Finite Group Databasebeta

← Group #11920553

Character table — Group #11920553

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222666666668888888812121212121212121212121212121212161616161616161624242424242424242424242424243636363636367272
order1222444436661212121244448888366612121212888812121212242424242424242436661212121224661212242424242424242488888888
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
χ51111-1-1-1-11111-1-1-1-111-1-1ii−i−i1111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11-111-1-1iiii−i−i−i−ii−iii−i−ii−i
χ61111-1-1-1-11111-1-1-1-111-1-1ii−i−i1111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-11-1-111iiii−i−i−i−ii−i−i−iii−ii
χ71111-1-1-1-11111-1-1-1-111-1-1−i−iii1111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11-111-1-1−i−i−i−iiiii−ii−i−iii−ii
χ81111-1-1-1-11111-1-1-1-111-1-1−i−iii1111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-11-1-111−i−i−i−iiiii−iiii−i−ii−i
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
χ132222-2-2-2-22222-2-2-2-222-2-22i2i−2i−2i-1-1-1-111110000-2-22200000000-1-1-1-11111000000−i−i−i−iiiii2i−2i000000
χ142222-2-2-2-22222-2-2-2-222-2-2−2i−2i2i2i-1-1-1-111110000-2-22200000000-1-1-1-11111000000iiii−i−i−i−i−2i2i000000
χ152222-2-2-2-2-1-1-1-1111122-2-200002222-2-2-2-222-2-211-1-1-1-1-1-11111-1-1-1-111112-2-1-1110000000000000000
χ162222-2-2-2-2-1-1-1-1111122-2-200002222-2-2-2-2-2-22211-1-11111-1-1-1-1-1-1-1-11111-2211-1-10000000000000000
χ1722-2-22i−2i2i−2i22-2-22i2i−2i−2i2-22i−2i000022-2-22i−2i2i−2i00002i−2i2-20000000022-2-22i2i−2i−2i0000000000000000000000
χ1822-2-22i−2i2i−2i22-2-22i2i−2i−2i2-22i−2i0000-1-111−ii−ii00002i−2i2-200000000-1-111−i−iii000000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ1300000000
χ1922-2-22i−2i2i−2i22-2-22i2i−2i−2i2-22i−2i0000-1-111−ii−ii00002i−2i2-200000000-1-111−i−iii000000ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ1300000000
χ2022-2-22i−2i2i−2i-1-111−i−iii2-22i−2i000022-2-22i−2i2i−2i0000−ii-11−i3−i3i3i333−3−3-1-111−i−iii00−i3i33−30000000000000000
χ2122-2-22i−2i2i−2i-1-111−i−iii2-22i−2i000022-2-22i−2i2i−2i0000−ii-11i3i3−i3−i3−3−333-1-111−i−iii00i3−i3−330000000000000000
χ2222-2-2−2i2i−2i2i22-2-2−2i−2i2i2i2-2−2i2i000022-2-2−2i2i−2i2i0000−2i2i2-20000000022-2-2−2i−2i2i2i0000000000000000000000
χ2322-2-2−2i2i−2i2i22-2-2−2i−2i2i2i2-2−2i2i0000-1-111i−ii−i0000−2i2i2-200000000-1-111ii−i−i000000ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ2300000000
χ2422-2-2−2i2i−2i2i22-2-2−2i−2i2i2i2-2−2i2i0000-1-111i−ii−i0000−2i2i2-200000000-1-111ii−i−i000000−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ2300000000
χ2522-2-2−2i2i−2i2i-1-111ii−i−i2-2−2i2i000022-2-2−2i2i−2i2i0000i−i-11−i3−i3i3i3−3−333-1-111ii−i−i00−i3i3−330000000000000000
χ2622-2-2−2i2i−2i2i-1-111ii−i−i2-2−2i2i000022-2-2−2i2i−2i2i0000i−i-11i3i3−i3−i333−3−3-1-111ii−i−i00i3−i33−30000000000000000
