Finite Group Databasebeta

← Group #11771992

Character table — Group #11771992

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1122222222222444444444444444444444444888888888888888888888242424242424242424242424242424242424242424242424144144
order12233446612121212366666888812121212121224242424242424244121212121212121224242424242424242424242416161616161616164848484848484848484848484848484824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ51111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-1
χ61111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-11
χ71111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-11
χ81111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-1
χ9222222222222222222222-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-200000000000000000000000000
χ102222222222222222222-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222200000000000000000000000000
χ112222-1222-122-1-1-12-1-1-1-122222-1-1-1-1-12222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000222200000000-1-1-1-1-1-1-1-100
χ122222-1222-122-1-1-12-1-1-1-122222-1-1-1-1-12222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000-2-2-2-2000000001111111100
χ132222-1222-122-1-1-12-1-1-1-122-2-22-1-1-1-1-122221111-2-2-2111111-1-1-1-1-1-1-2-21111000000000000000033−3−333−3−300
χ142222-1222-122-1-1-12-1-1-1-122-2-22-1-1-1-1-122221111-2-2-2111111-1-1-1-1-1-1-2-211110000000000000000−3−333−3−33300
χ152222-1222-122-1-1-12-1-1-1-1-2-2222-1-1-1-1-1-2-2-2-2-1-1-1-1-2-2-211111111111122-1-1-1-10000000000000000−i3−i3i3i3i3i3−i3−i300
χ162222-1222-122-1-1-12-1-1-1-1-2-2222-1-1-1-1-1-2-2-2-2-1-1-1-1-2-2-211111111111122-1-1-1-10000000000000000i3i3−i3−i3−i3−i3i3i300
χ172222-1222-122-1-1-12-1-1-1-1-2-2-2-22-1-1-1-1-1-2-2-2-21111222-1-1-1-1-1-1111111-2-2111100002i2i−2i−2i00000000−i−i−i−iiiii00
χ182222-1222-122-1-1-12-1-1-1-1-2-2-2-22-1-1-1-1-1-2-2-2-21111222-1-1-1-1-1-1111111-2-211110000−2i−2i2i2i00000000iiii−i−i−i−i00
χ19222-1222-12-1-122-1-12-1-1-12222-12-1-1-1-1-1-1-1-122222-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-10000000000
χ20222-1222-12-1-122-1-12-1-1-12222-12-1-1-1-1-1-1-1-122222-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-20000111111110000000000
χ21222-1222-12-1-122-1-12-1-1-122-2-2-12-1-1-1-1-1-1-1-1-2-2-2-2-211-2-2111122-1-1-1-111111100000000−i3−i3i3i3−i3−i3i3i30000000000
χ22222-1222-12-1-122-1-12-1-1-122-2-2-12-1-1-1-1-1-1-1-1-2-2-2-2-211-2-2111122-1-1-1-111111100000000i3i3−i3−i3i3i3−i3−i30000000000
χ23222-1222-12-1-122-1-12-1-1-1-2-222-12-1-1-1-111112222-211-2-21111-2-21111-1-1-1-1-1-10000000033−3−3−3−3330000000000
χ24222-1222-12-1-122-1-12-1-1-1-2-222-12-1-1-1-111112222-211-2-21111-2-21111-1-1-1-1-1-100000000−3−33333−3−30000000000
χ25222-1222-12-1-122-1-12-1-1-1-2-2-2-2-12-1-1-1-11111-2-2-2-22-1-122-1-1-1-1-2-211111111112i2i−2i−2i0000−i−i−i−iiiii0000000000
