Finite Group Databasebeta

← Group #11920924

Character table — Group #11920924

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size112223344666888812121616161616162424242424242424112223344666888812121616161616162424242424242424112223344666888812121616161616162424242424242424
order12244224424436664412121212121288888888366121266121261212366612121212121212122424242424242424366121266121261212366612121212121212122424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111-1-11111111-1-111-1-1-1-111-1-111-1-11111111-1-11111111-1-111-1-1-1-111-1-111-1-11111111-1-11111111-1-111-1-1-1-111-1-111-1-1
χ41111111-1-11111111-1-111-1-1-1-1-1-111-1-1111111111-1-11111111-1-111-1-1-1-1-1-111-1-1111111111-1-11111111-1-111-1-1-1-1-1-111-1-111
χ5111-1-1111-11-1-111111-1-1-111-1-1i−ii−ii−ii−i111-1-1111-11-1-111111-1-1-111-1-1i−ii−ii−ii−i111-1-1111-11-1-111111-1-1-111-1-1i−ii−ii−ii−i
χ6111-1-1111-11-1-111111-1-1-111-1-1−ii−ii−ii−ii111-1-1111-11-1-111111-1-1-111-1-1−ii−ii−ii−ii111-1-1111-11-1-111111-1-1-111-1-1−ii−ii−ii−ii
χ7111-1-111-111-1-11111-11-1-1-1-111i−i−iii−i−ii111-1-111-111-1-11111-11-1-1-1-111i−i−iii−i−ii111-1-111-111-1-11111-11-1-1-1-111i−i−iii−i−ii
χ8111-1-111-111-1-11111-11-1-1-1-111−iii−i−iii−i111-1-111-111-1-11111-11-1-1-1-111−iii−i−iii−i111-1-111-111-1-11111-11-1-1-1-111−iii−i−iii−i
χ9222222222222-1-1-1-122-1-1-1-1-1-100000000222222222222-1-1-1-122-1-1-1-1-1-100000000222222222222-1-1-1-122-1-1-1-1-1-100000000
χ102222222-2-2222-1-1-1-1-2-2-1-11111000000002222222-2-2222-1-1-1-1-2-2-1-11111000000002222222-2-2222-1-1-1-1-2-2-1-1111100000000
χ11222-2-2222-22-2-2-1-1-1-12-211-1-11100000000222-2-2222-22-2-2-1-1-1-12-211-1-11100000000222-2-2222-22-2-2-1-1-1-12-211-1-11100000000
χ12222-2-222-222-2-2-1-1-1-1-221111-1-100000000222-2-222-222-2-2-1-1-1-1-221111-1-100000000222-2-222-222-2-2-1-1-1-1-221111-1-100000000
χ1322-22-22200-22-22-2-22002-200000000000022-22-22200-22-22-2-22002-200000000000022-22-22200-22-22-2-22002-2000000000000
χ1422-22-22200-22-2-111-100-11−i3i3−i3i30000000022-22-22200-22-2-111-100-11−i3i3−i3i30000000022-22-22200-22-2-111-100-11−i3i3−i3i300000000
χ1522-22-22200-22-2-111-100-11i3−i3i3−i30000000022-22-22200-22-2-111-100-11i3−i3i3−i30000000022-22-22200-22-2-111-100-11i3−i3i3−i300000000
χ1622-2-222200-2-222-2-2200-2200000000000022-2-222200-2-222-2-2200-2200000000000022-2-222200-2-222-2-2200-22000000000000
χ1722-2-222200-2-22-111-1001-1−i3i3i3−i30000000022-2-222200-2-22-111-1001-1−i3i3i3−i30000000022-2-222200-2-22-111-1001-1−i3i3i3−i300000000
χ1822-2-222200-2-22-111-1001-1i3−i3−i3i30000000022-2-222200-2-22-111-1001-1i3−i3−i3i30000000022-2-222200-2-22-111-1001-1i3−i3−i3i300000000
χ1933333-1-133-1-1-10000-1-10000001111-1-1-1-133333-1-133-1-1-10000-1-10000001111-1-1-1-133333-1-133-1-1-10000-1-10000001111-1-1-1-1
χ2033333-1-133-1-1-10000-1-1000000-1-1-1-1111133333-1-133-1-1-10000-1-1000000-1-1-1-1111133333-1-133-1-1-10000-1-1000000-1-1-1-11111
χ2133333-1-1-3-3-1-1-100001100000011-1-1-1-11133333-1-1-3-3-1-1-100001100000011-1-1-1-11133333-1-1-3-3-1-1-100001100000011-1-1-1-111
χ2233333-1-1-3-3-1-1-1000011000000-1-11111-1-133333-1-1-3-3-1-1-1000011000000-1-11111-1-133333-1-1-3-3-1-1-1000011000000-1-11111-1-1
χ23333-3-3-1-13-3-1110000-11000000i−ii−i−ii−ii333-3-3-1-13-3-1110000-11000000i−ii−i−ii−ii333-3-3-1-13-3-1110000-11000000i−ii−i−ii−ii
χ24333-3-3-1-13-3-1110000-11000000−ii−iii−ii−i333-3-3-1-13-3-1110000-11000000−ii−iii−ii−i333-3-3-1-13-3-1110000-11000000−ii−iii−ii−i
