Finite Group Databasebeta

← Group #72226013

Character table — Group #72226013

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size111122444444446666666688888888888812121212121212121818181824242424242424243232323232323232323232323232323236363636363636364848484848484848484848484848484848484848
order124424336612121212222244443666661212121212124444888822446666121212123366666612121212121212124444888866121212121212121212122424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111−1−i32−1+i32111−1−i32−1+i321111111111111111−1−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+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
χ4111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111−1−i32−1+i32111−1−i32−1+i321111-1-1-1-1-1-1-1-11111−1−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+i32-1-1-1-1-1-1-1-111111+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32
χ5111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111−1+i32−1−i32111−1+i32−1−i321111111111111111−1+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−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
χ6111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111−1+i32−1−i32111−1+i32−1−i321111-1-1-1-1-1-1-1-11111−1+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−i32-1-1-1-1-1-1-1-111111−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32
χ71111-1-1111111111-1-1111-1-11-1-1-1-11-1-111-1-111-1-111-1-11-11-1-1-1111-11-111-1-1-1-11111-1-111-1-111-1-111-1-11-11-111-1-111-1-111-1-111-1-1
χ81111-1-1111111111-1-1111-1-11-1-1-1-11-1-111-1-1-1-111-1-1111-11-1-1-1111-11-111-1-1-1-11111-1-111-1-1-1-111-1-1111-11-1-1-111-1-111-1-111-1-111
χ91111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-1111-1-111+i321−i32-1-111+i321−i3211-1-111-1-111-1-11-11-11+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3211-1-111-1-11-11-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ101111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-1111-1-111+i321−i32-1-111+i321−i3211-1-1-1-111-1-1111-11-11+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-111-1-1111-11-11+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ111111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-1111-1-111−i321+i32-1-111−i321+i3211-1-111-1-111-1-11-11-11−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3211-1-111-1-11-11-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ121111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-1111-1-111−i321+i32-1-111−i321+i3211-1-1-1-111-1-1111-11-11−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-111-1-1111-11-11−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ1311-1-11-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1i−ii−ii−ii−i11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1i−ii−ii−ii−i-1-111i−ii−ii−ii−ii−ii−ii−ii−i
χ1411-1-11-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1−ii−ii−ii−ii11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−ii−ii−ii−ii-1-111−ii−ii−ii−ii−ii−ii−ii−ii
χ1511-1-11-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1-1-1-111111−1−i32−1+i321111+i321−i32-1-1-1-1i−ii−ii−ii−i11-1-11+i321−i321+i321−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−i32i−ii−ii−ii−i-1-111ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7
χ1611-1-11-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1-1-1-111111−1−i32−1+i321111+i321−i32-1-1-1-1−ii−ii−ii−ii11-1-11+i321−i321+i321−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−ii−ii−ii−ii-1-111−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7
χ1711-1-11-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1-1-1-111111−1+i32−1−i321111−i321+i32-1-1-1-1i−ii−ii−ii−i11-1-11−i321+i321−i321+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+i32i−ii−ii−ii−i-1-111ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11
χ1811-1-11-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1-1-1-111111−1+i32−1−i321111−i321+i32-1-1-1-1−ii−ii−ii−ii11-1-11−i321+i321−i321+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−ii−ii−ii−ii-1-111−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11
χ1911-1-1-111111-1-1-1-1-111-111-1-11-1-1-1-1111-1-111i−i−iii−i−ii1-1-1111-1-11-11-111-1-1-1-111-1-111-1-111i−i−iii−i−ii-111-1i−i−iii−i−iii−i−iii−i−ii
χ2011-1-1-111111-1-1-1-1-111-111-1-11-1-1-1-1111-1-111−iii−i−iii−i1-1-1111-1-11-11-111-1-1-1-111-1-111-1-111−iii−i−iii−i-111-1−iii−i−iii−i−iii−i−iii−i
χ2111-1-1-11−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-111-111-1-111+i321−i32-1-11−1−i32−1+i32-1-111i−i−iii−i−ii1-1-11−1−i32−1+i321+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32i−i−iii−i−ii-111-1ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7
χ2211-1-1-11−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-111-111-1-111+i321−i32-1-11−1−i32−1+i32-1-111−iii−i−iii−i1-1-11−1−i32−1+i321+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−iii−i−iii−i-111-1−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ7
