Finite Group Databasebeta

← Group #11923253

Character table — Group #11923253

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222444444444444444466666688888888888812121212121212161616161616161616161616161616161818242424242424242424242436363648484848
order12222236662334666666666612124444443366666666662444412126666666666121212121212221212121212121212121212244661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1111111111111-1-1111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111−1−i32−1+i3211111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111111−1−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+i3211111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32111−1−i32−1+i32−1−i32−1+i32
χ411111111111−1−i32−1+i3211111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-111111−1−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+i32-1-11111+i321+i321+i321+i321−i321−i321−i321−i32-1-1-11+i321−i321+i321−i32
χ511111111111−1+i32−1−i3211111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111111−1+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−i3211111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32111−1+i32−1−i32−1+i32−1−i32
χ611111111111−1+i32−1−i3211111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-111111−1+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−i32-1-11111−i321−i321−i321−i321+i321+i321+i321+i32-1-1-11−i321+i321−i321+i32
χ71111111111-111-111-1-1111111-1-1111111111111111111-1-1-11-111-1-111-1-111-1-1-1-1-1-1-1-111-11-1111111111-1-1-1-1-1-1
χ81111111111-111-111-1-1111111-1-111-1-1-1-111111111111111-11-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111
χ91111111111-1−1−i32−1+i32-111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-11-1111+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321−i321+i321+i321−i321−i3211-11-1−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321-1-11+i321−i321+i321−i32
χ101111111111-1−1−i32−1+i32-111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211-11-1111+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321−i321+i321+i321−i321−i32-1-1-11-11+i321+i321+i321+i321−i321−i321−i321−i32-111−1−i32−1+i32−1−i32−1+i32
χ111111111111-1−1+i32−1−i32-111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-11-1111−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321+i321−i321−i321+i321+i3211-11-1−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321-1-11−i321+i321−i321+i32
χ121111111111-1−1+i32−1−i32-111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211-11-1111−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321+i321−i321−i321+i321+i32-1-1-11-11−i321−i321−i321−i321+i321+i321+i321+i32-111−1+i32−1−i32−1+i32−1−i32
χ131111-1-11111111-1-1-111111111-1-11111-1-111-1-1-1-11111111-1-1-111111-1-111-1-111-1-1-1-1-1-111-1-1111-1-111-1-1-1-1111-1-1
χ141111-1-11111111-1-1-111111111-1-111-1-11111-1-1-1-1111111-11-1-111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-1-111
χ151111-1-111111−1−i32−1+i32-1-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-1-1-1111−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321−i321+i321+i321−i321−i3211-1-11−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-11−1−i32−1+i321+i321−i32
χ161111-1-111111−1−i32−1+i32-1-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-11-1-1111−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321−i321+i321+i321−i321−i32-1-1-1-111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3211-11+i321−i32−1−i32−1+i32
