Finite Group Databasebeta

← Group #11920696

Character table — Group #11920696

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222666666668888888812121212121212121212121212121212161616161616161624242424242424242424242424243636363636367272
order1222444436661212121222448888366612121212444466121212121212121212123666121212128824242424242424242424242488888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ311111111111111111111-1-1-1-111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111-1-1-1-11111-1-1-1-1-1-111ii−i−i1111-1-1-1-1ii−i−i-1-111iiii−i−i−i−i1111-1-1-1-1i−iii−i−iiiii−i−i−i−ii−i11-1-11-1
χ61111-1-1-1-11111-1-1-1-1-1-111ii−i−i1111-1-1-1-1−i−iii-1-111−i−i−i−iiiii1111-1-1-1-1−ii−i−iiiiiii−i−i−i−ii−i-1-111-11
χ71111-1-1-1-11111-1-1-1-1-1-111−i−iii1111-1-1-1-1ii−i−i-1-111iiii−i−i−i−i1111-1-1-1-1i−iii−i−i−i−i−i−iiiii−ii-1-111-11
χ81111-1-1-1-11111-1-1-1-1-1-111−i−iii1111-1-1-1-1−i−iii-1-111−i−i−i−iiiii1111-1-1-1-1−ii−i−iii−i−i−i−iiiii−ii11-1-11-1
χ9222222222222222222222222-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-122000000
χ1022222222222222222222-2-2-2-2-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-100000011111111-2-2000000
χ1122222222-1-1-1-1-1-1-1-122220000222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000000000000000
χ1222222222-1-1-1-1-1-1-1-12222000022222222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1-2-211110000000000000000
χ132222-2-2-2-22222-2-2-2-2-2-2222i2i−2i−2i-1-1-1-111110000-2-22200000000-1-1-1-11111000000−i−i−i−iiiii2i−2i000000
χ142222-2-2-2-22222-2-2-2-2-2-222−2i−2i2i2i-1-1-1-111110000-2-22200000000-1-1-1-11111000000iiii−i−i−i−i−2i2i000000
χ152222-2-2-2-2-1-1-1-11111-2-22200002222-2-2-2-22i2i−2i−2i11-1-1−i−i−i−iiiii-1-1-1-111112i−2i−i−iii0000000000000000
χ162222-2-2-2-2-1-1-1-11111-2-22200002222-2-2-2-2−2i−2i2i2i11-1-1iiii−i−i−i−i-1-1-1-11111−2i2iii−i−i0000000000000000
χ1722-2-222-2-22-2-2222-2-22-22-200002-2-2222-2-200002-22-2000000002-2-2222-2-20000000000000000000000
χ1822-2-222-2-22-2-2222-2-22-22-20000-111-1-1-11100002-22-200000000-111-1-1-11100000033−3−333−3−300000000
χ1922-2-222-2-22-2-2222-2-22-22-20000-111-1-1-11100002-22-200000000-111-1-1-111000000−3−333−3−33300000000
χ2022-2-222-2-2-111-1-1-1112-22-200002-2-2222-2-20000-11-1133−3−333−3−3-111-1-1-111003−33−30000000000000000
χ2122-2-222-2-2-111-1-1-1112-22-200002-2-2222-2-20000-11-11−3−333−3−333-111-1-1-11100−33−330000000000000000
χ2222-2-2-2-2222-2-22-2-222-222-200002-2-22-2-2220000-222-2000000002-2-22-2-2220000000000000000000000
χ2322-2-2-2-2222-2-22-2-222-222-20000-111-111-1-10000-222-200000000-111-111-1-1000000−i3−i3i3i3i3i3−i3−i300000000
χ2422-2-2-2-2222-2-22-2-222-222-20000-111-111-1-10000-222-200000000-111-111-1-1000000i3i3−i3−i3−i3−i3i3i300000000
χ2522-2-2-2-222-111-111-1-1-222-200002-2-22-2-22200001-1-11−i3−i3i3i3i3i3−i3−i3-111-111-1-100−i3i3i3−i30000000000000000
χ2622-2-2-2-222-111-111-1-1-222-200002-2-22-2-22200001-1-11i3i3−i3−i3−i3−i3i3i3-111-111-1-100i3−i3−i3i30000000000000000
χ272-22-22i−2i2i−2i22-2-22i−2i2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-11-11i−ii−i1+i−1−i1−i−1+i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i-11-11i−ii−i000000ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13002−2−i2i200
χ282-22-22i−2i2i−2i22-2-22i−2i2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-11-11i−ii−i−1−i1+i−1+i1−i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i-11-11i−ii−i000000ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ1300−22i2−i200