χ25333-3-3-1-1-33-11100001-1000000i−i−ii−iii−i333-3-3-1-1-33-11100001-1000000i−i−ii−iii−i333-3-3-1-1-33-11100001-1000000i−i−ii−iii−i
χ26333-3-3-1-1-33-11100001-1000000−iii−ii−i−ii333-3-3-1-1-33-11100001-1000000−iii−ii−i−ii333-3-3-1-1-33-11100001-1000000−iii−ii−i−ii
χ274-40004-400000400-400000000000000004-40004-400000400-400000000000000004-40004-400000400-40000000000000000
χ284-40004-400000-2−2i32i3200000000000000004-40004-400000-2−2i32i3200000000000000004-40004-400000-2−2i32i320000000000000000
χ294-40004-400000-22i3−2i3200000000000000004-40004-400000-22i3−2i3200000000000000004-40004-400000-22i3−2i320000000000000000
χ3066-66-6-2-2002-220000000000000000000066-66-6-2-2002-220000000000000000000066-66-6-2-2002-2200000000000000000000
χ3166-6-66-2-20022-20000000000000000000066-6-66-2-20022-20000000000000000000066-6-66-2-20022-200000000000000000000
χ3212-12000-44000000000000000000000000012-12000-44000000000000000000000000012-12000-440000000000000000000000000
χ3311111111111111111111111111111111−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ34111111111111111111111111-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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−i32−1−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−i321+i321+i321+i321+i321+i321+i321+i321+i32
χ351111111-1-11111111-1-111-1-1-1-111-1-111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−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−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ361111111-1-11111111-1-111-1-1-1-1-1-111-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ37111-1-1111-11-1-111111-1-1-111-1-1i−ii−ii−ii−i−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11
χ38111-1-1111-11-1-111111-1-1-111-1-1−ii−ii−ii−ii−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11
χ39111-1-111-111-1-11111-11-1-1-1-111i−i−iii−i−ii−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11
χ40111-1-111-111-1-11111-11-1-1-1-111−iii−i−iii−i−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11
χ41222222222222-1-1-1-122-1-1-1-1-1-100000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i3200000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i3200000000
χ422222222-2-2222-1-1-1-1-2-2-1-1111100000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i31−i31−i321−i32−1+i32−1+i32−1+i32−1+i3200000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i31+i31+i321+i32−1−i32−1−i32−1−i32−1−i3200000000
χ43222-2-2222-22-2-2-1-1-1-12-211-1-11100000000−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i31−i3−1+i31−i31−i31−i321−i321−i321−i32−1+i31−i3−1+i32−1+i321−i321−i32−1+i32−1+i3200000000−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i31+i3−1−i31+i31+i31+i321+i321+i321+i32−1−i31+i3−1−i32−1−i321+i321+i32−1−i32−1−i3200000000
χ44222-2-222-222-2-2-1-1-1-1-221111-1-100000000−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i3−1+i3−1+i31−i31−i31−i321−i321−i321−i321−i3−1+i3−1+i32−1+i32−1+i32−1+i321−i321−i3200000000−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i3−1−i3−1−i31+i31+i31+i321+i321+i321+i321+i3−1−i3−1−i32−1−i32−1−i32−1−i321+i321+i3200000000
χ4522-22-22200-22-22-2-22002-2000000000000−1+i3−1+i31−i3−1+i31−i3−1+i3−1+i3001−i3−1+i31−i3−1+i31−i31−i3−1+i300−1+i31−i3000000000000−1−i3−1−i31+i3−1−i31+i3−1−i3−1−i3001+i3−1−i31+i3−1−i31+i31+i3−1−i300−1−i31+i3000000000000
χ4622-22-22200-22-2-111-100-11−i3i3−i3i300000000−1+i3−1+i31−i3−1+i31−i3−1+i3−1+i3001−i3−1+i31−i31−i32−1+i32−1+i321−i32001−i32−1+i323+i32−3−i323+i32−3−i3200000000−1−i3−1−i31+i3−1−i31+i3−1−i3−1−i3001+i3−1−i31+i31+i32−1−i32−1−i321+i32001+i32−1−i32−3+i323−i32−3+i323−i3200000000
