Finite Group Databasebeta

← Group #67621

Character table — Group #67621

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222222222222222222244444444444444444444444444444444442424242424242424
order12222234444444466666661212121212121212444444444412121212121212121212121212121212121212121212121288888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ611111111111-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii
χ711111111111-1-1-1-1111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iii
χ811111111111-1-1-1-1111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i
χ91111-1-1111-1-111-1-1-1-1111-1-11111-1-1-1-11-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i
χ101111-1-1111-1-111-1-1-1-1111-1-11111-1-1-1-11-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii
χ111111-1-1111-1-111-1-1-1-1111-1-11111-1-1-1-11-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii
χ121111-1-1111-1-111-1-1-1-1111-1-11111-1-1-1-11-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i
χ131111-1-1111-1-1-1-111-1-1111-1-11111-1-1-1-1-11ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiii−i−ii-111-1
χ141111-1-1111-1-1-1-111-1-1111-1-11111-1-1-1-1-11ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−iii−i1-1-11
χ151111-1-1111-1-1-1-111-1-1111-1-11111-1-1-1-1-11−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−ii−i−ii1-1-11
χ161111-1-1111-1-1-1-111-1-1111-1-11111-1-1-1-1-11−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−iii−i-111-1
χ172222222-2-2-2-222-2-22222222-2-2-2-2-2-2-2-2-220000000022-2-222-2-2000000000000000000000000
χ182222222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-22-200000000-2-222-2-222000000000000000000000000
χ19222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ20222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000
χ21222222-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000
χ22222222-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000
χ23222222-1-2-2-2-222-2-2-1-1-1-1-1-1-111111111-2200000000-1-111-1-111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300000000
χ24222222-1-2-2-2-222-2-2-1-1-1-1-1-1-111111111-2200000000-1-111-1-111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300000000
χ25222222-1-2-2-2-2-2-222-1-1-1-1-1-1-1111111112-20000000011-1-111-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000
χ26222222-1-2-2-2-2-2-222-1-1-1-1-1-1-1111111112-20000000011-1-111-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000
χ272222-2-22-2-2222222-2-2222-2-2-2-2-2-22222-2-20000000022-2-2-2-222000000000000000000000000
χ282222-2-22-2-222-2-2-2-2-2-2222-2-2-2-2-2-222222200000000-2-22222-2-2000000000000000000000000
χ292222-2-2-122-2-222-2-211-1-1-111-1-1-1-111112-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii00000000
χ302222-2-2-122-2-222-2-211-1-1-111-1-1-1-111112-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i00000000
χ312222-2-2-122-2-2-2-22211-1-1-111-1-1-1-11111-222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000
χ322222-2-2-122-2-2-2-22211-1-1-111-1-1-1-11111-22−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000
χ332222-2-2-1-2-222222211-1-1-1111111-1-1-1-1-2-200000000-1-11111-1-133−3−3−3−33333−3−3−3−33300000000
χ342222-2-2-1-2-222222211-1-1-1111111-1-1-1-1-2-200000000-1-11111-1-1−3−33333−3−3−3−33333−3−300000000
χ352222-2-2-1-2-222-2-2-2-211-1-1-1111111-1-1-1-1220000000011-1-1-1-11133−3−3−3−333−3−33333−3−300000000
χ362222-2-2-1-2-222-2-2-2-211-1-1-1111111-1-1-1-1220000000011-1-1-1-111−3−33333−3−333−3−3−3−33300000000
χ3722-2-2002002i−2i2-22i−2i002-2-20000002i2i−2i−2i001+i−1−i1−i−1+i1+i−1−i1−i−1+i2-200002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ3822-2-2002002i−2i2-22i−2i002-2-20000002i2i−2i−2i00−1−i1+i−1+i1−i−1−i1+i−1+i1−i2-200002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ3922-2-2002002i−2i-22−2i2i002-2-20000002i2i−2i−2i001+i−1−i1−i−1+i−1−i1+i−1+i1−i-220000−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ4022-2-2002002i−2i-22−2i2i002-2-20000002i2i−2i−2i00−1−i1+i−1+i1−i1+i−1−i1−i−1+i-220000−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ4122-2-200200−2i2i2-2−2i2i002-2-2000000−2i−2i2i2i001−i−1+i1+i−1−i1−i−1+i1+i−1−i2-20000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ4222-2-200200−2i2i2-2−2i2i002-2-2000000−2i−2i2i2i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i2-20000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ4322-2-200200−2i2i-222i−2i002-2-2000000−2i−2i2i2i001−i−1+i1+i−1−i−1+i1−i−1−i1+i-2200002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ4422-2-200200−2i2i-222i−2i002-2-2000000−2i−2i2i2i00−1+i1−i−1−i1+i1−i−1+i1+i−1−i-2200002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ4522-2-200-1002i−2i2-22i−2i−i3i3-111−i3i333−3−3−i−iii001+i−1−i1−i−1+i1+i−1−i1−i−1+i-113−3−i3i3−ii−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ1100000000
