Finite Group Databasebeta

← Group #72274889

Character table — Group #72274889

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1122222444666612121212121212121212121212121212121212121212121212121212121216161616242424323232323232323232324848484864646464646472727272969696969696
order1222346661222242222224444666666666661212121212121212123366224336666661212666666661212444466661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32111−1+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−i32−1+i32−1−i32
χ311111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32111−1−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+i32−1−i32−1+i32
χ4111111111111111111-1-11111111111111111111111111111-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ5111111111111111111-1-1111111111111111111111111−1+i32−1−i32−1+i32−1−i32-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321+i32
χ6111111111111111111-1-1111111111111111111111111−1−i32−1+i32−1−i32−1+i32-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321−i32
χ7111-11-111-1-11-11-111-1-11111-1-1111111-1-1-1-1-11111-1-1-1-1-111111-1-1111-11-111-1-111111-11-1-1-111-1-11-11-1-1-1
χ8111-11-111-1-11-11-111-1-11111-1-1111111-1-1-1-1-11111-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321-1-1−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i321−i32−1−i321+i321−i321+i3211-1-1−1+i321−i32−1−i321+i321−i321+i32
χ9111-11-111-1-11-11-111-1-11111-1-1111111-1-1-1-1-11111-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321-1-1−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i321+i32−1+i321−i321+i321−i3211-1-1−1−i321+i32−1+i321−i321+i321−i32
χ10111-11-111-1-11-11-111-1-1-1-111-1-1111111-1-1-1-1-11111-1-1-1-1-11111-111111-11-111-1-1-1-1-1-11-11-1-1-1-1-111-11-1111
χ11111-11-111-1-11-11-111-1-1-1-111-1-1111111-1-1-1-1-11111-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32-111−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i321−i32−1−i321+i321−i321+i32-1-1111−i32−1+i321+i32−1−i32−1+i32−1−i32
χ12111-11-111-1-11-11-111-1-1-1-111-1-1111111-1-1-1-1-11111-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32-111−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i321+i32−1+i321−i321+i321−i32-1-1111+i32−1−i321−i32−1+i32−1−i32−1+i32
χ1311-111-11-11-1-111-11-11-1111-11-1111-1-1-1111-1-111-1-111-1-1-11111-11-111-11-1111-1-11111-11-11-1-11-11-1-11-11-1-1
χ1411-111-11-11-1-111-11-11-1111-11-1111-1-1-1111-1-111-1-111-1-1-1−1+i32−1−i32−1+i32−1−i32-11-1−1+i32−1−i321−i32−1+i321+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i32−1+i321+i32−1−i321−i321+i321-11-11−i32−1+i321+i32−1−i321−i321+i32
χ1511-111-11-11-1-111-11-11-1111-11-1111-1-1-1111-1-111-1-111-1-1-1−1−i32−1+i32−1−i32−1+i32-11-1−1−i32−1+i321+i32−1−i321−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i32−1−i321−i32−1+i321+i321−i321-11-11+i32−1−i321−i32−1+i321+i321−i32
χ1611-111-11-11-1-111-11-11-1-1-11-11-1111-1-1-1111-1-111-1-111-1-1-111111-1111-11-1111-1-1-1-1-1-1-11-11-1-1-11-111-11-111