χ4722-22-22200-22-2-111-100-11i3−i3i3−i300000000−1+i3−1+i31−i3−1+i31−i3−1+i3−1+i3001−i3−1+i31−i31−i32−1+i32−1+i321−i32001−i32−1+i32−3−i323+i32−3−i323+i3200000000−1−i3−1−i31+i3−1−i31+i3−1−i3−1−i3001+i3−1−i31+i31+i32−1−i32−1−i321+i32001+i32−1−i323−i32−3+i323−i32−3+i3200000000
χ4822-2-222200-2-222-2-2200-22000000000000−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i3001−i31−i3−1+i3−1+i31−i31−i3−1+i3001−i3−1+i3000000000000−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i3001+i31+i3−1−i3−1−i31+i31+i3−1−i3001+i3−1−i3000000000000
χ4922-2-222200-2-22-111-1001-1−i3i3i3−i300000000−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i3001−i31−i3−1+i31−i32−1+i32−1+i321−i3200−1+i321−i323+i32−3−i32−3−i323+i3200000000−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i3001+i31+i3−1−i31+i32−1−i32−1−i321+i3200−1−i321+i32−3+i323−i323−i32−3+i3200000000
χ5022-2-222200-2-22-111-1001-1i3−i3−i3i300000000−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i3001−i31−i3−1+i31−i32−1+i32−1+i321−i3200−1+i321−i32−3−i323+i323+i32−3−i3200000000−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i3001+i31+i3−1−i31+i32−1−i32−1−i321+i3200−1−i321+i323−i32−3+i32−3+i323−i3200000000
χ5133333-1-133-1-1-10000-1-10000001111-1-1-1-1−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i32−3+3i32−3+3i321−i321−i321−i3200001−i321−i32000000−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i32−3−3i32−3−3i321+i321+i321+i3200001+i321+i32000000−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ5233333-1-133-1-1-10000-1-1000000-1-1-1-11111−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i32−3+3i32−3+3i321−i321−i321−i3200001−i321−i320000001−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i32−3−3i32−3−3i321+i321+i321+i3200001+i321+i320000001+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ5333333-1-1-3-3-1-1-100001100000011-1-1-1-111−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i323−3i323−3i321−i321−i321−i320000−1+i32−1+i32000000−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i323+3i323+3i321+i321+i321+i320000−1−i32−1−i32000000−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
χ5433333-1-1-3-3-1-1-1000011000000-1-11111-1-1−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i323−3i323−3i321−i321−i321−i320000−1+i32−1+i320000001−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i323+3i323+3i321+i321+i321+i320000−1−i32−1−i320000001+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ55333-3-3-1-13-3-1110000-11000000i−ii−i−ii−ii−3+3i32−3+3i32−3+3i323−3i323−3i321−i321−i32−3+3i323−3i321−i32−1+i32−1+i3200001−i32−1+i32000000ζ7−ζ7ζ7−ζ7−ζ7ζ7−ζ7ζ7−3−3i32−3−3i32−3−3i323+3i323+3i321+i321+i32−3−3i323+3i321+i32−1−i32−1−i3200001+i32−1−i32000000ζ11−ζ11ζ11−ζ11−ζ11ζ11−ζ11ζ11
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χ9466-66-6-2-2002-2200000000000000000000−3−3i3−3−3i33+3i3−3−3i33+3i31+i31+i300−1−i31+i3−1−i300000000000000000000−3+3i3−3+3i33−3i3−3+3i33−3i31−i31−i300−1+i31−i3−1+i300000000000000000000
χ9566-6-66-2-20022-200000000000000000000−3−3i3−3−3i33+3i33+3i3−3−3i31+i31+i300−1−i3−1−i31+i300000000000000000000−3+3i3−3+3i33−3i33−3i3−3+3i31−i31−i300−1+i3−1+i31−i300000000000000000000
χ9612-12000-440000000000000000000000000−6−6i36+6i30002+2i3−2−2i30000000000000000000000000−6+6i36−6i30002−2i3−2+2i30000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.