Finite Group Databasebeta

← Group #11771757

Character table — Group #11771757

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1122222222222444444444444444444444444888888888888888888888242424242424242424242424242424242424242424242424144144
order12233446612121212234666666688121212121212121224242424666812121224242424242424242424242424248888161616162424242424242424484848484848484824
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
χ51111111111111-11-111-1-1111-1-1111111-1-1-1-1-1-1-1-1-11-1-1-111111111-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-1
χ61111111111111-11-111-1-1111-1-1111111-1-1-1-1-1-1-1-1-11-1-1-111111111-1-1-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-11
χ71111111111111-11-111-1-1111-1-1111111-1-1-1-1-1-1-1-1-11-1-1-111111111-1-1-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-11
χ81111111111111-11-111-1-1111-1-1111111-1-1-1-1-1-1-1-1-11-1-1-111111111-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-1
χ922222222222222222222222-2-222222222-2-2-2-2222-2222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000
χ102222222222222-22-222-2-222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222200000000000000000000000000
χ1122222-2-222-2-2-2-222-2222222200-2-2-2-2-2-2-2-200002220-2-2-2000000000000000000−i2i2−i2i200000000−i2−i2i2i2−i2−i2i2i200
χ1222222-2-222-2-2-2-222-2222222200-2-2-2-2-2-2-2-200002220-2-2-2000000000000000000i2−i2i2−i200000000i2i2−i2−i2i2i2−i2−i200
χ1322222-2-222-2-2-2-2-22222-2-222200-2-2-2-2-2-2220000-2-2-202220000000000000000002−2−220000000022−2−2−2−22200
χ1422222-2-222-2-2-2-2-22222-2-222200-2-2-2-2-2-2220000-2-2-20222000000000000000000−222−200000000−2−22222−2−200
χ152222-1222-122-1-12-122-122-1-1-122-1-1-12-1-122-1-1-1-1-1-1-12-1-1-1-1-122-1-1-1-122-1-1-1-10000222200000000-1-1-1-1-1-1-1-100
χ162222-1222-122-1-12-122-122-1-1-122-1-1-12-1-122-1-1-1-1-1-1-12-1-1-1-1-122-1-1-1-122-1-1-1-10000-2-2-2-2000000001111111100
χ172222-1222-122-1-12-122-122-1-1-1-2-2-1-1-12-1-1221111-1-1-1-2-1-1-111-2-21111-2-2111100000000000000003−33−33−33−300
χ182222-1222-122-1-12-122-122-1-1-1-2-2-1-1-12-1-1221111-1-1-1-2-1-1-111-2-21111-2-211110000000000000000−33−33−33−3300
χ192222-1222-122-1-1-2-1-22-1-2-2-1-1-122-1-1-12-1-1-2-2-1-1-1-1111-211111-2-2111122-1-1-1-10000000000000000−i3i3−i3i3i3−i3i3−i300
χ202222-1222-122-1-1-2-1-22-1-2-2-1-1-122-1-1-12-1-1-2-2-1-1-1-1111-211111-2-2111122-1-1-1-10000000000000000i3−i3i3−i3−i3i3−i3i300
χ212222-1222-122-1-1-2-1-22-1-2-2-1-1-1-2-2-1-1-12-1-1-2-211111112111-1-122-1-1-1-1-2-2111100002i2i−2i−2i00000000−i−i−i−iiiii00
χ222222-1222-122-1-1-2-1-22-1-2-2-1-1-1-2-2-1-1-12-1-1-2-211111112111-1-122-1-1-1-1-2-211110000−2i−2i2i2i00000000iiii−i−i−i−i00
χ232222-1-2-22-1-2-2112-1-22-122-1-1-100111-211-2-233−3−3-1-1-101113−30033−3−30033−3−30000−i2i2−i2i200000000ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ2300
