Finite Group Databasebeta

← Group #72243904

Character table — Group #72243904

Order 2916.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1222266666666666699181818181818181881818124444121212121212121212121212181836363636363636361621621623666618181818181818181818181827275454545454545454243243243
order133333333333333333333999999266333333333333333333333999999666266666666666666666666181818181818266
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1111111111111111111111111111-1-1-1111111111111111111111111111-1-1-1
χ311111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i3211111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i3211111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i32
χ411111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-11−i321+i3211111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-11−i321+i3211111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-11−i321+i32
χ511111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i3211111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i3211111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i32
χ611111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-11+i321−i3211111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-11+i321−i3211111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-11+i321−i32
χ722222222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-100022222222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-100022222222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1000
χ822222222-1-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i31−i321−i321−i321+i321+i321+i3200022222222-1-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i31−i321−i321−i321+i321+i321+i3200022222222-1-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i31−i321−i321−i321+i321+i321+i32000
χ922222222-1-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i31+i321+i321+i321−i321−i321−i3200022222222-1-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i31+i321+i321+i321−i321−i321−i3200022222222-1-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i31+i321+i321+i321−i321−i321−i32000
χ102-1-1-122-1-1222-1-1-1-1-1-122-1-12-1-12-1-10002-1-1-122-1-1222-1-1-1-1-1-122-1-12-1-12-1-10002-1-1-122-1-1222-1-1-1-1-1-122-1-12-1-12-1-1000
χ112-1-1-122-1-1222-1-1-1-1-1-1−1+i3−1−i31−i321+i32−1+i31−i321−i32−1−i31+i321+i320002-1-1-122-1-1222-1-1-1-1-1-1−1+i3−1−i31−i321+i32−1+i31−i321−i32−1−i31+i321+i320002-1-1-122-1-1222-1-1-1-1-1-1−1+i3−1−i31−i321+i32−1+i31−i321−i32−1−i31+i321+i32000
χ122-1-1-122-1-1222-1-1-1-1-1-1−1−i3−1+i31+i321−i32−1−i31+i321+i32−1+i31−i321−i320002-1-1-122-1-1222-1-1-1-1-1-1−1−i3−1+i31+i321−i32−1−i31+i321+i32−1+i31−i321−i320002-1-1-122-1-1222-1-1-1-1-1-1−1−i3−1+i31+i321−i32−1−i31+i321+i32−1+i31−i321−i32000
χ132-1-1-122-1-1-1-1-1222-1-1-122-1-1-12-1-12-10002-1-1-122-1-1-1-1-1222-1-1-122-1-1-12-1-12-10002-1-1-122-1-1-1-1-1222-1-1-122-1-1-12-1-12-1000
χ142-1-1-122-1-1-1-1-1222-1-1-1−1+i3−1−i31−i321+i321−i32−1+i31−i321+i32−1−i31+i320002-1-1-122-1-1-1-1-1222-1-1-1−1+i3−1−i31−i321+i321−i32−1+i31−i321+i32−1−i31+i320002-1-1-122-1-1-1-1-1222-1-1-1−1+i3−1−i31−i321+i321−i32−1+i31−i321+i32−1−i31+i32000
χ152-1-1-122-1-1-1-1-1222-1-1-1−1−i3−1+i31+i321−i321+i32−1−i31+i321−i32−1+i31−i320002-1-1-122-1-1-1-1-1222-1-1-1−1−i3−1+i31+i321−i321+i32−1−i31+i321−i32−1+i31−i320002-1-1-122-1-1-1-1-1222-1-1-1−1−i3−1+i31+i321−i321+i32−1−i31+i321−i32−1+i31−i32000
χ162-1-1-122-1-1-1-1-1-1-1-122222-1-1-1-12-1-120002-1-1-122-1-1-1-1-1-1-1-122222-1-1-1-12-1-120002-1-1-122-1-1-1-1-1-1-1-122222-1-1-1-12-1-12000
