Finite Group Databasebeta

← Group #72276745

Character table — Group #72276745

Order 5760.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111010151520202020242430301110101515202020202424303044404060608080808096961201204440406060808080809696120120444040606080808080969612012044404060608080808096961201206660609090120120120120144144180180
order12442236121251044224422661212101044361212663612121530121236121266361212153012126612126666121230301212661212666612123030121244444412121212202044
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211-1-11111-1-111-1-111-1-11111-1-111-1-111-1-11111-1-111-1-111-1-11111-1-111-1-111-1-11111-1-111-1-111-1-11111-1-111-1-111-1-11111-1-111-1-1
χ31-1i−i1-11-1i−i1-1i−i1-1i−i1-11-1i−i1-1i−i1-1i−i1-11-1i−i1-1i−i1-1i−i1-11-1i−i1-1i−i1-1i−i1-11-1i−i1-1i−i1-1i−i1-11-1i−i1-1i−i1-1i−i1-11-1i−i1-1i−i
χ41-1−ii1-11-1−ii1-1−ii1-1−ii1-11-1−ii1-1−ii1-1−ii1-11-1−ii1-1−ii1-1−ii1-11-1−ii1-1−ii1-1−ii1-11-1−ii1-1−ii1-1−ii1-11-1−ii1-1−ii1-1−ii1-11-1−ii1-1−ii
χ544220011-1-1-1-10044220011-1-1-1-10044220011-1-1-1-10044220011-1-1-1-10044220011-1-1-1-10044220011-1-1-1-10044220011-1-1-1-100
χ644-2-2001111-1-10044-2-2001111-1-10044-2-2001111-1-10044-2-2001111-1-10044-2-2001111-1-10044-2-2001111-1-10044-2-2001111-1-100
χ74-42i−2i001-1−ii-11004-42i−2i001-1−ii-11004-42i−2i001-1−ii-11004-42i−2i001-1−ii-11004-42i−2i001-1−ii-11004-42i−2i001-1−ii-11004-42i−2i001-1−ii-1100
χ84-4−2i2i001-1i−i-11004-4−2i2i001-1i−i-11004-4−2i2i001-1i−i-11004-4−2i2i001-1i−i-11004-4−2i2i001-1i−i-11004-4−2i2i001-1i−i-11004-4−2i2i001-1i−i-1100
χ9551111-1-11100-1-1551111-1-11100-1-1551111-1-11100-1-1551111-1-11100-1-1551111-1-11100-1-1551111-1-11100-1-1551111-1-11100-1-1
χ1055-1-111-1-1-1-1001155-1-111-1-1-1-1001155-1-111-1-1-1-1001155-1-111-1-1-1-1001155-1-111-1-1-1-1001155-1-111-1-1-1-1001155-1-111-1-1-1-10011
χ115-5i−i1-1-11i−i00−ii5-5i−i1-1-11i−i00−ii5-5i−i1-1-11i−i00−ii5-5i−i1-1-11i−i00−ii5-5i−i1-1-11i−i00−ii5-5i−i1-1-11i−i00−ii5-5i−i1-1-11i−i00−ii
χ125-5−ii1-1-11−ii00i−i5-5−ii1-1-11−ii00i−i5-5−ii1-1-11−ii00i−i5-5−ii1-1-11−ii00i−i5-5−ii1-1-11−ii00i−i5-5−ii1-1-11−ii00i−i5-5−ii1-1-11−ii00i−i
χ136600-2-2000011006600-2-2000011006600-2-2000011006600-2-2000011006600-2-2000011006600-2-2000011006600-2-200001100
χ146-600-2200001-1006-600-2200001-1006-600-2200001-1006-600-2200001-1006-600-2200001-1006-600-2200001-1006-600-2200001-100
χ151111111111111111111111111111−1+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−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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3211111111111111
χ1611-1-11111-1-111-1-111-1-11111-1-111-1-1−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i3211-1-11111-1-111-1-1