χ1711-111-11-11-1-111-11-11-1-1-11-11-1111-1-1-1111-1-111-1-111-1-1-1−1+i32−1−i32−1+i32−1−i321-11−1+i32−1−i321−i32−1+i321+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i321−i32−1+i321+i32−1−i321−i321+i32-11-11−1+i321−i32−1−i321+i32−1+i32−1−i32
χ1811-111-11-11-1-111-11-11-1-1-11-11-1111-1-1-1111-1-111-1-111-1-1-1−1−i32−1+i32−1−i32−1+i321-11−1−i32−1+i321+i32−1−i321−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i321+i32−1−i321−i32−1+i321+i321−i32-11-11−1−i321+i32−1+i321−i32−1−i32−1+i32
χ1911-1-1111-1-11-1-1111-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111111-1-1111-1-1-1-111111111-1-1-1-1111-1-11-1-1-1-111
χ2011-1-1111-1-11-1-1111-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1111−1+i32−1−i32−1+i32−1−i32-1-11−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1−i321-1-111−i321−i321+i321+i32−1+i32−1−i32
χ2111-1-1111-1-11-1-1111-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1111−1−i32−1+i32−1−i32−1+i32-1-11−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1+i321-1-111+i321+i321−i321−i32−1−i32−1+i32
χ2211-1-1111-1-11-1-1111-1-11-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1111111111-111-1-1-1-11111-1-1-1-1-1-1-1-111-111-11111-1-1
χ2311-1-1111-1-11-1-1111-1-11-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1111−1+i32−1−i32−1+i32−1−i3211-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1−i32-111-1−1+i32−1+i32−1−i32−1−i321−i321+i32
χ2411-1-1111-1-11-1-1111-1-11-1-11-1-11111-1-1-1-1-1-11111-1-1-1-1111−1−i32−1+i32−1−i32−1+i3211-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1+i32-111-1−1−i32−1−i32−1+i32−1+i321+i321−i32
χ252222-12-1-1-1-122222222002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000-1-12222-1-1220000-1-1-1-1-1-10000000000
χ262222-12-1-1-1-122222222002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i30001−i321+i32−1+i3−1+i3−1−i3−1−i31−i321+i32−1+i3−1−i300001−i321−i321+i321+i321−i321+i320000000000
χ272222-12-1-1-1-122222222002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i30001+i321−i32−1−i3−1−i3−1+i3−1+i31+i321−i32−1−i3−1+i300001+i321+i321−i321−i321+i321−i320000000000
χ28222-2-1-2-1-1112-22-222-2-20022-2-2-1-1-1-1-1-111111-1-1-1-1111112222000-1-12-22-2-1-1-2-20000-11-11110000000000
χ29222-2-1-2-1-1112-22-222-2-20022-2-2-1-1-1-1-1-111111-1-1-1-111111−1+i3−1−i3−1+i3−1−i30001−i321+i32−1+i31−i3−1−i31+i31−i321+i321−i31+i300001−i32−1+i321+i32−1−i32−1+i32−1−i320000000000
χ30222-2-1-2-1-1112-22-222-2-20022-2-2-1-1-1-1-1-111111-1-1-1-111111−1−i3−1+i3−1−i3−1+i30001+i321−i32−1−i31+i3−1+i31−i31+i321−i321+i31−i300001+i32−1−i321−i32−1+i32−1−i32−1+i320000000000
χ3122-22-1-2-11-11-222-22-22-2002-22-2-1-1-1111-1-1-111-1-111-1-11112222000-1-1-22-22-1-1-2-200001-11-1110000000000
χ3222-22-1-2-11-11-222-22-22-2002-22-2-1-1-1111-1-1-111-1-111-1-1111−1+i3−1−i3−1+i3−1−i30001−i321+i321−i3−1+i31+i3−1−i31−i321+i321−i31+i30000−1+i321−i32−1−i321+i32−1+i32−1−i320000000000
χ3322-22-1-2-11-11-222-22-22-2002-22-2-1-1-1111-1-1-111-1-111-1-1111−1−i3−1+i3−1−i3−1+i30001+i321−i321+i3−1−i31−i3−1+i31+i321−i321+i31−i30000−1−i321+i32−1+i321−i32−1−i32−1+i320000000000