χ172-1-1-122-1-1-1-1-1-1-1-1222−1+i3−1−i31−i321+i321−i321−i32−1+i31+i321+i32−1−i30002-1-1-122-1-1-1-1-1-1-1-1222−1+i3−1−i31−i321+i321−i321−i32−1+i31+i321+i32−1−i30002-1-1-122-1-1-1-1-1-1-1-1222−1+i3−1−i31−i321+i321−i321−i32−1+i31+i321+i32−1−i3000
χ182-1-1-122-1-1-1-1-1-1-1-1222−1−i3−1+i31+i321−i321+i321+i32−1−i31−i321−i32−1+i30002-1-1-122-1-1-1-1-1-1-1-1222−1−i3−1+i31+i321−i321+i321+i32−1−i31−i321−i32−1+i30002-1-1-122-1-1-1-1-1-1-1-1222−1−i3−1+i31+i321−i321+i321+i32−1−i31−i321−i32−1+i3000
χ1966666-3-3-3000000000000000000000066666-3-3-3000000000000000000000066666-3-3-30000000000000000000000
χ2066-3-3-300003-303-303-3000000000000066-3-3-300003-303-303-3000000000000066-3-3-300003-303-303-30000000000000
χ2166-3-3-30003-303-303-30000000000000066-3-3-30003-303-303-30000000000000066-3-3-30003-303-303-300000000000000
χ2266-3-3-3000-303-303-303000000000000066-3-3-3000-303-303-303000000000000066-3-3-3000-303-303-3030000000000000
χ236-36-3-300003-33-30-30300000000000006-36-3-300003-33-30-30300000000000006-36-3-300003-33-30-3030000000000000
χ246-36-3-30003-30-30303-300000000000006-36-3-30003-30-30303-300000000000006-36-3-30003-30-30303-30000000000000
χ256-36-3-3000-30303-33-3000000000000006-36-3-3000-30303-33-3000000000000006-36-3-3000-30303-33-300000000000000
χ266-3-36-300003-3-3033-3000000000000006-3-36-300003-3-3033-3000000000000006-3-36-300003-3-3033-300000000000000
χ276-3-36-30003-3003-3-30300000000000006-3-36-30003-3003-3-30300000000000006-3-36-30003-3003-3-3030000000000000
χ286-3-36-3000-3033-3003-300000000000006-3-36-3000-3033-3003-300000000000006-3-36-3000-3033-3003-30000000000000
χ296-3-3-36-36-300000000000000000000006-3-3-36-36-300000000000000000000006-3-3-36-36-30000000000000000000000
χ306-3-3-36-3-3600000000000000000000006-3-3-36-3-3600000000000000000000006-3-3-36-3-360000000000000000000000
χ31111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ32111111111111111111111111111-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ3311111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i3211111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321−i321−i321+i321+i321+i32-11−i321+i32
χ3411111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-11−i321+i3211111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-11−i321+i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321−i321−i321+i321+i321+i321−1+i32−1−i32
χ3511111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i3211111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321+i321+i321−i321−i321−i32-11+i321−i32
χ3611111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-11+i321−i3211111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-11+i321−i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321+i321+i321−i321−i321−i321−1−i32−1+i32
χ3722222222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-100022222222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1000-2-2-2-2-2-2-2-2111111111-2-2-2-2111111000
χ3822222222-1-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i31−i321−i321−i321+i321+i321+i3200022222222-1-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i31−i321−i321−i321+i321+i321+i32000-2-2-2-2-2-2-2-21111111111−i31+i31−i31+i3−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32000
χ3922222222-1-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i31+i321+i321+i321−i321−i321−i3200022222222-1-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i31+i321+i321+i321−i321−i321−i32000-2-2-2-2-2-2-2-21111111111+i31−i31+i31−i3−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32000
χ402-1-1-122-1-1222-1-1-1-1-1-122-1-12-1-12-1-10002-1-1-122-1-1222-1-1-1-1-1-122-1-12-1-12-1-1000-2111-2-211-2-2-2111111-2-211-211-211000