χ171111-1-111111−1+i32−1−i32-1-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-1-1-1111−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321+i321−i321−i321+i321+i3211-1-11−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-11−1+i32−1−i321−i321+i32
χ181111-1-111111−1+i32−1−i32-1-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-11-1-1111−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321+i321−i321−i321+i321+i32-1-1-1-111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3211-11−i321+i32−1+i32−1−i32
χ191111-1-11111-1111-1-1-1-1111111111111-1-111-1-1-1-1111111-111-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-111-1-1-11-1-1-111
χ201111-1-11111-1111-1-1-1-11111111111-1-11111-1-1-1-11111111-11-1-111-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1-1-111-1-1111-1111-1-1
χ211111-1-11111-1−1−i32−1+i321-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-111-1-1111+i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-11-11+i321−i32−1−i32−1+i32
χ221111-1-11111-1−1−i32−1+i321-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111-1-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-11-1-1111+i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11-1-11+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-11−1−i32−1+i321+i321−i32
χ231111-1-11111-1−1+i32−1−i321-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-111-1-1111−i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-11-11−i321+i32−1+i32−1−i32
χ241111-1-11111-1−1+i32−1−i321-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111-1-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-11-1-1111−i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11-1-11−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-11−1+i32−1−i321−i321+i32
χ25222222-1-1-1-12222-1-1-1-1222222-1-1220000-1-12222-1-1-1-1-1-100222-1-122-1-1-1-1-1-1-1-122-1-1-1-100-1-1-1000000000000000
χ26222222-1-1-1-12−1−i3−1+i32-1-1-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-12200001+i321−i32−1−i3−1−i3−1+i3−1+i31+i321+i321−i321−i321+i321−i3200222-1-1−1−i3−1+i31+i321+i321+i321+i321−i321−i321−i321−i32−1−i3−1+i31+i321+i321−i321−i3200-1-1-1000000000000000
χ27222222-1-1-1-12−1+i3−1−i32-1-1-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-12200001−i321+i32−1+i3−1+i3−1−i3−1−i31−i321−i321+i321+i321−i321+i3200222-1-1−1+i3−1−i31−i321−i321−i321−i321+i321+i321+i321+i32−1+i3−1−i31−i321−i321+i321+i3200-1-1-1000000000000000
χ28222222-1-1-1-1-222-2-1-11122222211220000-1-12222-1-1-1-1-1-100-22-2-1-1-2-2-1-111-1-111-2-21111001-11000000000000000
χ29222222-1-1-1-1-2−1−i3−1+i3-2-1-111−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3112200001+i321−i32−1−i3−1−i3−1+i3−1+i31+i321+i321−i321−i321+i321−i3200-22-2-1-11+i31−i31+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i31−i3−1−i32−1−i32−1+i32−1+i32001-11000000000000000
χ30222222-1-1-1-1-2−1+i3−1−i3-2-1-111−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3112200001−i321+i32−1+i3−1+i3−1−i3−1−i31−i321−i321+i321+i321−i321+i3200-22-2-1-11−i31+i31−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i31+i3−1+i32−1+i32−1−i32−1−i32001-11000000000000000
χ312222-2-2-1-1-1-1222-211-1-122222211220000-1-1-2-2-2-2-1-1-1-1-1-100-2-22-1-12211-1-111-1-1-2-211110011-1000000000000000
χ322222-2-2-1-1-1-12−1−i3−1+i3-211-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3112200001+i321−i321+i31+i31−i31−i31+i321+i321−i321−i321+i321−i3200-2-22-1-1−1−i3−1+i3−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i320011-1000000000000000
χ332222-2-2-1-1-1-12−1+i3−1−i3-211-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3112200001−i321+i321−i31−i31+i31+i31−i321−i321+i321+i321−i321+i3200-2-22-1-1−1+i3−1−i3−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i320011-1000000000000000