χ272-2-2222-2-22-2-222-22-200002i−2i2i−2i-111-1-1-111−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2-111-11-11-1000000i−ii−ii−ii−i002−22−200
χ282-2-2222-2-22-2-222-22-200002i−2i2i−2i-111-1-1-111i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2-111-11-11-1000000i−ii−ii−ii−i00−22−2200
χ292-2-2222-2-22-2-222-22-20000−2i2i−2i2i-111-1-1-111−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2-111-11-11-1000000−ii−ii−ii−ii00−22−2200
χ302-2-2222-2-22-2-222-22-20000−2i2i−2i2i-111-1-1-111i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2-111-11-11-1000000−ii−ii−ii−ii002−22−200
χ312-2-22-2-2222-2-22-22-2200002-2-22-111-111-1-1−i2i2i2−i20000−i2i2−i2i2i2−i2i2−i2-111-1-11-110000001-11-1-11-1100−i2i2i2−i200
χ322-2-22-2-2222-2-22-22-2200002-2-22-111-111-1-1i2−i2−i2i20000i2−i2i2−i2−i2i2−i2i2-111-1-11-110000001-11-1-11-1100i2−i2−i2i200
χ332-2-22-2-2222-2-22-22-220000-222-2-111-111-1-1−i2i2i2−i20000−i2i2−i2i2i2−i2i2−i2-111-1-11-11000000-11-111-11-100i2−i2−i2i200
χ342-2-22-2-2222-2-22-22-220000-222-2-111-111-1-1i2−i2−i2i20000i2−i2i2−i2−i2i2−i2i2-111-1-11-11000000-11-111-11-100−i2i2i2−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
χ393333-3-3-3-33333-3-3-3-3-1-1113i3i−3i−3i0000000011-1-111-1-11111-1-1-1-100000000-11-1-11100000000−iiii−i−i−ii
χ403333-3-3-3-33333-3-3-3-3-1-1113i3i−3i−3i00000000-1-11111-1-1-1-1-1-11111000000001-111-1-100000000−ii−i−iiii−i
χ413333-3-3-3-33333-3-3-3-3-1-111−3i−3i3i3i0000000011-1-111-1-11111-1-1-1-100000000-11-1-11100000000i−i−i−iiii−i
χ423333-3-3-3-33333-3-3-3-3-1-111−3i−3i3i3i00000000-1-11111-1-1-1-1-1-11111000000001-111-1-100000000i−iii−i−i−ii
χ4344444444-2-2-2-2-2-2-2-244440000-2-2-2-2-2-2-2-20000-2-2-2-200000000111111110000000000000000000000
χ444444-4-4-4-4-2-2-2-2222244-4-40000-2-2-2-22222000022-2-2000000001111-1-1-1-10000000000000000000000
χ4544-4-44i−4i4i−4i-2-222−2i−2i2i2i4-44i−4i0000-2-222−2i2i−2i2i0000−2i2i-220000000011-1-1ii−i−i0000000000000000000000
χ4644-4-4−4i4i−4i4i-2-2222i2i−2i−2i4-4−4i4i0000-2-2222i−2i2i−2i00002i−2i-220000000011-1-1−i−iii0000000000000000000000
χ474-44-44i−4i−4i4i4-44-44i−4i−4i4i000000001-11-1i−i−ii00000000000000001-11-1−iii−i000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300000000
χ484-44-44i−4i−4i4i4-44-44i−4i−4i4i000000001-11-1i−i−ii00000000000000001-11-1−iii−i000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300000000
χ494-44-44i−4i−4i4i4-44-44i−4i−4i4i00000000-22-22−2i2i2i−2i0000000000000000-22-222i−2i−2i2i0000000000000000000000
χ504-44-44i−4i−4i4i-22-22−2i2i2i−2i00000000-22-22−2i2i2i−2i000000006−6−66i6−i6−i6i61-11-1−iii−i0000000000000000000000
χ514-44-44i−4i−4i4i-22-22−2i2i2i−2i00000000-22-22−2i2i2i−2i00000000−666−6−i6i6i6−i61-11-1−iii−i0000000000000000000000
χ524-44-4−4i4i4i−4i4-44-4−4i4i4i−4i000000001-11-1−iii−i00000000000000001-11-1i−i−ii000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300000000
