Finite Group Databasebeta

← Group #11771740

Character table — Group #11771740

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1122222222222444444444444444444444444888888888888888888888242424242424242424242424242424242424242424242424144144
order12233446612121212234666666688121212121212121224242424666812121224242424242424242424242424244444121212121212121216161616484848484848484844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
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
χ51111111111111-11-111111-1-1-1-11-1-111111-1-1-1-1-1-1-11-1-1-111111111-1-1-1-1-1-1ii−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−i1-1
χ61111111111111-11-111111-1-1-1-11-1-111111-1-1-1-1-1-1-11-1-1-111111111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i−i−iii−i−i−i−iiiii-11
χ71111111111111-11-111111-1-1-1-11-1-111111-1-1-1-1-1-1-11-1-1-111111111-1-1-1-1-1-1−i−iii−i−i−i−iiiiiii−i−iiiii−i−i−i−i-11
χ81111111111111-11-111111-1-1-1-11-1-111111-1-1-1-1-1-1-11-1-1-111111111-1-1-1-1-1-1−i−iii−i−i−i−iiiii−i−iii−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
χ102222222222222-22-222222-2-2222-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222200000000000000000000000000
χ1122222-2-222-2-2-2-222-2222222200-2-2-2-2-2-2-2-200002220-2-2-2000000000000000000000000002−22−222−2−222−2−200
χ1222222-2-222-2-2-2-222-2222222200-2-2-2-2-2-2-2-200002220-2-2-200000000000000000000000000−22−22−2−222−2−22200
χ1322222-2-222-2-2-2-2-22222222-2-200-222-2-2-2-2-20000-2-2-2022200000000000000000000000000−i2i2i2−i2−i2−i2i2i2i2i2−i2−i200
χ1422222-2-222-2-2-2-2-22222222-2-200-222-2-2-2-2-20000-2-2-2022200000000000000000000000000i2−i2−i2i2i2i2−i2−i2−i2−i2i2i200
χ152222-1222-122-1-12-122-1-1-1-12222-122-1-12-1-1-1-1-1-1-1-1-12-1-1-1-1-122-1-1-1-122-1-1-1-10000000000002222-1-1-1-1-1-1-1-100
χ162222-1222-122-1-12-122-1-1-1-12222-122-1-12-1-1-1-1-1-1-1-1-12-1-1-1-1-122-1-1-1-122-1-1-1-1000000000000-2-2-2-21111111100
χ172222-1222-122-1-12-122-1-1-1-122-2-2-122-1-12-1-11111-1-1-1-2-1-1-111-2-21111-2-2111100000000000000003−33−33−33−300
χ182222-1222-122-1-12-122-1-1-1-122-2-2-122-1-12-1-11111-1-1-1-2-1-1-111-2-21111-2-211110000000000000000−33−33−33−3300
χ192222-1222-122-1-1-2-1-22-1-1-1-1-2-222-1-2-2-1-12-1-1-1-1-1-1111-211111-2-2111122-1-1-1-10000000000000000−i3i3−i3i3i3−i3i3−i300
χ202222-1222-122-1-1-2-1-22-1-1-1-1-2-222-1-2-2-1-12-1-1-1-1-1-1111-211111-2-2111122-1-1-1-10000000000000000i3−i3i3−i3−i3i3−i3i300
χ212222-1222-122-1-1-2-1-22-1-1-1-1-2-2-2-2-1-2-2-1-12-1-111111112111-1-122-1-1-1-1-2-211110000000000002i2i−2i−2i−i−i−i−iiiii00
χ222222-1222-122-1-1-2-1-22-1-1-1-1-2-2-2-2-1-2-2-1-12-1-111111112111-1-122-1-1-1-1-2-21111000000000000−2i−2i2i2iiiii−i−i−i−i00