χ3422-2-2-12-111-1-2-2222-2-22002-2-22-1-1-1111111-1-1-1-11111-1-1-12222000-1-1-2-2-2-2-1-12200001111-1-10000000000
χ3522-2-2-12-111-1-2-2222-2-22002-2-22-1-1-1111111-1-1-1-11111-1-1-1−1+i3−1−i3−1+i3−1−i30001−i321+i321−i31−i31+i31+i31−i321+i32−1+i3−1−i30000−1+i32−1+i32−1−i32−1−i321−i321+i320000000000
χ3622-2-2-12-111-1-2-2222-2-22002-2-22-1-1-1111111-1-1-1-11111-1-1-1−1−i3−1+i3−1−i3−1+i30001+i321−i321+i31+i31−i31−i31+i321−i32−1−i3−1+i30000−1−i32−1−i32−1+i32−1+i321+i321−i320000000000
χ3733333333333333-1-1-1-133-1-1-1-13-1-13-1-13-1-1-1-1-1-1-1-1-1-13-1-1000033300000000000000000000-1-1-1-1000000
χ3833333333333333-1-1-1-1-3-3-1-1-1-13-1-13-1-13-1-1-1-1-1-1-1-1-1-13-1-10000-3-3-3000000000000000000001111000000
χ39333-33-333-3-33-33-3-1-11133-1-1113-1-13-1-1-31111-1-1-1-111-31100003-3-300000000000000000000-1-111000000
χ40333-33-333-3-33-33-3-1-111-3-3-1-1113-1-13-1-1-31111-1-1-1-111-3110000-3330000000000000000000011-1-1000000
χ4133-333-33-33-3-333-3-11-1133-11-113-1-1-3113-1-111-1-111-1-1-3110000-33-300000000000000000000-11-11000000
χ4233-333-33-33-3-333-3-11-11-3-3-11-113-1-1-3113-1-111-1-111-1-1-31100003-33000000000000000000001-11-1000000
χ4333-3-3333-3-33-3-333-111-133-111-13-1-1-311-311-1-1-1-111113-1-10000-3-3300000000000000000000-111-1000000
χ4433-3-3333-3-33-3-333-111-1-3-3-111-13-1-1-311-311-1-1-1-111113-1-1000033-3000000000000000000001-1-11000000
χ456666666666-2-2-2-2222-200-2-2-22-222-222-222-2-2-2-2-2-2-2-2-2220000000000000000000000000000000000000
χ466666666666-2-2-2-2-2-2-2200222-2-2-2-2-2-2-2-2-2-222222222-2-2-20000000000000000000000000000000000000
χ476666-36-3-3-3-36666-2-2-2-200-2-2-2-2-311-311-31111111111-3110000000000000000000000000000000000000
χ486666-36-3-3-3-3-2-2-2-2222-200-2-2-221−1+2i3−1−2i31−1+2i3−1−2i31−1+2i3−1−2i3111111111−1+2i3−1−2i30000000000000000000000000000000000000
χ496666-36-3-3-3-3-2-2-2-2222-200-2-2-221−1−2i3−1+2i31−1−2i3−1+2i31−1−2i3−1+2i3111111111−1−2i3−1+2i30000000000000000000000000000000000000
χ506666-36-3-3-3-3-2-2-2-2-2-2-2200222-2111111111−1+2i3−1−2i3−1+2i3−1−2i3−1+2i3−1−2i3−1+2i3−1−2i31110000000000000000000000000000000000000
χ516666-36-3-3-3-3-2-2-2-2-2-2-2200222-2111111111−1−2i3−1+2i3−1−2i3−1+2i3−1−2i3−1+2i3−1−2i3−1+2i31110000000000000000000000000000000000000
χ52666-66-666-6-6-22-2222-2200-2-22-2-222-2222-2-222-2-2-2-2222-2-20000000000000000000000000000000000000
χ53666-66-666-6-6-22-22-2-22-20022-22-2-2-2-2-2-2222-2-22222-2-22220000000000000000000000000000000000000
χ54666-6-3-6-3-3336-66-6-2-22200-2-222-311-3113-1-1-1-11111-1-13-1-10000000000000000000000000000000000000
χ55666-6-3-6-3-333-22-2222-2200-2-22-21−1+2i3−1−2i31−1+2i3−1−2i3-11−2i31+2i3-1-11111-1-1-11−2i31+2i30000000000000000000000000000000000000
χ56666-6-3-6-3-333-22-2222-2200-2-22-21−1−2i3−1+2i31−1−2i3−1+2i3-11+2i31−2i3-1-11111-1-1-11+2i31−2i30000000000000000000000000000000000000
χ57666-6-3-6-3-333-22-22-2-22-20022-22111111-1-1-11+2i31−2i3−1−2i3−1+2i3−1−2i3−1+2i31+2i31−2i3-1-1-10000000000000000000000000000000000000
