3−1−i3−1+i3−1−i3−1+i31+i31−i31+i31+i31−i31−i300-2-200220000−1−i3−1+i31+i31−i30000000000000000000000000000
χ4222-2-222-22-2-2−1+i3−1−i32−1+i3−1−i300-21−i31−i31+i31+i30000-2-2220000−1+i3−1−i3−1+i3−1−i3−1+i3−1−i31−i31+i31−i31−i31+i31+i300-2-200220000−1+i3−1−i31−i31+i30000000000000000000000000000
χ4322-2-22-1-2-11122-122001-2-2-2-23−3−33-2-2220000-1-1-1-122-2-21111001100-1-13−3−33-1-11100003−3−333−3−330000000000000000
χ4422-2-22-1-2-11122-122001-2-2-2-2−333−3-2-2220000-1-1-1-122-2-21111001100-1-1−333−3-1-1110000−333−3−333−30000000000000000
χ4522-2-22-1-2-111−1−i3−1+i3-1−1−i3−1+i30011+i31+i31−i31−i33−3−33-2-22200001+i321−i321+i321−i32−1−i3−1+i31+i31−i3−1−i32−1−i32−1+i32−1+i32001100-1-13−3−331+i321−i32−1−i32−1+i3200002ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ11−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ110000000000000000
χ4622-2-22-1-2-111−1−i3−1+i3-1−1−i3−1+i30011+i31+i31−i31−i3−333−3-2-22200001+i321−i321+i321−i32−1−i3−1+i31+i31−i3−1−i32−1−i32−1+i32−1+i32001100-1-1−333−31+i321−i32−1−i32−1+i320000−2ζ7−ζ112ζ7+ζ112ζ7+ζ11−2ζ7−ζ11ζ7+2ζ11−ζ7−2ζ11−ζ7−2ζ11ζ7+2ζ110000000000000000
χ4722-2-22-1-2-111−1+i3−1−i3-1−1+i3−1−i30011−i31−i31+i31+i33−3−33-2-22200001−i321+i321−i321+i32−1+i3−1−i31−i31+i3−1+i32−1+i32−1−i32−1−i32001100-1-13−3−331−i321+i32−1+i32−1−i320000−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ112ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ110000000000000000
χ4822-2-22-1-2-111−1+i3−1−i3-1−1+i3−1−i30011−i31−i31+i31+i3−333−3-2-22200001−i321+i321−i321+i32−1+i3−1−i31−i31+i3−1+i32−1+i32−1−i32−1−i32001100-1-1−333−31−i321+i32−1+i32−1−i320000ζ7+2ζ11−ζ7−2ζ11−ζ7−2ζ11ζ7+2ζ11−2ζ7−ζ112ζ7+ζ112ζ7+ζ11−2ζ7−ζ110000000000000000
χ4922-2-2-2-12-111221222i−2i-1-2-2-2-2−i−iii2-22-20000-1-1-1-1-2-222111100-112i−2i-11−i−iii11-1-12i−2i2i−2i−i−iii−i−iii0000000000000000
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χ908-8−8i8i0-4044i−4i2−2i32+2i30−2+2i3−2−2i3000−4ζ74ζ7−4ζ114ζ11000000000000−1+i3−1−i31−i31+i300002ζ7−2ζ72ζ11−2ζ1100000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.