χ26222-1222-12-1-122-1-12-1-1-1-2-2-2-2-12-1-1-1-11111-2-2-2-22-1-122-1-1-1-1-2-21111111111−2i−2i2i2i0000iiii−i−i−i−i0000000000
χ2722-2222-22222-2-22-2-22-2-2002i−2i-2222-2-200002i2i−2i−2i0000000000000002i−2i2i2i−2i−2i1+i−1−i1−i−1+i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ2822-2222-22222-2-22-2-22-2-2002i−2i-2222-2-200002i2i−2i−2i0000000000000002i−2i2i2i−2i−2i−1−i1+i−1+i1−i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ2922-2222-22222-2-22-2-22-2-200−2i2i-2222-2-20000−2i−2i2i2i000000000000000−2i2i−2i−2i2i2i1−i−1+i1+i−1−i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ3022-2222-22222-2-22-2-22-2-200−2i2i-2222-2-20000−2i−2i2i2i000000000000000−2i2i−2i−2i2i2i−1+i1−i−1−i1+i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ3122-222-2222-2-2222-2-22-2-22i−2i002-2-2-2222i2i−2i−2i00000000000002i−2i2i2i−2i−2i00000000001+i−1−i1−i−1+i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00
χ3222-222-2222-2-2222-2-22-2-22i−2i002-2-2-2222i2i−2i−2i00000000000002i−2i2i2i−2i−2i0000000000−1−i1+i−1+i1−i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00
χ3322-222-2222-2-2222-2-22-2-2−2i2i002-2-2-222−2i−2i2i2i0000000000000−2i2i−2i−2i2i2i00000000001−i−1+i1+i−1−i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00
χ3422-222-2222-2-2222-2-22-2-2−2i2i002-2-2-222−2i−2i2i2i0000000000000−2i2i−2i−2i2i2i0000000000−1+i1−i−1−i1+i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00
χ3522-22-1-222-1-2-2-1-1-1-21-1112i−2i002111-1-12i2i−2i−2i−i3i3−i3i30003−333−3−3−ii−i−iii00−i3i3−i3i300001+i−1−i1−i−1+i00000000−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ700
χ3622-22-1-222-1-2-2-1-1-1-21-1112i−2i002111-1-12i2i−2i−2i−i3i3−i3i30003−333−3−3−ii−i−iii00−i3i3−i3i30000−1−i1+i−1+i1−i00000000ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ700
χ3722-22-1-222-1-2-2-1-1-1-21-1112i−2i002111-1-12i2i−2i−2ii3−i3i3−i3000−33−3−333−ii−i−iii00i3−i3i3−i300001+i−1−i1−i−1+i00000000−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ1100
χ3822-22-1-222-1-2-2-1-1-1-21-1112i−2i002111-1-12i2i−2i−2ii3−i3i3−i3000−33−3−333−ii−i−iii00i3−i3i3−i30000−1−i1+i−1+i1−i00000000ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ1100
χ3922-22-1-222-1-2-2-1-1-1-21-111−2i2i002111-1-1−2i−2i2i2i−i3i3−i3i3000−33−3−333i−iii−i−i00−i3i3−i3i300001−i−1+i1+i−1−i00000000−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ700
χ4022-22-1-222-1-2-2-1-1-1-21-111−2i2i002111-1-1−2i−2i2i2i−i3i3−i3i3000−33−3−333i−iii−i−i00−i3i3−i3i30000−1+i1−i−1−i1+i00000000ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ700
χ4122-22-1-222-1-2-2-1-1-1-21-111−2i2i002111-1-1−2i−2i2i2ii3−i3i3−i30003−333−3−3i−iii−i−i00i3−i3i3−i300001−i−1+i1+i−1−i00000000−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ1100