χ2311-1-1-11−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-111-111-1-111−i321+i32-1-11−1+i32−1−i32-1-111i−i−iii−i−ii1-1-11−1+i32−1−i321−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32i−i−iii−i−ii-111-1ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11
χ2411-1-1-11−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-111-111-1-111−i321+i32-1-11−1+i32−1−i32-1-111−iii−i−iii−i1-1-11−1+i32−1−i321−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−iii−i−iii−i-111-1−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ11
χ252222222222222222222222-122-1-1-122-1-1-1-100000000222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-10000000000000000
χ26222222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i322222222-1−1−i3−1+i3-1-1-1−1−i3−1+i3-1-1-1-1000000002222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i31+i321−i321+i321+i321−i321−i321+i321−i321+i321+i321+i321+i321−i321−i321−i321−i3200000000-1-1-1-10000000000000000
χ27222222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i322222222-1−1+i3−1−i3-1-1-1−1+i3−1−i3-1-1-1-1000000002222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i31−i321+i321−i321−i321+i321+i321−i321+i321−i321−i321−i321−i321+i321+i321+i321+i3200000000-1-1-1-10000000000000000
χ282222-2-2222222222-2-2222-2-2-1-2-211-1-2-2-1-111000000002-22-2-2-2222-22-2-1-11111-1-1-1-111-1-11100000000-11-110000000000000000
χ292222-2-2−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i32-2-2222-2-2-11+i31−i311-11+i31−i3-1-111000000002-22-21+i31−i3−1−i3−1+i3−1−i31+i3−1+i31−i31+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3200000000-11-110000000000000000
χ302222-2-2−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i32-2-2222-2-2-11−i31+i311-11−i31+i3-1-111000000002-22-21−i31+i3−1+i3−1−i3−1+i31−i3−1−i31+i31−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3200000000-11-110000000000000000
χ3122-2-22-22222-2-2-2-2-2-2-2-22222-122-1-1-1-2-211110000000022-2-2-2-2-2-22222-1-1-1-1-1-1-1-1111111110000000011-1-10000000000000000
χ3222-2-22-2−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i3-2-2-2-22222-1−1−i3−1+i3-1-1-11+i31−i311110000000022-2-21+i31−i31+i31−i3−1−i3−1−i3−1+i3−1+i31+i321−i321+i321+i321−i321−i321+i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i320000000011-1-10000000000000000
χ3322-2-22-2−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i3-2-2-2-22222-1−1+i3−1−i3-1-1-11−i31+i311110000000022-2-21−i31+i31−i31+i3−1+i3−1+i3−1−i3−1−i31−i321+i321−i321−i321+i321+i321−i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i320000000011-1-10000000000000000
χ3422-2-2-222222-2-2-2-2-222-222-2-2-1-2-211-12211-1-1000000002-2-2222-2-22-22-2-1-11111-1-111-1-111-1-1000000001-1-110000000000000000
χ3522-2-2-22−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i3-222-222-2-2-11+i31−i311-1−1−i3−1+i311-1-1000000002-2-22−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i31+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32000000001-1-110000000000000000
χ3622-2-2-22−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i3-222-222-2-2-11−i31+i311-1−1+i3−1−i311-1-1000000002-2-22−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i31−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32000000001-1-110000000000000000
χ3733333300000000-13-133-13-130033300333333333333-1-1-1-1000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ3833333300000000-13-133-13-1300333003333-3-3-3-3-3-3-3-3-1-1-1-100000000000000000000000011111111-1-1-1-10000000000000000
χ39333333333333333-13-1-13-130330003300001111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000001111-1-1-1-1000011111111-1-1-1-1-1-1-1-1
χ40333333333333333-13-1-13-13033000330000-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-111110000-1-1-1-1-1-1-1-111111111
χ41333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i323-13-1-13-130−3−3i32−3+3i32000−3−3i32−3+3i3200001111-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i3200000000000000001111-1-1-1-10000−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32
χ42333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i323-13-1-13-130−3−3i32−3+3i32000−3−3i32−3+3i320000-1-1-1-11111-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i320000000000000000-1-1-1-1111100001+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ43333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i323-13-1-13-130−3+3i32−3−3i32000−3+3i32−3−3i3200001111-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i3200000000000000001111-1-1-1-10000−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32
χ44333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i323-13-1-13-130−3+3i32−3−3i32000−3+3i32−3−3i320000-1-1-1-11111-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i320000000000000000-1-1-1-1111100001−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ453333-3-300000000-1-3133-1-31300-3-330033-3-333-3-333-3-3-11-11000000000000000000000000-1-111-1-111-11-110000000000000000
χ463333-3-300000000-1-3133-1-31300-3-330033-3-3-3-333-3-333-11-1100000000000000000000000011-1-111-1-1-11-110000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.