Finite Group Databasebeta

← Group #11771739

Character table — Group #11771739

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1122222222222444444444444444444448888888888888888888888824242424242424242424242448484848484872727272
order12233446666121223466668812121212121212242424246666812121212242424242424242424242424242416161616484848484848484844121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-11-11111-1-11111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1-1-1-111ii−i−i
χ61111111111111-11-11111-1-11111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1111-1-1−i−iii
χ71111111111111-11-11111-1-11111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1−i−iii−i−i−i−iiiii1-1-1-111−i−iii
χ81111111111111-11-11111-1-11111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1111-1-1ii−i−i
χ922222222222222222222-2-22222222-2-2-2-22222-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000
χ102222222222222-22-222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000000000
χ1122222-2-22222-2-222-2222200-2-2-2-2-2-2-2000022220-2-2-2-2000000000000002−22−222−2−222−2−20000000000
χ1222222-2-22222-2-222-2222200-2-2-2-2-2-2-2000022220-2-2-2-200000000000000−22−22−2−222−2−2220000000000
χ1322222-2-22222-2-2-222222200-2-2-2-2-2-2-20000-2-2-2-20222200000000000000−i2i2i2−i2−i2−i2i2i2i2i2−i2−i20000000000
χ1422222-2-22222-2-2-222222200-2-2-2-2-2-2-20000-2-2-2-20222200000000000000i2−i2−i2i2i2i2−i2−i2−i2−i2i2i20000000000
χ152222-1222-1-1-1222-122-1-1-1222-1-1-1-1-1-122222-1-1-122-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000
χ162222-1222-1-1-1222-122-1-1-1222-1-1-1-1-1-122222-1-1-122-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-211110000
χ172222-1222-1-1-1222-122-1-1-1-2-22-1-1-1-1-1-1-2-2-2-22-1-1-1-22-1-1-1-2-211111111111100000000000000−i3i3−i3i30000
χ182222-1222-1-1-1222-122-1-1-1-2-22-1-1-1-1-1-1-2-2-2-22-1-1-1-22-1-1-1-2-211111111111100000000000000i3−i3i3−i30000
χ192222-1222-1-1-122-2-1-22-1-1-1222-1-1-1-1-1-12222-2111-2-2111-2-2111111-1-1-1-1-1-100000000000000−i3i3i3−i30000
χ202222-1222-1-1-122-2-1-22-1-1-1222-1-1-1-1-1-12222-2111-2-2111-2-2111111-1-1-1-1-1-100000000000000i3−i3−i3i30000
χ212222-1222-1-1-122-2-1-22-1-1-1-2-22-1-1-1-1-1-1-2-2-2-2-21112-211122-1-1-1-1-1-11111110000000000002-211-1-10000
χ222222-1222-1-1-122-2-1-22-1-1-1-2-22-1-1-1-1-1-1-2-2-2-2-21112-211122-1-1-1-1-1-1111111000000000000-22-1-1110000
χ23222-1222-1222-1-12-12-1-1-1-122-12-1-12-1-1-1-1-1-1-12-1-12-12-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ24222-1222-1222-1-12-12-1-1-1-122-12-1-12-1-1-1-1-1-1-12-1-12-12-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-2111111110000000000
χ25222-1222-1222-1-12-12-1-1-1-1-2-2-12-1-12-1-11111-12-1-1-2-12-1-111-2-21111-2-2111100003−33−33−33−30000000000
χ26222-1222-1222-1-12-12-1-1-1-1-2-2-12-1-12-1-11111-12-1-1-2-12-1-111-2-21111-2-211110000−33−33−33−330000000000
χ27222-1222-1222-1-1-2-1-2-1-1-1-122-12-1-12-1-1-1-1-1-11-211-21-21111-2-2111122-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000