χ232222-1-2-22-1-2-2112-1-22-1-1-1-122001-2-211-21133−3−3-1-1-101113−30033−3−30033−3−30000000000002−22−2ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ2300
χ242222-1-2-22-1-2-2112-1-22-1-1-1-122001-2-211-21133−3−3-1-1-101113−30033−3−30033−3−3000000000000−22−22−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ2300
χ252222-1-2-22-1-2-2112-1-22-1-1-1-122001-2-211-211−3−333-1-1-10111−3300−3−33300−3−3330000000000002−22−2ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ700
χ262222-1-2-22-1-2-2112-1-22-1-1-1-122001-2-211-211−3−333-1-1-10111−3300−3−33300−3−333000000000000−22−22−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ700
χ272222-1-2-22-1-2-211-2-122-1-1-1-1-2-20012211-21133−3−31110-1-1-1−3300−3−3330033−3−3000000000000−i2i2i2−i2ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ2300
χ282222-1-2-22-1-2-211-2-122-1-1-1-1-2-20012211-21133−3−31110-1-1-1−3300−3−3330033−3−3000000000000i2−i2−i2i2−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ2300
χ292222-1-2-22-1-2-211-2-122-1-1-1-1-2-20012211-211−3−3331110-1-1-13−30033−3−300−3−333000000000000−i2i2i2−i2ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ700
χ302222-1-2-22-1-2-211-2-122-1-1-1-1-2-20012211-211−3−3331110-1-1-13−30033−3−300−3−333000000000000i2−i2−i2i2−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ700
χ31222-1222-12-1-1222-12-12-1-1-1-1-1222-1-1-1-1-1-1-122222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ32222-1222-12-1-1222-12-12-1-1-1-1-1222-1-1-1-1-1-1-122222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ33222-1222-12-1-1222-12-12-1-1-1-1-1-2-22-1-1-1-1-1-1-1-2-2-2-22-1-1-22-1-1-2-21111111111110000−i3−i3i3i3−i3−i3i3i300000000000000
χ34222-1222-12-1-1222-12-12-1-1-1-1-1-2-22-1-1-1-1-1-1-1-2-2-2-22-1-1-22-1-1-2-21111111111110000i3i3−i3−i3i3i3−i3−i300000000000000
χ35222-1222-12-1-122-2-1-2-12-1-1-11122211-1-1-1-1-12222-211-2-211-2-2111111-1-1-1-1-1-1000033−3−3−3−33300000000000000
χ36222-1222-12-1-122-2-1-2-12-1-1-11122211-1-1-1-1-12222-211-2-211-2-2111111-1-1-1-1-1-10000−3−33333−3−300000000000000
χ37222-1222-12-1-122-2-1-2-12-1-1-111-2-2211-1-1-1-1-1-2-2-2-2-2112-21122-1-1-1-1-1-11111112i2i−2i−2i−i−i−i−iiiii00000000000000
χ38222-1222-12-1-122-2-1-2-12-1-1-111-2-2211-1-1-1-1-1-2-2-2-2-2112-21122-1-1-1-1-1-1111111−2i−2i2i2iiiii−i−i−i−i00000000000000
χ3922-2222-22222-2-2020-2-2-2-22002i−2i20022-2-2-22i−2i2i−2i0000000000000002i−2i2i−2i2i−2i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ4022-2222-22222-2-2020-2-2-2-22002i−2i20022-2-2-22i−2i2i−2i0000000000000002i−2i2i−2i2i−2i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ4122-2222-22222-2-2020-2-2-2-2200−2i2i20022-2-2-2−2i2i−2i2i000000000000000−2i2i−2i2i−2i2i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ4222-2222-22222-2-2020-2-2-2-2200−2i2i20022-2-2-2−2i2i−2i2i000000000000000−2i2i−2i2i−2i2i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ4322-2-122-2-12-1-1-2-20-101-211-1−i3i32i−2i2−i3i3-1-11112i−2i2i−2i0−i3i300−i3i3003−33−33−3−ii−ii−ii1+i−1−i1−i−1+i−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ2200000000000000