χ4622-2-200-1002i−2i2-22i−2i−i3i3-111−i3i333−3−3−i−iii00−1−i1+i−1+i1−i−1−i1+i−1+i1−i-113−3−i3i3−iiζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ1100000000
χ4722-2-200-1002i−2i2-22i−2ii3−i3-111i3−i3−3−333−i−iii001+i−1−i1−i−1+i1+i−1−i1−i−1+i-11−33i3−i3−ii−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ700000000
χ4822-2-200-1002i−2i2-22i−2ii3−i3-111i3−i3−3−333−i−iii00−1−i1+i−1+i1−i−1−i1+i−1+i1−i-11−33i3−i3−iiζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ700000000
χ4922-2-200-1002i−2i-22−2i2i−i3i3-111−i3i333−3−3−i−iii001+i−1−i1−i−1+i−1−i1+i−1+i1−i1-1−33i3−i3i−i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ1100000000
χ5022-2-200-1002i−2i-22−2i2i−i3i3-111−i3i333−3−3−i−iii00−1−i1+i−1+i1−i1+i−1−i1−i−1+i1-1−33i3−i3i−iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ1100000000
χ5122-2-200-1002i−2i-22−2i2ii3−i3-111i3−i3−3−333−i−iii001+i−1−i1−i−1+i−1−i1+i−1+i1−i1-13−3−i3i3i−i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ700000000
χ5222-2-200-1002i−2i-22−2i2ii3−i3-111i3−i3−3−333−i−iii00−1−i1+i−1+i1−i1+i−1−i1−i−1+i1-13−3−i3i3i−iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ700000000
χ5322-2-200-100−2i2i2-2−2i2i−i3i3-111−i3i3−3−333ii−i−i001−i−1+i1+i−1−i1−i−1+i1+i−1−i-11−33−i3i3i−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ1100000000
χ5422-2-200-100−2i2i2-2−2i2i−i3i3-111−i3i3−3−333ii−i−i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i-11−33−i3i3i−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ1100000000
χ5522-2-200-100−2i2i2-2−2i2ii3−i3-111i3−i333−3−3ii−i−i001−i−1+i1+i−1−i1−i−1+i1+i−1−i-113−3i3−i3i−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ700000000
χ5622-2-200-100−2i2i2-2−2i2ii3−i3-111i3−i333−3−3ii−i−i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i-113−3i3−i3i−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ700000000
χ5722-2-200-100−2i2i-222i−2i−i3i3-111−i3i3−3−333ii−i−i001−i−1+i1+i−1−i−1+i1−i−1−i1+i1-13−3i3−i3−ii−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ1100000000
χ5822-2-200-100−2i2i-222i−2i−i3i3-111−i3i3−3−333ii−i−i00−1+i1−i−1−i1+i1−i−1+i1+i−1−i1-13−3i3−i3−iiζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ1100000000
χ5922-2-200-100−2i2i-222i−2ii3−i3-111i3−i333−3−3ii−i−i001−i−1+i1+i−1−i−1+i1−i−1−i1+i1-1−33−i3i3−ii−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ700000000
χ6022-2-200-100−2i2i-222i−2ii3−i3-111i3−i333−3−3ii−i−i00−1+i1−i−1−i1+i1−i−1+i1+i−1−i1-1−33−i3i3−iiζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ700000000
χ614-44-40044i−4i00000000-44-4004i−4i4i−4i0000000000000000000000000000000000000000000000
χ624-44-4004−4i4i00000000-44-400−4i4i−4i4i0000000000000000000000000000000000000000000000
χ634-44-400-24i−4i000000−2i32i32-222i3−2i3−2i2i−2i2i23−2323−23000000000000000000000000000000000000000000
χ644-44-400-24i−4i0000002i3−2i32-22−2i32i3−2i2i−2i2i−2323−2323000000000000000000000000000000000000000000
χ654-44-400-2−4i4i000000−2i32i32-222i3−2i32i−2i2i−2i−2323−2323000000000000000000000000000000000000000000
χ664-44-400-2−4i4i0000002i3−2i32-22−2i32i32i−2i2i−2i23−2323−23000000000000000000000000000000000000000000
χ674-4-444-440000000044-4-44-4-400000000000000000000000000000000000000000000000000
χ684-4-444-4-200000000-2-222-222−2i32i32i3−2i3−2i32i32i3−2i3000000000000000000000000000000000000000000
χ694-4-444-4-200000000-2-222-2222i3−2i3−2i32i32i3−2i3−2i32i3000000000000000000000000000000000000000000
χ704-4-44-44400000000-4-4-4-444400000000000000000000000000000000000000000000000000
χ714-4-44-44-2000000002222-2-2-2−2i32i32i3−2i32i3−2i3−2i32i3000000000000000000000000000000000000000000
χ724-4-44-44-2000000002222-2-2-22i3−2i3−2i32i3−2i32i32i3−2i3000000000000000000000000000000000000000000

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