χ412-1-1-122-1-1222-1-1-1-1-1-1−1+i3−1−i31−i321+i32−1+i31−i321−i32−1−i31+i321+i320002-1-1-122-1-1222-1-1-1-1-1-1−1+i3−1−i31−i321+i32−1+i31−i321−i32−1−i31+i321+i32000-2111-2-211-2-2-21111111−i31+i3−1+i32−1−i321−i3−1+i32−1+i321+i3−1−i32−1−i32000
χ422-1-1-122-1-1222-1-1-1-1-1-1−1−i3−1+i31+i321−i32−1−i31+i321+i32−1+i31−i321−i320002-1-1-122-1-1222-1-1-1-1-1-1−1−i3−1+i31+i321−i32−1−i31+i321+i32−1+i31−i321−i32000-2111-2-211-2-2-21111111+i31−i3−1−i32−1+i321+i3−1−i32−1−i321−i3−1+i32−1+i32000
χ432-1-1-122-1-1-1-1-1222-1-1-122-1-1-12-1-12-10002-1-1-122-1-1-1-1-1222-1-1-122-1-1-12-1-12-1000-2111-2-211111-2-2-2111-2-2111-211-21000
χ442-1-1-122-1-1-1-1-1222-1-1-1−1+i3−1−i31−i321+i321−i32−1+i31−i321+i32−1−i31+i320002-1-1-122-1-1-1-1-1222-1-1-1−1+i3−1−i31−i321+i321−i32−1+i31−i321+i32−1−i31+i32000-2111-2-211111-2-2-21111−i31+i3−1+i32−1−i32−1+i321−i3−1+i32−1−i321+i3−1−i32000
χ452-1-1-122-1-1-1-1-1222-1-1-1−1−i3−1+i31+i321−i321+i32−1−i31+i321−i32−1+i31−i320002-1-1-122-1-1-1-1-1222-1-1-1−1−i3−1+i31+i321−i321+i32−1−i31+i321−i32−1+i31−i32000-2111-2-211111-2-2-21111+i31−i3−1−i32−1+i32−1−i321+i3−1−i32−1+i321−i3−1+i32000
χ462-1-1-122-1-1-1-1-1-1-1-122222-1-1-1-12-1-120002-1-1-122-1-1-1-1-1-1-1-122222-1-1-1-12-1-12000-2111-2-211111111-2-2-2-2-21111-211-2000
χ472-1-1-122-1-1-1-1-1-1-1-1222−1+i3−1−i31−i321+i321−i321−i32−1+i31+i321+i32−1−i30002-1-1-122-1-1-1-1-1-1-1-1222−1+i3−1−i31−i321+i321−i321−i32−1+i31+i321+i32−1−i3000-2111-2-211111111-2-2-21−i31+i3−1+i32−1−i32−1+i32−1+i321−i3−1−i32−1−i321+i3000
χ482-1-1-122-1-1-1-1-1-1-1-1222−1−i3−1+i31+i321−i321+i321+i32−1−i31−i321−i32−1+i30002-1-1-122-1-1-1-1-1-1-1-1222−1−i3−1+i31+i321−i321+i321+i32−1−i31−i321−i32−1+i3000-2111-2-211111111-2-2-21+i31−i3−1−i32−1+i32−1−i32−1−i321+i3−1+i32−1+i321−i3000
χ4966666-3-3-3000000000000000000000066666-3-3-30000000000000000000000-6-6-6-6-63330000000000000000000000
χ5066-3-3-300003-303-303-3000000000000066-3-3-300003-303-303-30000000000000-6-63330000-330-330-330000000000000
χ5166-3-3-30003-303-303-30000000000000066-3-3-30003-303-303-300000000000000-6-6333000-330-330-3300000000000000
χ5266-3-3-3000-303-303-303000000000000066-3-3-3000-303-303-3030000000000000-6-633300030-330-330-30000000000000
χ536-36-3-300003-33-30-30300000000000006-36-3-300003-33-30-3030000000000000-63-6330000-33-33030-30000000000000
χ546-36-3-30003-30-30303-300000000000006-36-3-30003-30-30303-30000000000000-63-633000-33030-30-330000000000000
χ556-36-3-3000-30303-33-3000000000000006-36-3-3000-30303-33-300000000000000-63-63300030-30-33-3300000000000000
χ566-3-36-300003-3-3033-3000000000000006-3-36-300003-3-3033-300000000000000-633-630000-3330-3-3300000000000000
χ576-3-36-30003-3003-3-30300000000000006-3-36-30003-3003-3-3030000000000000-633-63000-3300-3330-30000000000000
χ586-3-36-3000-3033-3003-300000000000006-3-36-3000-3033-3003-30000000000000-633-6300030-3-3300-330000000000000
χ596-3-3-36-36-300000000000000000000006-3-3-36-36-30000000000000000000000-6333-63-630000000000000000000000
χ606-3-3-36-3-3600000000000000000000006-3-3-36-3-360000000000000000000000-6333-633-60000000000000000000000
χ61222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000
χ62222222222222222222222222222-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111000000000000000000000000000000
χ6322222222222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i32−1+i3−1−i3-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321−i321−i321+i321+i321+i32-11−i321+i32000000000000000000000000000000
χ6422222222222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-21−i31+i3-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321−i321−i321+i321+i321+i321−1+i32−1−i32000000000000000000000000000000
χ6522222222222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i32−1−i3−1+i3-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321+i321+i321−i321−i321−i32-11+i321−i32000000000000000000000000000000