χ242222-1-2-22-1-2-2112-1-22-122-1-1-100111-211-2-233−3−3-1-1-101113−30033−3−30033−3−30000i2−i2i2−i200000000−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ2300
χ252222-1-2-22-1-2-2112-1-22-122-1-1-100111-211-2-2−3−333-1-1-10111−3300−3−33300−3−3330000−i2i2−i2i200000000ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ700
χ262222-1-2-22-1-2-2112-1-22-122-1-1-100111-211-2-2−3−333-1-1-10111−3300−3−33300−3−3330000i2−i2i2−i200000000−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ700
χ272222-1-2-22-1-2-211-2-122-1-2-2-1-1-100111-2112233−3−31110-1-1-1−3300−3−3330033−3−300002−2−2200000000ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ2300
χ282222-1-2-22-1-2-211-2-122-1-2-2-1-1-100111-2112233−3−31110-1-1-1−3300−3−3330033−3−30000−222−200000000−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ2300
χ292222-1-2-22-1-2-211-2-122-1-2-2-1-1-100111-21122−3−3331110-1-1-13−30033−3−300−3−33300002−2−2200000000ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ700
χ302222-1-2-22-1-2-211-2-122-1-2-2-1-1-100111-21122−3−3331110-1-1-13−30033−3−300−3−3330000−222−200000000−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ700
χ31222-1222-12-1-1222-12-12-1-1-1-1-1222-1-1-1-1-1-1-122222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-10000000000
χ32222-1222-12-1-1222-12-12-1-1-1-1-1222-1-1-1-1-1-1-122222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000111111110000000000
χ33222-1222-12-1-1222-12-12-1-1-1-1-1-2-22-1-1-1-1-1-1-1-2-2-2-22-1-1-22-1-1-2-211111111111100000000−i3−i3i3i3−i3−i3i3i30000000000
χ34222-1222-12-1-1222-12-12-1-1-1-1-1-2-22-1-1-1-1-1-1-1-2-2-2-22-1-1-22-1-1-2-211111111111100000000i3i3−i3−i3i3i3−i3−i30000000000
χ35222-1222-12-1-122-2-1-2-1211-1-1-1222-1-1-1-1-1112222-211-2-211-2-2111111-1-1-1-1-1-10000000033−3−3−3−3330000000000
χ36222-1222-12-1-122-2-1-2-1211-1-1-1222-1-1-1-1-1112222-211-2-211-2-2111111-1-1-1-1-1-100000000−3−33333−3−30000000000
χ37222-1222-12-1-122-2-1-2-1211-1-1-1-2-22-1-1-1-1-111-2-2-2-2-2112-21122-1-1-1-1-1-11111112i2i−2i−2i0000−i−i−i−iiiii0000000000
χ38222-1222-12-1-122-2-1-2-1211-1-1-1-2-22-1-1-1-1-111-2-2-2-2-2112-21122-1-1-1-1-1-1111111−2i−2i2i2i0000iiii−i−i−i−i0000000000
χ3922-2222-22222-2-2020-2-200-2-222i−2i222-2-2-2002i−2i2i−2i0000000000000002i−2i2i−2i2i−2i1+i−1−i1−i−1+i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ4022-2222-22222-2-2020-2-200-2-222i−2i222-2-2-2002i−2i2i−2i0000000000000002i−2i2i−2i2i−2i−1−i1+i−1+i1−i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ4122-2222-22222-2-2020-2-200-2-22−2i2i222-2-2-200−2i2i−2i2i000000000000000−2i2i−2i2i−2i2i1−i−1+i1+i−1−i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ4222-2222-22222-2-2020-2-200-2-22−2i2i222-2-2-200−2i2i−2i2i000000000000000−2i2i−2i2i−2i2i−1+i1−i−1−i1+i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ4322-2-122-2-12-1-1-2-20-101-2−i3i311-12i−2i2-1-1111−i3i32i−2i2i−2i0−i3i300−i3i3003−33−33−3−ii−ii−ii1+i−1−i1−i−1+i0000−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ220000000000
