Finite Group Databasebeta

← Group #11771758

Character table — Group #11771758

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1122222222222444444444444444444448888888888888888888888824242424242424242424242448484848484872727272
order12233446666121223466666688121212121212121212666812121224242424242424242424242424242424888824242424242424242466121216161616
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
χ51111111111111-11-11-1-1111-1-11111111-1-1-1-1-11-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1-111-1-1ii−i−i
χ61111111111111-11-11-1-1111-1-11111111-1-1-1-1-11-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-11-1-111−i−iii
χ71111111111111-11-11-1-1111-1-11111111-1-1-1-1-11-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii1-111-1-1−i−iii
χ81111111111111-11-11-1-1111-1-11111111-1-1-1-1-11-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii-11-1-111ii−i−i
χ92222222222222222222222-2-2222222222222-2222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000
χ102222222222222-22-22-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000
χ1122222-2-22222-2-222-222222200-2-2-2-2-2-2-2-2-22220-2-2-20000000000000000000000000000000000−i2i2−i2i2
χ1222222-2-22222-2-222-222222200-2-2-2-2-2-2-2-2-22220-2-2-20000000000000000000000000000000000i2−i2i2−i2
χ1322222-2-22222-2-2-2222-2-222200-2-2-2-2-2-2-222-2-2-2022200000000000000000000000000000000002−2−22
χ1422222-2-22222-2-2-2222-2-222200-2-2-2-2-2-2-222-2-2-202220000000000000000000000000000000000−222−2
χ152222-1222-1-1-1222-12222-1-1-122-1-1-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100000000000022-1-1-1-10000
χ162222-1222-1-1-1222-12222-1-1-122-1-1-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000-2-211110000
χ172222-1222-1-1-1222-12222-1-1-1-2-2-1-1-12-1-1-122-1-1-1-2-1-1-1-2-2111111-2-211111100000000000000−i3i3−i3i30000
χ182222-1222-1-1-1222-12222-1-1-1-2-2-1-1-12-1-1-122-1-1-1-2-1-1-1-2-2111111-2-211111100000000000000i3−i3i3−i30000
χ192222-1222-1-1-122-2-1-22-2-2-1-1-122-1-1-12-1-1-1-2-2111-2111-2-211111122-1-1-1-1-1-100000000000000−i3i3i3−i30000
χ202222-1222-1-1-122-2-1-22-2-2-1-1-122-1-1-12-1-1-1-2-2111-2111-2-211111122-1-1-1-1-1-100000000000000i3−i3−i3i30000
χ212222-1222-1-1-122-2-1-22-2-2-1-1-1-2-2-1-1-12-1-1-1-2-2111211122-1-1-1-1-1-1-2-21111110000000000002-2-1-1110000
χ222222-1222-1-1-122-2-1-22-2-2-1-1-1-2-2-1-1-12-1-1-1-2-2111211122-1-1-1-1-1-1-2-2111111000000000000-2211-1-10000
χ23222-1222-1222-1-12-12-1-1-1-1-1-1222-1-1-12-1-1-1-12-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ24222-1222-1222-1-12-12-1-1-1-1-1-1222-1-1-12-1-1-1-12-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1-2-2-2-2111111110000000000
χ25222-1222-1222-1-12-12-1-1-1-1-1-1-2-22-1-1-12-1-1-1-12-1-1-22-1-111-2-2111111-2-211110000−i3−i3i3i3−i3−i3i3i30000000000
χ26222-1222-1222-1-12-12-1-1-1-1-1-1-2-22-1-1-12-1-1-1-12-1-1-22-1-111-2-2111111-2-211110000i3i3−i3−i3i3i3−i3−i30000000000
χ27222-1222-1222-1-1-2-1-2-111-1-1-1222-1-1-12-1-111-211-2-21111-2-21111-1-122-1-1-1-1000033−3−3−3−3330000000000
χ28222-1222-1222-1-1-2-1-2-111-1-1-1222-1-1-12-1-111-211-2-21111-2-21111-1-122-1-1-1-10000−3−33333−3−30000000000