χ6622222222222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-21+i31−i3-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321+i321+i321−i321−i321−i321−1−i32−1+i32000000000000000000000000000000
χ6744444444-2-2-2-2-2-2-2-2-24444-2-2-2-2-2-2000-2-2-2-2-2-2-2-2111111111-2-2-2-2111111000000000000000000000000000000000
χ6844444444-2-2-2-2-2-2-2-2-2−2+2i3−2−2i3−2+2i3−2−2i31−i31−i31−i31+i31+i31+i3000-2-2-2-2-2-2-2-21111111111−i31+i31−i31+i3−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32000000000000000000000000000000000
χ6944444444-2-2-2-2-2-2-2-2-2−2−2i3−2+2i3−2−2i3−2+2i31+i31+i31+i31−i31−i31−i3000-2-2-2-2-2-2-2-21111111111+i31−i31+i31−i3−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32000000000000000000000000000000000
χ704-2-2-244-2-2444-2-2-2-2-2-244-2-24-2-24-2-2000-2111-2-211-2-2-2111111-2-211-211-211000000000000000000000000000000000
χ714-2-2-244-2-2444-2-2-2-2-2-2−2+2i3−2−2i31−i31+i3−2+2i31−i31−i3−2−2i31+i31+i3000-2111-2-211-2-2-21111111−i31+i3−1+i32−1−i321−i3−1+i32−1+i321+i3−1−i32−1−i32000000000000000000000000000000000
χ724-2-2-244-2-2444-2-2-2-2-2-2−2−2i3−2+2i31+i31−i3−2−2i31+i31+i3−2+2i31−i31−i3000-2111-2-211-2-2-21111111+i31−i3−1−i32−1+i321+i3−1−i32−1−i321−i3−1+i32−1+i32000000000000000000000000000000000
χ734-2-2-244-2-2-2-2-2444-2-2-244-2-2-24-2-24-2000-2111-2-211111-2-2-2111-2-2111-211-21000000000000000000000000000000000
χ744-2-2-244-2-2-2-2-2444-2-2-2−2+2i3−2−2i31−i31+i31−i3−2+2i31−i31+i3−2−2i31+i3000-2111-2-211111-2-2-21111−i31+i3−1+i32−1−i32−1+i321−i3−1+i32−1−i321+i3−1−i32000000000000000000000000000000000
χ754-2-2-244-2-2-2-2-2444-2-2-2−2−2i3−2+2i31+i31−i31+i3−2−2i31+i31−i3−2+2i31−i3000-2111-2-211111-2-2-21111+i31−i3−1−i32−1+i32−1−i321+i3−1−i32−1+i321−i3−1+i32000000000000000000000000000000000
χ764-2-2-244-2-2-2-2-2-2-2-244444-2-2-2-24-2-24000-2111-2-211111111-2-2-2-2-21111-211-2000000000000000000000000000000000
χ774-2-2-244-2-2-2-2-2-2-2-2444−2+2i3−2−2i31−i31+i31−i31−i3−2+2i31+i31+i3−2−2i3000-2111-2-211111111-2-2-21−i31+i3−1+i32−1−i32−1+i32−1+i321−i3−1−i32−1−i321+i3000000000000000000000000000000000
χ784-2-2-244-2-2-2-2-2-2-2-2444−2−2i3−2+2i31+i31−i31+i31+i3−2−2i31−i31−i3−2+2i3000-2111-2-211111111-2-2-21+i31−i3−1−i32−1+i32−1−i32−1−i321+i3−1+i32−1+i321−i3000000000000000000000000000000000
χ791212121212-6-6-60000000000000000000000-6-6-6-6-63330000000000000000000000000000000000000000000000000000
χ801212-6-6-600006-606-606-60000000000000-6-63330000-330-330-330000000000000000000000000000000000000000000
χ811212-6-6-60006-606-606-600000000000000-6-6333000-330-330-3300000000000000000000000000000000000000000000
χ821212-6-6-6000-606-606-6060000000000000-6-633300030-330-330-30000000000000000000000000000000000000000000
χ8312-612-6-600006-66-60-6060000000000000-63-6330000-33-33030-30000000000000000000000000000000000000000000
χ8412-612-6-60006-60-60606-60000000000000-63-633000-33030-30-330000000000000000000000000000000000000000000
χ8512-612-6-6000-60606-66-600000000000000-63-63300030-30-33-3300000000000000000000000000000000000000000000
χ8612-6-612-600006-6-6066-600000000000000-633-630000-3330-3-3300000000000000000000000000000000000000000000
χ8712-6-612-60006-6006-6-6060000000000000-633-63000-3300-3330-30000000000000000000000000000000000000000000
χ8812-6-612-6000-6066-6006-60000000000000-633-6300030-3-3300-330000000000000000000000000000000000000000000
χ8912-6-6-612-612-60000000000000000000000-6333-63-630000000000000000000000000000000000000000000000000000
χ9012-6-6-612-6-6120000000000000000000000-6333-633-60000000000000000000000000000000000000000000000000000

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