χ4422-2-122-2-12-1-1-2-20-101-2−i3i311-12i−2i2-1-1111−i3i32i−2i2i−2i0−i3i300−i3i3003−33−33−3−ii−ii−ii−1−i1+i−1+i1−i0000ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ220000000000
χ4522-2-122-2-12-1-1-2-20-101-2−i3i311-1−2i2i2-1-1111−i3i3−2i2i−2i2i0−i3i300−i3i300−33−33−33i−ii−ii−i1−i−1+i1+i−1−i0000−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ220000000000
χ4622-2-122-2-12-1-1-2-20-101-2−i3i311-1−2i2i2-1-1111−i3i3−2i2i−2i2i0−i3i300−i3i300−33−33−33i−ii−ii−i−1+i1−i−1−i1+i0000ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ220000000000
χ4722-2-122-2-12-1-1-2-20-101-2i3−i311-12i−2i2-1-1111i3−i32i−2i2i−2i0i3−i300i3−i300−33−33−33−ii−ii−ii1+i−1−i1−i−1+i0000−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ140000000000
χ4822-2-122-2-12-1-1-2-20-101-2i3−i311-12i−2i2-1-1111i3−i32i−2i2i−2i0i3−i300i3−i300−33−33−33−ii−ii−ii−1−i1+i−1+i1−i0000ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ140000000000
χ4922-2-122-2-12-1-1-2-20-101-2i3−i311-1−2i2i2-1-1111i3−i3−2i2i−2i2i0i3−i300i3−i3003−33−33−3i−ii−ii−i1−i−1+i1+i−1−i0000−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ140000000000
χ5022-2-122-2-12-1-1-2-20-101-2i3−i311-1−2i2i2-1-1111i3−i3−2i2i−2i2i0i3−i300i3−i3003−33−33−3i−ii−ii−i−1+i1−i−1−i1+i0000ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ140000000000
χ51444-24-4-4-2422-4-44-2-4-24-2-2-2-2-200-4222222200004-2-20-4220000000000000000000000000000000000000000
χ52444-24-4-4-2422-4-4-4-24-2422-2-2-200-422222-2-20000-42204-2-20000000000000000000000000000000000000000
χ53444-2-244-2-2-2-2-2-2414-2-2-2-211144-211-211-2-2-2-2-2-2-2114-211-2-2-2-21111-2-2111100000000000000000000000000
χ54444-2-244-2-2-2-2-2-2414-2-2-2-2111-4-4-211-211-2-22222-211-4-2112222-1-1-1-122-1-1-1-100000000000000000000000000
χ55444-2-244-2-2-2-2-2-2-41-4-2-22211144-211-21122-2-2-2-22-1-1-42-1-12222-1-1-1-1-2-2111100000000000000000000000000
χ56444-2-244-2-2-2-2-2-2-41-4-2-222111-4-4-211-2112222222-1-142-1-1-2-2-2-2111122-1-1-1-100000000000000000000000000
χ57444-2-2-4-4-2-2222241-4-2-2-2-2111002-1-12-1-1222323−23−23-21102-1-123−2300−3−33300−3−33300000000000000000000000000
χ58444-2-2-4-4-2-2222241-4-2-2-2-2111002-1-12-1-122−23−232323-21102-1-1−23230033−3−30033−3−300000000000000000000000000
χ59444-2-2-4-4-2-22222-414-2-222111002-1-12-1-1-2-22323−23−232-1-10-211−23230033−3−300−3−33300000000000000000000000000
χ60444-2-2-4-4-2-22222-414-2-222111002-1-12-1-1-2-2−23−2323232-1-10-21123−2300−3−3330033−3−300000000000000000000000000