χ29222-1222-1222-1-1-2-1-2-111-1-1-1-2-22-1-1-12-1-111-2112-211-1-122-1-1-1-111-2-211112i2i−2i−2i−i−i−i−iiiii0000000000
χ30222-1222-1222-1-1-2-1-2-111-1-1-1-2-22-1-1-12-1-111-2112-211-1-122-1-1-1-111-2-21111−2i−2i2i2iiiii−i−i−i−i0000000000
χ3122-2222-222-2-222020-200-2-222i−2i222-2-2-2-2000000000000000002i−2i2i−2i2i2i−2i−2i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ3222-2222-222-2-222020-200-2-222i−2i222-2-2-2-2000000000000000002i−2i2i−2i2i2i−2i−2i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ3322-2222-222-2-222020-200-2-22−2i2i222-2-2-2-200000000000000000−2i2i−2i2i−2i−2i2i2i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ3422-2222-222-2-222020-200-2-22−2i2i222-2-2-2-200000000000000000−2i2i−2i2i−2i−2i2i2i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ3522-2-122-2-12-2-2-1-10-101−i3i311-12i−2i2-1-11-211−i3i30−i3i300−i3i33−30033−3−3−ii2i−2i−i−iii1+i−1−i1−i−1+i−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ220000000000
χ3622-2-122-2-12-2-2-1-10-101−i3i311-12i−2i2-1-11-211−i3i30−i3i300−i3i33−30033−3−3−ii2i−2i−i−iii−1−i1+i−1+i1−iζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ220000000000
χ3722-2-122-2-12-2-2-1-10-101−i3i311-1−2i2i2-1-11-211−i3i30−i3i300−i3i3−3300−3−333i−i−2i2iii−i−i1−i−1+i1+i−1−i−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ220000000000
χ3822-2-122-2-12-2-2-1-10-101−i3i311-1−2i2i2-1-11-211−i3i30−i3i300−i3i3−3300−3−333i−i−2i2iii−i−i−1+i1−i−1−i1+iζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ220000000000
χ3922-2-122-2-12-2-2-1-10-101i3−i311-12i−2i2-1-11-211i3−i30i3−i300i3−i3−3300−3−333−ii2i−2i−i−iii1+i−1−i1−i−1+i−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ140000000000
χ4022-2-122-2-12-2-2-1-10-101i3−i311-12i−2i2-1-11-211i3−i30i3−i300i3−i3−3300−3−333−ii2i−2i−i−iii−1−i1+i−1+i1−iζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ140000000000
χ4122-2-122-2-12-2-2-1-10-101i3−i311-1−2i2i2-1-11-211i3−i30i3−i300i3−i33−30033−3−3i−i−2i2iii−i−i1−i−1+i1+i−1−i−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ140000000000
χ4222-2-122-2-12-2-2-1-10-101i3−i311-1−2i2i2-1-11-211i3−i30i3−i300i3−i33−30033−3−3i−i−2i2iii−i−i−1+i1−i−1−i1+iζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ140000000000
χ434444-2-4-44-2-2-2-4-44-2-4444-2-2-200222-4222-4-4-2-2-2022200000000000000000000000000000000000000
χ444444-2-4-44-2-2-2-4-4-4-244-4-4-2-2-200222-4222442220-2-2-200000000000000000000000000000000000000
χ45444-24-4-4-2444224-2-4-2-2-2-2-2-200-4222-422224-2-20-42200000000000000000000000000000000000000
χ46444-24-4-4-244422-4-24-222-2-2-200-4222-422-2-2-42204-2-200000000000000000000000000000000000000
χ47444-2-244-2-2-2-2-2-2414-2-2-211144-211-2-211-2-2-2114-211-2-2-2-21111-2-2-2-211110000000000000000000000
χ48444-2-244-2-2-2-2-2-2414-2-2-2111-4-4-211-2-211-2-2-211-4-2112222-1-1-1-12222-1-1-1-10000000000000000000000
χ49444-2-244-2-2-2-2-2-2-41-4-22211144-211-2-211222-1-1-42-1-12222-1-1-1-1-2-2-2-211110000000000000000000000
χ50444-2-244-2-2-2-2-2-2-41-4-222111-4-4-211-2-211222-1-142-1-1-2-2-2-211112222-1-1-1-10000000000000000000000