χ171-1i−i1-11-1i−i1-1i−i1-1i−i1-11-1i−i1-1i−i−1+i321−i32ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7−1+i321−i32ζ7−ζ7−1−i321+i32ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11−1−i321+i32ζ11−ζ11−1+i321−i32ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7−1+i321−i32ζ7−ζ7−1−i321+i32ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11−1−i321+i32ζ11−ζ111-1i−i1-11-1i−i1-1i−i
χ181-1−ii1-11-1−ii1-1−ii1-1−ii1-11-1−ii1-1−ii−1+i321−i32−ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7−1+i321−i32−ζ7ζ7−1−i321+i32−ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11−1−i321+i32−ζ11ζ11−1+i321−i32−ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7−1+i321−i32−ζ7ζ7−1−i321+i32−ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11−1−i321+i32−ζ11ζ111-1−ii1-11-1−ii1-1−ii
χ1944220011-1-1-1-10044220011-1-1-1-100−2+2i3−2+2i3−1+i3−1+i300−1+i32−1+i321−i321−i321−i321−i3200−2−2i3−2−2i3−1−i3−1−i300−1−i32−1−i321+i321+i321+i321+i3200−2+2i3−2+2i3−1+i3−1+i300−1+i32−1+i321−i321−i321−i321−i3200−2−2i3−2−2i3−1−i3−1−i300−1−i32−1−i321+i321+i321+i321+i320044220011-1-1-1-100
χ2044-2-2001111-1-10044-2-2001111-1-100−2+2i3−2+2i31−i31−i300−1+i32−1+i32−1+i32−1+i321−i321−i3200−2−2i3−2−2i31+i31+i300−1−i32−1−i32−1−i32−1−i321+i321+i3200−2+2i3−2+2i31−i31−i300−1+i32−1+i32−1+i32−1+i321−i321−i3200−2−2i3−2−2i31+i31+i300−1−i32−1−i32−1−i32−1−i321+i321+i320044-2-2001111-1-100
χ214-42i−2i001-1−ii-11004-42i−2i001-1−ii-1100−2+2i32−2i32ζ7−2ζ700−1+i321−i32−ζ7ζ71−i32−1+i3200−2−2i32+2i32ζ11−2ζ1100−1−i321+i32−ζ11ζ111+i32−1−i3200−2+2i32−2i32ζ7−2ζ700−1+i321−i32−ζ7ζ71−i32−1+i3200−2−2i32+2i32ζ11−2ζ1100−1−i321+i32−ζ11ζ111+i32−1−i32004-42i−2i001-1−ii-1100
χ224-4−2i2i001-1i−i-11004-4−2i2i001-1i−i-1100−2+2i32−2i3−2ζ72ζ700−1+i321−i32ζ7−ζ71−i32−1+i3200−2−2i32+2i3−2ζ112ζ1100−1−i321+i32ζ11−ζ111+i32−1−i3200−2+2i32−2i3−2ζ72ζ700−1+i321−i32ζ7−ζ71−i32−1+i3200−2−2i32+2i3−2ζ112ζ1100−1−i321+i32ζ11−ζ111+i32−1−i32004-4−2i2i001-1i−i-1100
χ23551111-1-11100-1-1551111-1-11100-1-1−5+5i32−5+5i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32001−i321−i32−5−5i32−5−5i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32001+i321+i32−5+5i32−5+5i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32001−i321−i32−5−5i32−5−5i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32001+i321+i32551111-1-11100-1-1
χ2455-1-111-1-1-1-1001155-1-111-1-1-1-10011−5+5i32−5+5i321−i321−i32−1+i32−1+i321−i321−i321−i321−i3200−1+i32−1+i32−5−5i32−5−5i321+i321+i32−1−i32−1−i321+i321+i321+i321+i3200−1−i32−1−i32−5+5i32−5+5i321−i321−i32−1+i32−1+i321−i321−i321−i321−i3200−1+i32−1+i32−5−5i32−5−5i321+i321+i32−1−i32−1−i321+i321+i321+i321+i3200−1−i32−1−i3255-1-111-1-1-1-10011