χ6144-444-4444-4-444040-4-400-4-4400-4-4-444400000000000000000000000000000000000000000000000000000
χ6244-44-24-44-244220-20-420022-24i−4i-2-2-2-42200−2i2i−2i2i0000000000000004i−4i−2i2i−2i2i00000000000000000000000000
χ6344-44-24-44-244220-20-420022-2−4i4i-2-2-2-422002i−2i2i−2i000000000000000−4i4i2i−2i2i−2i00000000000000000000000000
χ6444-44-2-444-2-4-4-2-20-20-420022-2002224-2-200−2i32i32i3−2i300000000000000000−2i32i32i3−2i300000000000000000000000000
χ6544-44-2-444-2-4-4-2-20-20-420022-2002224-2-2002i3−2i3−2i32i3000000000000000002i3−2i3−2i32i300000000000000000000000000
χ6644-4-24-44-2422440-202-4−2i32i322-200-422-2-2-22i3−2i300000−2i32i3002i3−2i30000000000000000000000000000000000000000
χ6744-4-24-44-2422440-202-42i3−2i322-200-422-2-2-2−2i32i3000002i3−2i300−2i32i30000000000000000000000000000000000000000
χ6844-4-2-24-4-2-2-2-22201022−2i32i3-1-114i−4i-2112-1-1−2i32i3−2i2i−2i2i0i3−i300i3−i30023−23−33−33−2i2ii−ii−i00000000000000000000000000
χ6944-4-2-24-4-2-2-2-22201022−2i32i3-1-11−4i4i-2112-1-1−2i32i32i−2i2i−2i0i3−i300i3−i300−23233−33−32i−2i−ii−ii00000000000000000000000000
χ7044-4-2-24-4-2-2-2-222010222i3−2i3-1-114i−4i-2112-1-12i3−2i3−2i2i−2i2i0−i3i300−i3i300−23233−33−3−2i2ii−ii−i00000000000000000000000000
χ7144-4-2-24-4-2-2-2-222010222i3−2i3-1-11−4i4i-2112-1-12i3−2i32i−2i2i−2i0−i3i300−i3i30023−23−33−332i−2i−ii−ii00000000000000000000000000
χ7244-4-2-2-44-2-222-2-201022−2i32i3-1-11002-1-1-2112i3−2i3−2i32i32i3−2i30i3−i300−i3i30000-333-300i3−i3−i3i300000000000000000000000000
χ7344-4-2-2-44-2-222-2-201022−2i32i3-1-11002-1-1-2112i3−2i32i3−2i3−2i32i30i3−i300−i3i300003-3-3300−i3i3i3−i300000000000000000000000000
χ7444-4-2-2-44-2-222-2-2010222i3−2i3-1-11002-1-1-211−2i32i3−2i32i32i3−2i30−i3i300i3−i300003-3-3300i3−i3−i3i300000000000000000000000000
χ7544-4-2-2-44-2-222-2-2010222i3−2i3-1-11002-1-1-211−2i32i32i3−2i3−2i32i30−i3i300i3−i30000-333-300−i3i3i3−i300000000000000000000000000
χ768-808800-8-80000080000000-80000000000000000000000000000000000000000000000000000000000000
χ778-808-400-840043−430-40000000400000043−4300000000000000000000000000000000000000000000000000000
χ788-808-400-8400−43430-400000004000000−434300000000000000000000000000000000000000000000000000000
χ798-80-48004-843−43000-40000000400043−4300000000000000000000000000000000000000000000000000000000
χ808-80-48004-8−4343000-400000004000−434300000000000000000000000000000000000000000000000000000000
χ818-80-4-4004443−4343−4302000006-6-2000−23230−232300000000000000000000000000000000000000000000000000000
χ828-80-4-4004443−43−43430200000-66-2000−2323023−2300000000000000000000000000000000000000000000000000000
χ838-80-4-40044−434343−430200000-66-200023−230−232300000000000000000000000000000000000000000000000000000
χ848-80-4-40044−4343−434302000006-6-200023−23023−2300000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.