χ534-44-4−4i4i4i−4i4-44-4−4i4i4i−4i000000001-11-1−iii−i00000000000000001-11-1i−i−ii000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300000000
χ544-44-4−4i4i4i−4i4-44-4−4i4i4i−4i00000000-22-222i−2i−2i2i0000000000000000-22-22−2i2i2i−2i0000000000000000000000
χ554-44-4−4i4i4i−4i-22-222i−2i−2i2i00000000-22-222i−2i−2i2i000000006−6−66−i6i6i6−i61-11-1i−i−ii0000000000000000000000
χ564-44-4−4i4i4i−4i-22-222i−2i−2i2i00000000-22-222i−2i−2i2i00000000−666−6i6−i6−i6i61-11-1i−i−ii0000000000000000000000
χ574-4-4444-4-44-4-444-44-400004i−4i4i−4i1-1-1111-1-100000000000000001-1-11-11-11000000−ii−ii−ii−ii00000000
χ584-4-4444-4-44-4-444-44-40000−4i4i−4i4i1-1-1111-1-100000000000000001-1-11-11-11000000i−ii−ii−ii−i00000000
χ594-4-4444-4-4-222-2-22-2200000000-222-2-2-222−2i22i2−2i22i20000i2−i2i2−i2i2−i2i2−i21-1-11-11-110000000000000000000000
χ604-4-4444-4-4-222-2-22-2200000000-222-2-2-2222i2−2i22i2−2i20000−i2i2−i2i2−i2i2−i2i21-1-11-11-110000000000000000000000
χ614-4-44-4-4444-4-44-44-4400004-4-441-1-11-1-11100000000000000001-1-111-11-1000000-11-111-11-100000000
χ624-4-44-4-4444-4-44-44-440000-444-41-1-11-1-11100000000000000001-1-111-11-10000001-11-1-11-1100000000
χ634-4-44-4-444-222-22-22-200000000-222-222-2-2−2i22i22i2−2i20000i2−i2i2−i2−i2i2−i2i21-1-111-11-10000000000000000000000
χ644-4-44-4-444-222-22-22-200000000-222-222-2-22i2−2i2−2i22i20000−i2i2−i2i2i2−i2i2−i21-1-111-11-10000000000000000000000
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
χ676666-6-6-6-6-3-3-3-33333-2-22200000000000022-2-2-1-111-1-1-1-1111100000000-2211-1-10000000000000000
χ686666-6-6-6-6-3-3-3-33333-2-222000000000000-2-222-1-1111111-1-1-1-1000000002-2-1-1110000000000000000
χ6966-6-66i−6i6i−6i66-6-66i6i−6i−6i-22−2i2i0000000000000000−2i2i-2200000000000000000000000000000000000000
χ7066-6-66i−6i6i−6i-3-333−3i−3i3i3i-22−2i2i0000000000000000i−i1-1−i3−i3i3i333−3−30000000000i3−i3−330000000000000000
χ7166-6-66i−6i6i−6i-3-333−3i−3i3i3i-22−2i2i0000000000000000i−i1-1i3i3−i3−i3−3−3330000000000−i3i33−30000000000000000
χ7266-6-6−6i6i−6i6i66-6-6−6i−6i6i6i-222i−2i00000000000000002i−2i-2200000000000000000000000000000000000000
χ7366-6-6−6i6i−6i6i-3-3333i3i−3i−3i-222i−2i0000000000000000−ii1-1−i3−i3i3i3−3−3330000000000i3−i33−30000000000000000
χ7466-6-6−6i6i−6i6i-3-3333i3i−3i−3i-222i−2i0000000000000000−ii1-1i3i3−i3−i333−3−30000000000−i3i3−330000000000000000
χ758-88-88i−8i−8i8i-44-44−4i4i4i−4i000000002-22-22i−2i−2i2i0000000000000000-11-11i−i−ii0000000000000000000000
χ768-88-8−8i8i8i−8i-44-444i−4i−4i4i000000002-22-2−2i2i2i−2i0000000000000000-11-11−iii−i0000000000000000000000
χ778-8-8888-8-8-444-4-44-44000000002-2-2222-2-20000000000000000-111-11-11-10000000000000000000000
χ788-8-88-8-888-444-44-44-4000000002-2-22-2-2220000000000000000-111-1-11-110000000000000000000000

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