χ4222-22-1-222-1-2-2-1-1-1-21-111−2i2i002111-1-1−2i−2i2i2ii3−i3i3−i30003−333−3−3i−iii−i−i00i3−i3i3−i30000−1+i1−i−1−i1+i00000000ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ1100
χ4322-2-122-2-12-1-1-2-2-11-2-111002i−2i12-1-111−i3i3−i3i32i2i−2i−2i03−3003−33−300−i3i3−i3i3−ii−i−iii1+i−1−i1−i−1+i0000−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ110000000000
χ4422-2-122-2-12-1-1-2-2-11-2-111002i−2i12-1-111−i3i3−i3i32i2i−2i−2i03−3003−33−300−i3i3−i3i3−ii−i−iii−1−i1+i−1+i1−i0000ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ110000000000
χ4522-2-122-2-12-1-1-2-2-11-2-111002i−2i12-1-111i3−i3i3−i32i2i−2i−2i0−3300−33−3300i3−i3i3−i3−ii−i−iii1+i−1−i1−i−1+i0000−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ70000000000
χ4622-2-122-2-12-1-1-2-2-11-2-111002i−2i12-1-111i3−i3i3−i32i2i−2i−2i0−3300−33−3300i3−i3i3−i3−ii−i−iii−1−i1+i−1+i1−i0000ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ70000000000
χ4722-2-122-2-12-1-1-2-2-11-2-11100−2i2i12-1-111−i3i3−i3i3−2i−2i2i2i0−3300−33−3300−i3i3−i3i3i−iii−i−i1−i−1+i1+i−1−i0000−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ110000000000
χ4822-2-122-2-12-1-1-2-2-11-2-11100−2i2i12-1-111−i3i3−i3i3−2i−2i2i2i0−3300−33−3300−i3i3−i3i3i−iii−i−i−1+i1−i−1−i1+i0000ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ110000000000
χ4922-2-122-2-12-1-1-2-2-11-2-11100−2i2i12-1-111i3−i3i3−i3−2i−2i2i2i03−3003−33−300i3−i3i3−i3i−iii−i−i1−i−1+i1+i−1−i0000−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ70000000000
χ5022-2-122-2-12-1-1-2-2-11-2-11100−2i2i12-1-111i3−i3i3−i3−2i−2i2i2i03−3003−33−300i3−i3i3−i3i−iii−i−i−1+i1−i−1−i1+i0000ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ70000000000
χ5144444-4-444-4-4-4-44444440000-4-4-4-4-4-40000000000000000000000000000000000000000000000000000000
χ524444-2-4-44-2-4-422-24-2-2-2-20000-422222000023−23−23230000000000000000023−23−232300000000000000000000000000
χ534444-2-4-44-2-4-422-24-2-2-2-20000-4222220000−232323−2300000000000000000−232323−2300000000000000000000000000
χ54444-24-4-4-2422-4-4-2-24-2-2-200002-4222223−23−232300000000000000023−23−232300000000000000000000000000000000
χ55444-24-4-4-2422-4-4-2-24-2-2-200002-42222−232323−23000000000000000−232323−2300000000000000000000000000000000
χ56444-2-244-2-2-2-2-2-21-2-21114444-2-21111-2-2-2-2-2-2-2-24-2-2-2-21111-2-21111-2-2111100000000000000000000000000
χ57444-2-244-2-2-2-2-2-21-2-211144-4-4-2-21111-2-2-2-22222-42222-1-1-1-1-2-2111122-1-1-1-100000000000000000000000000
χ58444-2-244-2-2-2-2-2-21-2-2111-4-444-2-211112222-2-2-2-2-42222-1-1-1-122-1-1-1-1-2-2111100000000000000000000000000
χ59444-2-244-2-2-2-2-2-21-2-2111-4-4-4-4-2-21111222222224-2-2-2-2111122-1-1-1-122-1-1-1-100000000000000000000000000
χ60444-2-2-4-4-2-222221-2-2111000022-1-1-1-123−23−232323−23−2323000003-3-3300−333−300−333−300000000000000000000000000
χ61444-2-2-4-4-2-222221-2-2111000022-1-1-1-123−23−2323−232323−2300000-333-300−333−3003−3−3300000000000000000000000000