χ51444-2-2-4-4-2-2-2-22241-4-2-2-2111002-1-122-1-122-21102-1-100003i−3i3i−3i00003i−3i3i−3i0000000000000000000000
χ52444-2-2-4-4-2-2-2-22241-4-2-2-2111002-1-122-1-122-21102-1-10000−3i3i−3i3i0000−3i3i−3i3i0000000000000000000000
χ53444-2-2-4-4-2-2-2-222-414-222111002-1-122-1-1-2-22-1-10-21100003i−3i3i−3i0000−3i3i−3i3i0000000000000000000000
χ54444-2-2-4-4-2-2-2-222-414-222111002-1-122-1-1-2-22-1-10-2110000−3i3i−3i3i00003i−3i3i−3i0000000000000000000000
χ5544-444-4444-4-4-4-4040-400-4-4400-4-4-4444400000000000000000000000000000000000000000000000
χ5644-44-24-44-222440-20-40022-24i−4i-2-2-2-4222000000000000000004i−4i−2i2i−2i−2i2i2i0000000000000000000000
χ5744-44-24-44-222440-20-40022-2−4i4i-2-2-2-422200000000000000000−4i4i2i−2i2i2i−2i−2i0000000000000000000000
χ5844-44-2-444-222-4-40-20-40022-2002224-2-2-200000000000−2i32i3−2i32i32i3−2i3000000000000000000000000000000
χ5944-44-2-444-222-4-40-20-40022-2002224-2-2-2000000000002i3−2i32i3−2i3−2i32i3000000000000000000000000000000
χ6044-4-24-44-24-4-4220-202−2i32i322-200-422-24-2-22i3−2i30−2i32i3002i3−2i300000000000000000000000000000000000000
χ6144-4-24-44-24-4-4220-2022i3−2i322-200-422-24-2-2−2i32i302i3−2i300−2i32i300000000000000000000000000000000000000
χ6244-4-2-24-4-2-222-2-20102−2i32i3-1-114i−4i-21122-1-1−2i32i30i3−i300i3−i323−2300−3−333−2i2i−2i2iii−i−i0000000000000000000000
χ6344-4-2-24-4-2-222-2-20102−2i32i3-1-11−4i4i-21122-1-1−2i32i30i3−i300i3−i3−23230033−3−32i−2i2i−2i−i−iii0000000000000000000000
χ6444-4-2-24-4-2-222-2-201022i3−2i3-1-114i−4i-21122-1-12i3−2i30−i3i300−i3i3−23230033−3−3−2i2i−2i2iii−i−i0000000000000000000000
χ6544-4-2-24-4-2-222-2-201022i3−2i3-1-11−4i4i-21122-1-12i3−2i30−i3i300−i3i323−2300−3−3332i−2i2i−2i−i−iii0000000000000000000000
χ6644-4-2-2-44-2-222220102−2i32i3-1-11002-1-1-2-2112i3−2i30i3−i300−i3i300−2i32i3i3−i3−i3i30000-333-30000000000000000000000
χ6744-4-2-2-44-2-222220102−2i32i3-1-11002-1-1-2-2112i3−2i30i3−i300−i3i3002i3−2i3−i3i3i3−i300003-3-330000000000000000000000
χ6844-4-2-2-44-2-2222201022i3−2i3-1-11002-1-1-2-211−2i32i30−i3i300i3−i300−2i32i3i3−i3−i3i300003-3-330000000000000000000000
χ6944-4-2-2-44-2-2222201022i3−2i3-1-11002-1-1-2-211−2i32i30−i3i300i3−i3002i3−2i3−i3i3i3−i30000-333-30000000000000000000000
χ708-808800-8-8000008000000-800000000000000000000000000000000000000000000000000000000
χ718-808-400-84−4i34i3000-40000−4i34i3400000000000000000000000000000000000000000000000000000000
χ728-808-400-844i3−4i3000-400004i3−4i3400000000000000000000000000000000000000000000000000000000
χ738-80-48004-80043−430-4000000400043−43000000000000000000000000000000000000000000000000000
χ748-80-48004-800−43430-40000004000−4343000000000000000000000000000000000000000000000000000
χ758-80-4-40044−4i34i343−430200002i3−2i3-2000−2323006i−6i00000000000000000000000000000000000000000000000
χ768-80-4-40044−4i34i3−43430200002i3−2i3-200023−2300−6i6i00000000000000000000000000000000000000000000000
χ778-80-4-400444i3−4i343−43020000−2i32i3-2000−232300−6i6i00000000000000000000000000000000000000000000000
χ788-80-4-400444i3−4i3−4343020000−2i32i3-200023−23006i−6i00000000000000000000000000000000000000000000000

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