χ255-5i−i1-1-11i−i00−ii5-5i−i1-1-11i−i00−ii−5+5i325−5i32ζ7−ζ7−1+i321−i321−i32−1+i32ζ7−ζ700−ζ7ζ7−5−5i325+5i32ζ11−ζ11−1−i321+i321+i32−1−i32ζ11−ζ1100−ζ11ζ11−5+5i325−5i32ζ7−ζ7−1+i321−i321−i32−1+i32ζ7−ζ700−ζ7ζ7−5−5i325+5i32ζ11−ζ11−1−i321+i321+i32−1−i32ζ11−ζ1100−ζ11ζ115-5i−i1-1-11i−i00−ii
χ265-5−ii1-1-11−ii00i−i5-5−ii1-1-11−ii00i−i−5+5i325−5i32−ζ7ζ7−1+i321−i321−i32−1+i32−ζ7ζ700ζ7−ζ7−5−5i325+5i32−ζ11ζ11−1−i321+i321+i32−1−i32−ζ11ζ1100ζ11−ζ11−5+5i325−5i32−ζ7ζ7−1+i321−i321−i32−1+i32−ζ7ζ700ζ7−ζ7−5−5i325+5i32−ζ11ζ11−1−i321+i321+i32−1−i32−ζ11ζ1100ζ11−ζ115-5−ii1-1-11−ii00i−i
χ276600-2-2000011006600-2-200001100−3+3i3−3+3i3001−i31−i30000−1+i32−1+i3200−3−3i3−3−3i3001+i31+i30000−1−i32−1−i3200−3+3i3−3+3i3001−i31−i30000−1+i32−1+i3200−3−3i3−3−3i3001+i31+i30000−1−i32−1−i32006600-2-200001100
χ286-600-2200001-1006-600-2200001-100−3+3i33−3i3001−i3−1+i30000−1+i321−i3200−3−3i33+3i3001+i3−1−i30000−1−i321+i3200−3+3i33−3i3001−i3−1+i30000−1+i321−i3200−3−3i33+3i3001+i3−1−i30000−1−i321+i32006-600-2200001-100
χ291111111111111111111111111111−1−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+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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3211111111111111
χ3011-1-11111-1-111-1-111-1-11111-1-111-1-1−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i3211-1-11111-1-111-1-1
χ311-1i−i1-11-1i−i1-1i−i1-1i−i1-11-1i−i1-1i−i−1−i321+i32ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11−1−i321+i32ζ11−ζ11−1+i321−i32ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7−1+i321−i32ζ7−ζ7−1−i321+i32ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11−1−i321+i32ζ11−ζ11−1+i321−i32ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7−1+i321−i32ζ7−ζ71-1i−i1-11-1i−i1-1i−i
χ321-1−ii1-11-1−ii1-1−ii1-1−ii1-11-1−ii1-1−ii−1−i321+i32−ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11−1−i321+i32−ζ11ζ11−1+i321−i32−ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7−1+i321−i32−ζ7ζ7−1−i321+i32−ζ11ζ11−1−i321+i32−1−i321+i32−ζ11ζ11−1−i321+i32−ζ11ζ11−1+i321−i32−ζ7ζ7−1+i321−i32−1+i321−i32−ζ7ζ7−1+i321−i32−ζ7ζ71-1−ii1-11-1−ii1-1−ii
χ3344220011-1-1-1-10044220011-1-1-1-100−2−2i3−2−2i3−1−i3−1−i300−1−i32−1−i321+i321+i321+i321+i3200−2+2i3−2+2i3−1+i3−1+i300−1+i32−1+i321−i321−i321−i321−i3200−2−2i3−2−2i3−1−i3−1−i300−1−i32−1−i321+i321+i321+i321+i3200−2+2i3−2+2i3−1+i3−1+i300−1+i32−1+i321−i321−i321−i321−i320044220011-1-1-1-100
χ3444-2-2001111-1-10044-2-2001111-1-100−2−2i3−2−2i31+i31+i300−1−i32−1−i32−1−i32−1−i321+i321+i3200−2+2i3−2+2i31−i31−i300−1+i32−1+i32−1+i32−1+i321−i321−i3200−2−2i3−2−2i31+i31+i300−1−i32−1−i32−1−i32−1−i321+i321+i3200−2+2i3−2+2i31−i31−i300−1+i32−1+i32−1+i32−1+i321−i321−i320044-2-2001111-1-100