χ4422-2-122-2-12-1-1-2-20-101-211-1−i3i32i−2i2−i3i3-1-11112i−2i2i−2i0−i3i300−i3i3003−33−33−3−ii−ii−ii−1−i1+i−1+i1−iζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ2200000000000000
χ4522-2-122-2-12-1-1-2-20-101-211-1−i3i3−2i2i2−i3i3-1-1111−2i2i−2i2i0−i3i300−i3i300−33−33−33i−ii−ii−i1−i−1+i1+i−1−i−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ2200000000000000
χ4622-2-122-2-12-1-1-2-20-101-211-1−i3i3−2i2i2−i3i3-1-1111−2i2i−2i2i0−i3i300−i3i300−33−33−33i−ii−ii−i−1+i1−i−1−i1+iζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ2200000000000000
χ4722-2-122-2-12-1-1-2-20-101-211-1i3−i32i−2i2i3−i3-1-11112i−2i2i−2i0i3−i300i3−i300−33−33−33−ii−ii−ii1+i−1−i1−i−1+i−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ1400000000000000
χ4822-2-122-2-12-1-1-2-20-101-211-1i3−i32i−2i2i3−i3-1-11112i−2i2i−2i0i3−i300i3−i300−33−33−33−ii−ii−ii−1−i1+i−1+i1−iζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ1400000000000000
χ4922-2-122-2-12-1-1-2-20-101-211-1i3−i3−2i2i2i3−i3-1-1111−2i2i−2i2i0i3−i300i3−i3003−33−33−3i−ii−ii−i1−i−1+i1+i−1−i−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ1400000000000000
χ5022-2-122-2-12-1-1-2-20-101-211-1i3−i3−2i2i2i3−i3-1-1111−2i2i−2i2i0i3−i300i3−i3003−33−33−3i−ii−ii−i−1+i1−i−1−i1+iζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ1400000000000000
χ51444-24-4-4-2422-4-44-2-4-24-2-2-2-2-200-4222222200004-2-20-4220000000000000000000000000000000000000000
χ52444-24-4-4-2422-4-4-4-24-24-2-2-22200-4-2-2222220000-42204-2-20000000000000000000000000000000000000000
χ53444-2-244-2-2-2-2-2-2414-2-2111-2-244-2-2-211-211-2-2-2-2-2114-211-2-2-2-21111-2-2111100000000000000000000000000
χ54444-2-244-2-2-2-2-2-2414-2-2111-2-2-4-4-2-2-211-2112222-211-4-2112222-1-1-1-122-1-1-1-100000000000000000000000000
χ55444-2-244-2-2-2-2-2-2-41-4-2-21112244-22211-211-2-2-2-22-1-1-42-1-12222-1-1-1-1-2-2111100000000000000000000000000
χ56444-2-244-2-2-2-2-2-2-41-4-2-211122-4-4-22211-21122222-1-142-1-1-2-2-2-2111122-1-1-1-100000000000000000000000000
χ57444-2-2-4-4-2-2222241-4-2-2111-2-200222-1-12-1-12323−23−23-21102-1-123−2300−3−33300−3−33300000000000000000000000000
χ58444-2-2-4-4-2-2222241-4-2-2111-2-200222-1-12-1-1−23−232323-21102-1-1−23230033−3−30033−3−300000000000000000000000000
χ59444-2-2-4-4-2-22222-414-2-211122002-2-2-1-12-1-12323−23−232-1-10-211−23230033−3−300−3−33300000000000000000000000000
χ60444-2-2-4-4-2-22222-414-2-211122002-2-2-1-12-1-1−23−2323232-1-10-21123−2300−3−3330033−3−300000000000000000000000000
χ6144-444-4444-4-444040-4-4-4-440000-400-4-4444000000000000000000000000000000000000000000000000000