χ62444-2-2-4-4-2-222221-2-2111000022-1-1-1-1−232323−2323−23−232300000-333-3003−3−3300−333−300000000000000000000000000
χ63444-2-2-4-4-2-222221-2-2111000022-1-1-1-1−232323−23−232323−23000003-3-33003−3−33003−3−3300000000000000000000000000
χ6444-44-24-44-24422-2-42-222004i−4i-4-2-2-2220000−2i−2i2i2i0000000000000004i−4i−2i−2i2i2i00000000000000000000000000
χ6544-44-24-44-24422-2-42-22200−4i4i-4-2-2-22200002i2i−2i−2i000000000000000−4i4i2i2i−2i−2i00000000000000000000000000
χ6644-4-24-44-242244-22-4-2224i−4i00-2-422-2-2−2i−2i2i2i00000000000004i−4i−2i−2i2i2i00000000000000000000000000000000
χ6744-4-24-44-242244-22-4-222−4i4i00-2-422-2-22i2i−2i−2i0000000000000−4i4i2i2i−2i−2i00000000000000000000000000000000
χ6844-4-2-24-4-2-2-2-2221221-1-1004i−4i2-211-1-1−2i32i3−2i32i3−2i−2i2i2i023−2300−33−3300i3−i3i3−i3−2i2iii−i−i00000000000000000000000000
χ6944-4-2-24-4-2-2-2-2221221-1-1004i−4i2-211-1-12i3−2i32i3−2i3−2i−2i2i2i0−2323003−33−300−i3i3−i3i3−2i2iii−i−i00000000000000000000000000
χ7044-4-2-24-4-2-2-2-2221221-1-100−4i4i2-211-1-1−2i32i3−2i32i32i2i−2i−2i0−2323003−33−300i3−i3i3−i32i−2i−i−iii00000000000000000000000000
χ7144-4-2-24-4-2-2-2-2221221-1-100−4i4i2-211-1-12i3−2i32i3−2i32i2i−2i−2i023−2300−33−3300−i3i3−i3i32i−2i−i−iii00000000000000000000000000
χ7244-4-2-2-44-2-222-2-21221-1-14i−4i00-22-1-111−2i−2i2i2i−2i32i3−2i32i300023−23−3−333−2i2iii−i−i00i3−i3i3−i300000000000000000000000000
χ7344-4-2-2-44-2-222-2-21221-1-14i−4i00-22-1-111−2i−2i2i2i2i3−2i32i3−2i3000−232333−3−3−2i2iii−i−i00−i3i3−i3i300000000000000000000000000
χ7444-4-2-2-44-2-222-2-21221-1-1−4i4i00-22-1-1112i2i−2i−2i−2i32i3−2i32i3000−232333−3−32i−2i−i−iii00i3−i3i3−i300000000000000000000000000
χ7544-4-2-2-44-2-222-2-21221-1-1−4i4i00-22-1-1112i2i−2i−2i2i3−2i32i3−2i300023−23−3−3332i−2i−i−iii00−i3i3−i3i300000000000000000000000000
χ768-808800-8-80000800-80000000000000000000000000000000000000000000000000000000000000000000
χ778-808-400-840043−43-4004000000000043−430000000000000000000000000000000000000000000000000000000
χ788-808-400-8400−4343-40040000000000−43430000000000000000000000000000000000000000000000000000000
χ798-80-48004-843−4300-40040000000043−43000000000000000000000000000000000000000000000000000000000
χ808-80-48004-8−434300-400400000000−4343000000000000000000000000000000000000000000000000000000000
χ818-80-4-4004443−4343−43200-26-6000000−2323−23230000000000000000000000000000000000000000000000000000000
χ828-80-4-4004443−43−4343200-2-66000000−232323−230000000000000000000000000000000000000000000000000000000
χ838-80-4-40044−434343−43200-2-6600000023−23−23230000000000000000000000000000000000000000000000000000000
χ848-80-4-40044−4343−4343200-26-600000023−2323−230000000000000000000000000000000000000000000000000000000

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