χ58666-6-3-6-3-333-22-22-2-22-20022-22111111-1-1-11−2i31+2i3−1+2i3−1−2i3−1+2i3−1−2i31−2i31+2i3-1-1-10000000000000000000000000000000000000
χ5966-666-66-66-62-2-222-22200-22-2-2-2222-2-2-22222-2-222-2-22-2-20000000000000000000000000000000000000
χ6066-666-66-66-62-2-22-22-2-2002-222-2-2-2222-2-2-2-2-222-2-2222220000000000000000000000000000000000000
χ6166-66-3-6-33-332-2-222-22200-22-2-21−1+2i3−1−2i3-11−2i31+2i31−1+2i3−1−2i3-1-111-1-111-11−2i31+2i30000000000000000000000000000000000000
χ6266-66-3-6-33-332-2-222-22200-22-2-21−1−2i3−1+2i3-11+2i31−2i31−1−2i3−1+2i3-1-111-1-111-11+2i31−2i30000000000000000000000000000000000000
χ6366-66-3-6-33-332-2-22-22-2-2002-222111-1-1-11111+2i31−2i3−1−2i3−1+2i31+2i31−2i3−1−2i3−1+2i3-1-1-10000000000000000000000000000000000000
χ6466-66-3-6-33-332-2-22-22-2-2002-222111-1-1-11111−2i31+2i3−1+2i3−1−2i31−2i31+2i3−1+2i3−1−2i3-1-1-10000000000000000000000000000000000000
χ6566-66-3-6-33-33-666-6-22-2200-22-22-3113-1-1-311-1-111-1-1113-1-10000000000000000000000000000000000000
χ6666-6-6666-6-6622-2-22-2-2-200-2222-2222-2-22-2-2-2-2-2-22222-2220000000000000000000000000000000000000
χ6766-6-6666-6-6622-2-2-2222002-2-2-2-2-2-22222222222-2-2-2-2-2-2-20000000000000000000000000000000000000
χ6866-6-6-36-333-322-2-22-2-2-200-22221−1+2i3−1−2i3-11−2i31+2i3-11−2i31+2i31111-1-1-1-11−1+2i3−1−2i30000000000000000000000000000000000000
χ6966-6-6-36-333-322-2-22-2-2-200-22221−1−2i3−1+2i3-11+2i31−2i3-11+2i31−2i31111-1-1-1-11−1−2i3−1+2i30000000000000000000000000000000000000
χ7066-6-6-36-333-322-2-2-2222002-2-2-2111-1-1-1-1-1-1−1+2i3−1−2i3−1+2i3−1−2i31−2i31+2i31−2i31+2i31110000000000000000000000000000000000000
χ7166-6-6-36-333-322-2-2-2222002-2-2-2111-1-1-1-1-1-1−1−2i3−1+2i3−1−2i3−1+2i31+2i31−2i31+2i31−2i31110000000000000000000000000000000000000
χ7266-6-6-36-333-3-6-666-222-200-222-2-3113-1-13-1-11111-1-1-1-1-3110000000000000000000000000000000000000
χ738-80080-8000000000004-400000000000000000000000022-2-2000220000-2-2002-22-20000000000000000
χ748-80080-8000000000004-4000000000000000000000000−1+i3−1−i31−i31+i3000−1+i3−1−i300001−i31+i300−1+i31−i3−1−i31+i30000000000000000
χ758-80080-8000000000004-4000000000000000000000000−1−i3−1+i31+i31−i3000−1−i3−1+i300001+i31−i300−1−i31+i3−1+i31−i30000000000000000
χ768-80080-800000000000-4400000000000000000000000022-2-2000220000-2-200-22-220000000000000000
χ778-80080-800000000000-44000000000000000000000000−1+i3−1−i31−i31+i3000−1+i3−1−i300001−i31+i3001−i3−1+i31+i3−1−i30000000000000000
χ788-80080-800000000000-44000000000000000000000000−1−i3−1+i31+i31−i3000−1−i3−1+i300001+i31−i3001+i3−1−i31−i3−1+i30000000000000000
χ7916-1600-808000000000000000000000000000000000000044-4-4000-2-20000220000000000000000000000
χ8016-1600-8080000000000000000000000000000000000000−2+2i3−2−2i32−2i32+2i30001−i31+i30000−1+i3−1−i30000000000000000000000
χ8116-1600-8080000000000000000000000000000000000000−2−2i3−2+2i32+2i32−2i30001+i31−i30000−1−i3−1+i30000000000000000000000

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