χ342222-2-2-1-1-1-1-22221111222222-1-1220000-1-1-2-2-2-2-1-1-1-1-1-1002-2-2-1-1-2-21111111122-1-1-1-100-111000000000000000
χ352222-2-2-1-1-1-1-2−1−i3−1+i321111−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-12200001+i321−i321+i31+i31−i31−i31+i321+i321−i321−i321+i321−i32002-2-2-1-11+i31−i3−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i3−1+i31+i321+i321−i321−i3200-111000000000000000
χ362222-2-2-1-1-1-1-2−1+i3−1−i321111−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-12200001−i321+i321−i31−i31+i31+i31−i321−i321+i321+i321−i321+i32002-2-2-1-11−i31+i3−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i3−1−i31−i321−i321+i321+i3200-111000000000000000
χ372-2-22002-2-2202200000-2-2-2-222002-22-2002200002-22-2-2-2000002-200000000000000002-20002-2002-2000000000
χ382-2-22002-2-2202200000-2-2-2-222002-2-22002200002-22-2-2-2000002-20000000000000000-22000-2200-22000000000
χ392-2-22002-2-220−1−i3−1+i3000001+i31−i31+i31−i3−1−i3−1+i3002-22-200−1−i3−1+i30000−1−i31+i3−1+i31−i31+i31−i3000002-200000000000000002-2000−1−i31+i300−1+i31−i3000000000
χ402-2-22002-2-220−1−i3−1+i3000001+i31−i31+i31−i3−1−i3−1+i3002-2-2200−1−i3−1+i30000−1−i31+i3−1+i31−i31+i31−i3000002-20000000000000000-220001+i3−1−i3001−i3−1+i3000000000
χ412-2-22002-2-220−1+i3−1−i3000001−i31+i31−i31+i3−1+i3−1−i3002-22-200−1+i3−1−i30000−1+i31−i3−1−i31+i31−i31+i3000002-200000000000000002-2000−1+i31−i300−1−i31+i3000000000
χ422-2-22002-2-220−1+i3−1−i3000001−i31+i31−i31+i3−1+i3−1−i3002-2-2200−1+i3−1−i30000−1+i31−i3−1−i31+i31−i31+i3000002-20000000000000000-220001−i3−1+i3001+i3−1−i3000000000
χ4333333333333003333300000033-1-1333300000000000033-1-1-1-1-10000000000000000-1-1-1-1-100000000-1-1-10000
χ4433333333333003333300000033-1-1-3-3-3-3000000000000-3-3-1-1-1-1-1000000000000000011-1-1-1000000001110000
χ453333333333-300-333-3-3000000-3-3-1-13333000000000000-3-31-11-1-10000000000000000-1-11-1100000000-1110000
χ463333333333-300-333-3-3000000-3-3-1-1-3-3-3-3000000000000331-11-1-10000000000000000111-11000000001-1-10000
χ473333-3-33333300-3-3-333000000-3-3-1-133-3-30000000000003-311-1-1-10000000000000000-1-111-10000000011-10000
χ483333-3-33333300-3-3-333000000-3-3-1-1-3-333000000000000-3311-1-1-100000000000000001111-100000000-1-110000
χ493333-3-33333-3003-3-3-3-300000033-1-133-3-3000000000000-33-111-1-10000000000000000-1-1-111000000001-110000
χ503333-3-33333-3003-3-3-3-300000033-1-1-3-3330000000000003-3-111-1-1000000000000000011-11100000000-11-10000
χ5144-4-44-444-4-40-2-204-40022-2-22200000000-2-22-22-22222-2-20000000002-2002-20000000000000000000000000000
χ5244-4-44-444-4-401+i31−i304-400−1−i3−1+i31+i31−i3−1−i3−1+i3000000001+i31−i3−1−i31+i3−1+i31−i3−1−i3−1−i3−1+i3−1+i31+i31−i3000000000−1−i31+i300−1+i31−i30000000000000000000000000000
χ5344-4-44-444-4-401−i31+i304-400−1+i3−1−i31−i31+i3−1+i3−1−i3000000001−i31+i3−1+i31−i3−1−i31+i3−1+i3−1+i3−1−i3−1−i31−i31+i3000000000−1+i31−i300−1−i31+i30000000000000000000000000000
χ5444-4-44-4-2-2220-2-20-22−2i32i322-2-222−2i32i3000000112-22-2-1-1-1-111000000000-11−i3i3-11−i3i300−i3i3−i3i300000000000000000000
χ5544-4-44-4-2-2220-2-20-222i3−2i322-2-2222i3−2i3000000112-22-2-1-1-1-111000000000-11i3−i3-11i3−i300i3−i3i3−i300000000000000000000
χ5644-4-44-4-2-22201+i31−i30-22−2i32i3−1−i3−1+i31+i31−i3−1−i3−1+i3−2i32i3000000−1−i32−1+i32−1−i31+i3−1+i31−i31+i321+i321−i321−i32−1−i32−1+i320000000001+i32−1−i32−3+i323−i321−i32−1+i323+i32−3−i3200−3+i323−i323+i32−3−i3200000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.