χ28222-1222-1222-1-1-2-1-2-1-1-1-122-12-1-12-1-1-1-1-1-11-211-21-21111-2-2111122-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000
χ29222-1222-1222-1-1-2-1-2-1-1-1-1-2-2-12-1-12-1-111111-21121-211-1-122-1-1-1-1-2-211112i2i−2i−2i−i−i−i−iiiii0000000000
χ30222-1222-1222-1-1-2-1-2-1-1-1-1-2-2-12-1-12-1-111111-21121-211-1-122-1-1-1-1-2-21111−2i−2i2i2iiiii−i−i−i−i0000000000
χ31222-12-2-2-1222112-1-2-1-1-1-1001-211-21133−3−3-12-1-101-2113−30033−3−30033−3−32−22−2ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ230000000000
χ32222-12-2-2-1222112-1-2-1-1-1-1001-211-21133−3−3-12-1-101-2113−30033−3−30033−3−3−22−22−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ230000000000
χ33222-12-2-2-1222112-1-2-1-1-1-1001-211-211−3−333-12-1-101-211−3300−3−33300−3−3332−22−2ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ70000000000
χ34222-12-2-2-1222112-1-2-1-1-1-1001-211-211−3−333-12-1-101-211−3300−3−33300−3−333−22−22−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ70000000000
χ35222-12-2-2-122211-2-12-1-1-1-1001-211-21133−3−31-2110-12-1-1−3300−3−3330033−3−3−i2i2i2−i2ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000
χ36222-12-2-2-122211-2-12-1-1-1-1001-211-21133−3−31-2110-12-1-1−3300−3−3330033−3−3i2−i2−i2i2−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000
χ37222-12-2-2-122211-2-12-1-1-1-1001-211-211−3−3331-2110-12-1-13−30033−3−300−3−333−i2i2i2−i2ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000
χ38222-12-2-2-122211-2-12-1-1-1-1001-211-211−3−3331-2110-12-1-13−30033−3−300−3−333i2−i2−i2i2−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000
χ3922-2222-22-2-22-2-2020-2-2-222i−2i2222-2-2-22i−2i2i−2i000000000000000002i−2i2i−2i2i−2i0000000000000000001+i−1−i1−i−1+i
χ4022-2222-22-2-22-2-2020-2-2-222i−2i2222-2-2-22i−2i2i−2i000000000000000002i−2i2i−2i2i−2i000000000000000000−1−i1+i−1+i1−i
χ4122-2222-22-2-22-2-2020-2-2-22−2i2i2222-2-2-2−2i2i−2i2i00000000000000000−2i2i−2i2i−2i2i0000000000000000001−i−1+i1+i−1−i
χ4222-2222-22-2-22-2-2020-2-2-22−2i2i2222-2-2-2−2i2i−2i2i00000000000000000−2i2i−2i2i−2i2i000000000000000000−1+i1−i−1−i1+i
χ434444-2-4-44-2-2-2-4-44-2-44-2-2-200-422222200004-2-2-20-4222000000000000000000000000000000000000
χ444444-2-4-44-2-2-2-4-4-4-244-2-2-200-42222220000-422204-2-2-2000000000000000000000000000000000000
χ45444-2-244-2-2-2-2-2-2414-211144-2-211-211-2-2-2-2-2-2114-2-211-2-2-2-21111-2-211110000000000000000000000
χ46444-2-244-2-2-2-2-2-2414-2111-4-4-2-211-2112222-2-211-4-2-2112222-1-1-1-122-1-1-1-10000000000000000000000
χ47444-2-244-2-2-2-2-2-2-41-4-211144-2-211-211-2-2-2-222-1-1-422-1-12222-1-1-1-1-2-211110000000000000000000000
χ48444-2-244-2-2-2-2-2-2-41-4-2111-4-4-2-211-211222222-1-1422-1-1-2-2-2-2111122-1-1-1-10000000000000000000000
χ49444-2-2-4-4-2-2-2-22241-4-21110022-1-12-1-12323−23−23-2-211022-1-123−2300−3−33300−3−3330000000000000000000000
χ50444-2-2-4-4-2-2-2-22241-4-21110022-1-12-1-1−23−232323-2-211022-1-1−23230033−3−30033−3−30000000000000000000000
χ51444-2-2-4-4-2-2-2-222-414-21110022-1-12-1-12323−23−2322-1-10-2-211−23230033−3−300−3−3330000000000000000000000