χ354-42i−2i001-1−ii-11004-42i−2i001-1−ii-1100−2−2i32+2i32ζ11−2ζ1100−1−i321+i32−ζ11ζ111+i32−1−i3200−2+2i32−2i32ζ7−2ζ700−1+i321−i32−ζ7ζ71−i32−1+i3200−2−2i32+2i32ζ11−2ζ1100−1−i321+i32−ζ11ζ111+i32−1−i3200−2+2i32−2i32ζ7−2ζ700−1+i321−i32−ζ7ζ71−i32−1+i32004-42i−2i001-1−ii-1100
χ364-4−2i2i001-1i−i-11004-4−2i2i001-1i−i-1100−2−2i32+2i3−2ζ112ζ1100−1−i321+i32ζ11−ζ111+i32−1−i3200−2+2i32−2i3−2ζ72ζ700−1+i321−i32ζ7−ζ71−i32−1+i3200−2−2i32+2i3−2ζ112ζ1100−1−i321+i32ζ11−ζ111+i32−1−i3200−2+2i32−2i3−2ζ72ζ700−1+i321−i32ζ7−ζ71−i32−1+i32004-4−2i2i001-1i−i-1100
χ37551111-1-11100-1-1551111-1-11100-1-1−5−5i32−5−5i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32001+i321+i32−5+5i32−5+5i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32001−i321−i32−5−5i32−5−5i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32001+i321+i32−5+5i32−5+5i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32001−i321−i32551111-1-11100-1-1
χ3855-1-111-1-1-1-1001155-1-111-1-1-1-10011−5−5i32−5−5i321+i321+i32−1−i32−1−i321+i321+i321+i321+i3200−1−i32−1−i32−5+5i32−5+5i321−i321−i32−1+i32−1+i321−i321−i321−i321−i3200−1+i32−1+i32−5−5i32−5−5i321+i321+i32−1−i32−1−i321+i321+i321+i321+i3200−1−i32−1−i32−5+5i32−5+5i321−i321−i32−1+i32−1+i321−i321−i321−i321−i3200−1+i32−1+i3255-1-111-1-1-1-10011
χ395-5i−i1-1-11i−i00−ii5-5i−i1-1-11i−i00−ii−5−5i325+5i32ζ11−ζ11−1−i321+i321+i32−1−i32ζ11−ζ1100−ζ11ζ11−5+5i325−5i32ζ7−ζ7−1+i321−i321−i32−1+i32ζ7−ζ700−ζ7ζ7−5−5i325+5i32ζ11−ζ11−1−i321+i321+i32−1−i32ζ11−ζ1100−ζ11ζ11−5+5i325−5i32ζ7−ζ7−1+i321−i321−i32−1+i32ζ7−ζ700−ζ7ζ75-5i−i1-1-11i−i00−ii
χ405-5−ii1-1-11−ii00i−i5-5−ii1-1-11−ii00i−i−5−5i325+5i32−ζ11ζ11−1−i321+i321+i32−1−i32−ζ11ζ1100ζ11−ζ11−5+5i325−5i32−ζ7ζ7−1+i321−i321−i32−1+i32−ζ7ζ700ζ7−ζ7−5−5i325+5i32−ζ11ζ11−1−i321+i321+i32−1−i32−ζ11ζ1100ζ11−ζ11−5+5i325−5i32−ζ7ζ7−1+i321−i321−i32−1+i32−ζ7ζ700ζ7−ζ75-5−ii1-1-11−ii00i−i
χ416600-2-2000011006600-2-200001100−3−3i3−3−3i3001+i31+i30000−1−i32−1−i3200−3+3i3−3+3i3001−i31−i30000−1+i32−1+i3200−3−3i3−3−3i3001+i31+i30000−1−i32−1−i3200−3+3i3−3+3i3001−i31−i30000−1+i32−1+i32006600-2-200001100
χ426-600-2200001-1006-600-2200001-100−3−3i33+3i3001+i3−1−i30000−1−i321+i3200−3+3i33−3i3001−i3−1+i30000−1+i321−i3200−3−3i33+3i3001+i3−1−i30000−1−i321+i3200−3+3i33−3i3001−i3−1+i30000−1+i321−i32006-600-2200001-100
χ4322222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111100000000000000
χ4422-2-22222-2-222-2-2-2-222-2-2-2-222-2-222-1-111-1-1-1-111-1-111-1-111-1-1-1-111-1-11111-1-11111-1-111-1-111-1-11111-1-111-1-100000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.