χ6244-44-24-44-244220-20-4222-2004i−4i-200-2-2-422−2i2i−2i2i0000000000000004i−4i−2i2i−2i2i00000000000000000000000000
χ6344-44-24-44-244220-20-4222-200−4i4i-200-2-2-4222i−2i2i−2i000000000000000−4i4i2i−2i2i−2i00000000000000000000000000
χ6444-44-2-444-2-4-4-2-20-20-4222-20000200224-2-2−2i32i32i3−2i300000000000000000−2i32i32i3−2i300000000000000000000000000
χ6544-44-2-444-2-4-4-2-20-20-4222-20000200224-2-22i3−2i3−2i32i3000000000000000002i3−2i3−2i32i300000000000000000000000000
χ6644-4-24-44-2422440-202-422-2−2i32i300-42i3−2i322-2-2-200000−2i32i3002i3−2i30000000000000000000000000000000000000000
χ6744-4-24-44-2422440-202-422-22i3−2i300-4−2i32i322-2-2-2000002i3−2i300−2i32i30000000000000000000000000000000000000000
χ6844-4-2-24-4-2-2-2-22201022-1-11−2i32i34i−4i-2−2i32i3112-1-1−2i2i−2i2i0i3−i300i3−i30023−23−33−33−2i2ii−ii−i00000000000000000000000000
χ6944-4-2-24-4-2-2-2-22201022-1-11−2i32i3−4i4i-2−2i32i3112-1-12i−2i2i−2i0i3−i300i3−i300−23233−33−32i−2i−ii−ii00000000000000000000000000
χ7044-4-2-24-4-2-2-2-22201022-1-112i3−2i34i−4i-22i3−2i3112-1-1−2i2i−2i2i0−i3i300−i3i300−23233−33−3−2i2ii−ii−i00000000000000000000000000
χ7144-4-2-24-4-2-2-2-22201022-1-112i3−2i3−4i4i-22i3−2i3112-1-12i−2i2i−2i0−i3i300−i3i30023−23−33−332i−2i−ii−ii00000000000000000000000000
χ7244-4-2-2-44-2-222-2-201022-1-11−2i32i30022i3−2i3-1-1-211−2i32i32i3−2i30i3−i300−i3i30000-333-300i3−i3−i3i300000000000000000000000000
χ7344-4-2-2-44-2-222-2-201022-1-11−2i32i30022i3−2i3-1-1-2112i3−2i3−2i32i30i3−i300−i3i300003-3-3300−i3i3i3−i300000000000000000000000000
χ7444-4-2-2-44-2-222-2-201022-1-112i3−2i3002−2i32i3-1-1-211−2i32i32i3−2i30−i3i300i3−i300003-3-3300i3−i3−i3i300000000000000000000000000
χ7544-4-2-2-44-2-222-2-201022-1-112i3−2i3002−2i32i3-1-1-2112i3−2i3−2i32i30−i3i300i3−i30000-333-300−i3i3i3−i300000000000000000000000000
χ768-808800-8-800000800000-8000000000000000000000000000000000000000000000000000000000000000
χ778-808-400-840043−430-4000004000000000043−43000000000000000000000000000000000000000000000000000
χ788-808-400-8400−43430-40000040000000000−4343000000000000000000000000000000000000000000000000000
χ798-80-48004-843−43000-4000004000000043−43000000000000000000000000000000000000000000000000000000
χ808-80-48004-8−4343000-40000040000000−4343000000000000000000000000000000000000000000000000000000
χ818-80-4-4004443−4343−43020006-6-20000000−23230−2323000000000000000000000000000000000000000000000000000
χ828-80-4-4004443−43−434302000-66-20000000−2323023−23000000000000000000000000000000000000000000000000000
χ838-80-4-40044−434343−4302000-66-2000000023−230−2323000000000000000000000000000000000000000000000000000
χ848-80-4-40044−4343−4343020006-6-2000000023−23023−23000000000000000000000000000000000000000000000000000

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