χ52444-2-2-4-4-2-2-2-222-414-21110022-1-12-1-1−23−23232322-1-10-2-21123−2300−3−3330033−3−30000000000000000000000
χ5344-444-444-4-4444040-4-4-4400-4-4-4-44440000000000000000000000000000000000000000000000000
χ5444-44-24-4422-2-4-40-20-422-24i−4i4-2-2-22224i−4i4i−4i00000000000000000−2i2i−2i2i−2i2i0000000000000000000000
χ5544-44-24-4422-2-4-40-20-422-2−4i4i4-2-2-2222−4i4i−4i4i000000000000000002i−2i2i−2i2i−2i0000000000000000000000
χ5644-44-2-44422-2440-20-422-200-4222-2-2-2000000000000000−2i32i3−2i32i3−2i32i30000000000000000000000000000
χ5744-44-2-44422-2440-20-422-200-4222-2-2-20000000000000002i3−2i32i3−2i32i3−2i30000000000000000000000000000
χ5844-4-244-4-2-4-44220-20222-24i−4i-24-2-2-422−2i2i−2i2i000000000000000004i−4i−2i2i−2i2i0000000000000000000000
χ5944-4-244-4-2-4-44220-20222-2−4i4i-24-2-2-4222i−2i2i−2i00000000000000000−4i4i2i−2i2i−2i0000000000000000000000
χ6044-4-24-44-2-4-44-2-20-20222-2002-4224-2-2−2i32i32i3−2i30000000000000000000−2i32i32i3−2i30000000000000000000000
χ6144-4-24-44-2-4-44-2-20-20222-2002-4224-2-22i3−2i3−2i32i300000000000000000002i3−2i3−2i32i30000000000000000000000
χ6244-4-2-24-4-222-2220102-1-114i−4i-2-2112-1-1−2i2i−2i2i003-30003-300003i−3i−3i3i−2i2ii−ii−i0000000000000000000000
χ6344-4-2-24-4-222-2220102-1-114i−4i-2-2112-1-1−2i2i−2i2i00-33000-330000−3i3i3i−3i−2i2ii−ii−i0000000000000000000000
χ6444-4-2-24-4-222-2220102-1-11−4i4i-2-2112-1-12i−2i2i−2i003-30003-30000−3i3i3i−3i2i−2i−ii−ii0000000000000000000000
χ6544-4-2-24-4-222-2220102-1-11−4i4i-2-2112-1-12i−2i2i−2i00-33000-3300003i−3i−3i3i2i−2i−ii−ii0000000000000000000000
χ6644-4-2-2-44-222-2-2-20102-1-110022-1-1-211−2i32i32i3−2i3003-3000-33002i3−2i3−i3i3−i3i300i3−i3−i3i30000000000000000000000
χ6744-4-2-2-44-222-2-2-20102-1-110022-1-1-211−2i32i32i3−2i300-330003-300−2i32i3i3−i3i3−i300i3−i3−i3i30000000000000000000000
χ6844-4-2-2-44-222-2-2-20102-1-110022-1-1-2112i3−2i3−2i32i3003-3000-3300−2i32i3i3−i3i3−i300−i3i3i3−i30000000000000000000000
χ6944-4-2-2-44-222-2-2-20102-1-110022-1-1-2112i3−2i3−2i32i300-330003-3002i3−2i3−i3i3−i3i300−i3i3i3−i30000000000000000000000
χ708-808800-800-800080000-80000000000000000000000000000000000000000000000000000000000
χ718-808-400-8−4i34i34000-400−4i34i340000000000000000000000000000000000000000000000000000000000
χ728-808-400-84i3−4i34000-4004i3−4i340000000000000000000000000000000000000000000000000000000000
χ738-80-4800400-843−430-400004000000043−430000000000000000000000000000000000000000000000000
χ748-80-4800400-8−43430-4000040000000−43430000000000000000000000000000000000000000000000000
χ758-80-4-4004−4i34i3443−4302002i3−2i3-200006i−6i0−23230000000000000000000000000000000000000000000000000
χ768-80-4-4004−4i34i34−434302002i3−2i3-20000−6i6i023−230000000000000000000000000000000000000000000000000
χ778-80-4-40044i3−4i3443−430200−2i32i3-20000−6i6i0−23230000000000000000000000000000000000000000000000000
χ788-80-4-40044i3−4i34−43430200−2i32i3-200006i−6i023−230000000000000000000000000000000000000000000000000

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