χ292-22-22i−2i2i−2i22-2-22i−2i2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-11-11i−ii−i1+i−1−i1−i−1+i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i-11-11i−ii−i000000−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ1300−22i2−i200
χ302-22-22i−2i2i−2i22-2-22i−2i2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-11-11i−ii−i−1−i1+i−1+i1−i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i-11-11i−ii−i000000−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13002−2−i2i200
χ312-22-2−2i2i−2i2i22-2-2−2i2i−2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23-11-11−ii−ii1−i−1+i1+i−1−i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i-11-11−ii−ii000000−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23002−2i2−i200
χ322-22-2−2i2i−2i2i22-2-2−2i2i−2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23-11-11−ii−ii−1+i1−i−1−i1+i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i-11-11−ii−ii000000−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ2300−22−i2i200
χ332-22-2−2i2i−2i2i22-2-2−2i2i−2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23-11-11−ii−ii1−i−1+i1+i−1−i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i-11-11−ii−ii000000ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ2300−22−i2i200
χ342-22-2−2i2i−2i2i22-2-2−2i2i−2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23-11-11−ii−ii−1+i1−i−1−i1+i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i-11-11−ii−ii000000ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23002−2i2−i200
χ353333333333333333-1-1-1-13333000000001111-1-1-1-11111111100000000-1-1-1-1-1-100000000-1-11111-1-1
χ363333333333333333-1-1-1-1333300000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000011111100000000-1-1-1-1-1-111
χ373333333333333333-1-1-1-1-3-3-3-3000000001111-1-1-1-11111111100000000-1-1-1-1-1-10000000011-1-1-1-111
χ383333333333333333-1-1-1-1-3-3-3-300000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000011111100000000111111-1-1
χ393333-3-3-3-33333-3-3-3-311-1-13i3i−3i−3i00000000ii−i−i11-1-1iiii−i−i−i−i00000000−ii−i−iii00000000−ii11-1-1-11
χ403333-3-3-3-33333-3-3-3-311-1-13i3i−3i−3i00000000−i−iii11-1-1−i−i−i−iiiii00000000i−iii−i−i00000000−ii-1-1111-1
χ413333-3-3-3-33333-3-3-3-311-1-1−3i−3i3i3i00000000ii−i−i11-1-1iiii−i−i−i−i00000000−ii−i−iii00000000i−i-1-1111-1
χ423333-3-3-3-33333-3-3-3-311-1-1−3i−3i3i3i00000000−i−iii11-1-1−i−i−i−iiiii00000000i−iii−i−i00000000i−i11-1-1-11
χ4344444444-2-2-2-2-2-2-2-244440000-2-2-2-2-2-2-2-20000-2-2-2-200000000111111110000000000000000000000
χ444444-4-4-4-4-2-2-2-22222-4-4440000-2-2-2-22222000022-2-2000000001111-1-1-1-10000000000000000000000
χ4544-4-444-4-4-222-2-2-2224-44-40000-222-2-2-2220000-22-22000000001-1-1111-1-10000000000000000000000
χ4644-4-4-4-444-222-222-2-2-444-40000-222-222-2-200002-2-22000000001-1-11-1-1110000000000000000000000
χ474-44-44i−4i4i−4i44-4-44i−4i4i−4i00004ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ131-11-1−ii−ii00000000000000001-11-1−ii−ii000000−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ1300000000
χ484-44-44i−4i4i−4i44-4-44i−4i4i−4i0000−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ131-11-1−ii−ii00000000000000001-11-1−ii−ii000000ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ1300000000
χ494-44-44i−4i4i−4i-2-222−2i2i−2i2i00000000-22-222i−2i2i−2i2+2i−2−2i2−2i−2+2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1-11-1−ii−ii0000000000000000000000
χ504-44-44i−4i4i−4i-2-222−2i2i−2i2i00000000-22-222i−2i2i−2i−2−2i2+2i−2+2i2−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i1-11-1−ii−ii0000000000000000000000
χ514-44-4−4i4i−4i4i44-4-4−4i4i−4i4i0000−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ231-11-1i−ii−i00000000000000001-11-1i−ii−i000000ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ2300000000
χ524-44-4−4i4i−4i4i44-4-4−4i4i−4i4i00004ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ231-11-1i−ii−i00000000000000001-11-1i−ii−i000000−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ2300000000
χ534-44-4−4i4i−4i4i-2-2222i−2i2i−2i00000000-22-22−2i2i−2i2i2−2i−2+2i2+2i−2−2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1-11-1i−ii−i0000000000000000000000
χ544-44-4−4i4i−4i4i-2-2222i−2i2i−2i00000000-22-22−2i2i−2i2i−2+2i2−2i−2−2i2+2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i1-11-1i−ii−i0000000000000000000000
χ554-4-444i−4i−4i4i4-44-44i−4i−4i4i0000000011-1-1−iii−i000000000000000011-1-1−iii−i000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300000000
χ564-4-444i−4i−4i4i4-44-44i−4i−4i4i0000000011-1-1−iii−i000000000000000011-1-1−iii−i000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300000000
χ574-4-444i−4i−4i4i4-44-44i−4i−4i4i00000000-2-2222i−2i−2i2i0000000000000000-2-2222i−2i−2i2i0000000000000000000000
χ584-4-444i−4i−4i4i-22-22−2i2i2i−2i00000000-2-2222i−2i−2i2i00000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2211-1-1−iii−i0000000000000000000000
χ594-4-444i−4i−4i4i-22-22−2i2i2i−2i00000000-2-2222i−2i−2i2i00000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2211-1-1−iii−i0000000000000000000000
χ604-4-44−4i4i4i−4i4-44-4−4i4i4i−4i0000000011-1-1i−i−ii000000000000000011-1-1i−i−ii000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300000000
χ614-4-44−4i4i4i−4i4-44-4−4i4i4i−4i0000000011-1-1i−i−ii000000000000000011-1-1i−i−ii000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300000000
χ624-4-44−4i4i4i−4i4-44-4−4i4i4i−4i00000000-2-222−2i2i2i−2i0000000000000000-2-222−2i2i2i−2i0000000000000000000000
χ634-4-44−4i4i4i−4i-22-222i−2i−2i2i00000000-2-222−2i2i2i−2i00000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2211-1-1i−i−ii0000000000000000000000
χ644-4-44−4i4i4i−4i-22-222i−2i−2i2i00000000-2-222−2i2i2i−2i00000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2211-1-1i−i−ii0000000000000000000000
χ6566666666-3-3-3-3-3-3-3-3-2-2-2-200000000000022221111-1-1-1-1-1-1-1-100000000-2-211110000000000000000
χ6666666666-3-3-3-3-3-3-3-3-2-2-2-2000000000000-2-2-2-21111111111110000000022-1-1-1-10000000000000000
χ676666-6-6-6-6-3-3-3-3333322-2-20000000000002i2i−2i−2i-1-111−i−i−i−iiiii00000000−2i2iii−i−i0000000000000000
χ686666-6-6-6-6-3-3-3-3333322-2-2000000000000−2i−2i2i2i-1-111iiii−i−i−i−i000000002i−2i−i−iii0000000000000000
χ6966-6-666-6-66-6-6666-6-6-22-220000000000000000-22-2200000000000000000000000000000000000000
χ7066-6-666-6-6-333-3-3-333-22-2200000000000000001-11-133−3−333−3−30000000000−33−330000000000000000
χ7166-6-666-6-6-333-3-3-333-22-2200000000000000001-11-1−3−333−3−33300000000003−33−30000000000000000
χ7266-6-6-6-6666-6-66-6-6662-2-2200000000000000002-2-2200000000000000000000000000000000000000
χ7366-6-6-6-666-333-333-3-32-2-220000000000000000-111-1−i3−i3i3i3i3i3−i3−i30000000000i3−i3−i3i30000000000000000
χ7466-6-6-6-666-333-333-3-32-2-220000000000000000-111-1i3i3−i3−i3−i3−i3i3i30000000000−i3i3i3−i30000000000000000
χ758-88-88i−8i8i−8i-4-444−4i4i−4i4i000000002-22-2−2i2i−2i2i0000000000000000-11-11i−ii−i0000000000000000000000
χ768-88-8−8i8i−8i8i-4-4444i−4i4i−4i000000002-22-22i−2i2i−2i0000000000000000-11-11−ii−ii0000000000000000000000
χ778-8-888i−8i−8i8i-44-44−4i4i4i−4i0000000022-2-2−2i2i2i−2i0000000000000000-1-111i−i−ii0000000000000000000000
χ788-8-88−8i8i8i−8i-44-444i−4i−4i4i0000000022-2-22i−2i−2i2i0000000000000000-1-111−iii−i0000000000000000000000

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