Finite Group Databasebeta

← Group #14282794

Character table — Group #14282794

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111122224444466668888888810101010151515151616161616161616162020202020202020202020202424242424404040404040404040484860606060606060606080120
order12223666451010104444212152020303030224444446101030303030606044446688881212420202020412121212242424242020444448888124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111
χ31111111111111111111111111-1-1-1-1-1-1-1-1111111111ii−i−i-1-1ii−i−i-1-111111-1ii−i−iii−i−i11-1ii−i−iii−i−i-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1111111111−i−iii-1-1−i−iii-1-111111-1−i−iii−i−iii11-1−i−iii−i−iii-1-1
χ511111111111111111-1111111111111111-1-1-1-1-1-1-111111111-1-1-1-111-11111-11111-1-1-1-1-1-111111-1-1-1-1-1-1
χ611111111111111111-1111111111111111-1-1-1-1-1-1-111-1-1-1-111111111-11111-1-1-1-1-11111-1-11-1-1-1-11111-1-1
χ711111111111111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i-1-1−i−iii-1-1-111111ii−i−i−i−iii-1-1-1ii−i−i−i−iii11
χ811111111111111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii-1-1ii−i−i-1-1-111111−i−iiiii−i−i-1-1-1−i−iiiii−i−i11
χ91111111111111-1-1-1-1111111111111-1-1-1-1111111111111111111111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-11-1
χ101111111111111-1-1-1-1111111111111-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1111111111-1
χ111111111111111-1-1-1-111111111-1-1-1-11111111111111ii−i−i-1-1ii−i−i-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-11−i−iii−i−iii-11
χ121111111111111-1-1-1-111111111-1-1-1-11111111111111−i−iii-1-1−i−iii-1-1-1-1-1-1-1-1−i−iii−i−iii-1-11ii−i−iii−i−i-11
χ131111111111111-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-1-11111-1-1-1-111-1-1-1-1-11111-11
χ141111111111111-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-11
χ151111111111111-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-111ii−i−i-1-1−i−iii-1-11-1-1-1-11ii−i−i−i−iii111−i−iiiii−i−i1-1
χ161111111111111-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-111−i−iii-1-1ii−i−i-1-11-1-1-1-11−i−iiiii−i−i111ii−i−i−i−iii1-1
χ1722222222-2222222-2-20-22-2-222222-2-2-2-2-2-20000000-2-20000220000-2-2022-2-20000000000020000000000
χ1822222222-2222222-2-20-22-2-2222-2-22222220000000-2-20000-2-2000022022-2-200000000000-20000000000
χ1922222222-22222-2-2220-22-2-222222-2-222220000000-2-20000220000-2-20-2-22200000000000-20000000000
χ2022222222-22222-2-2220-22-2-2222-2-222-2-2-2-20000000-2-20000-2-20000220-2-2220000000000020000000000
χ212222-1-1-1-12222200002-1-122-1-1-122220000-122-1-1-1-1-1-12222-1-12222-1-1000002-1-1-1-1-1-1-1-100000000000-10
χ222222-1-1-1-12222200002-1-122-1-1-122220000-122-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-2-1-10000021111111100000000000-10
χ232222-1-1-1-12222200002-1-122-1-1-1-2-2-2-20000-122-1-1-1-1-1-12i2i−2i−2i112i2i−2i−2i1100000-2−i−iii−i−iii0000000000010
χ242222-1-1-1-12222200002-1-122-1-1-1-2-2-2-20000-122-1-1-1-1-1-1−2i−2i2i2i11−2i−2i2i2i1100000-2ii−i−iii−i−i0000000000010
χ252222-1-1-1-1222220000-2-1-122-1-1-1222200001-2-21111-1-12222-1-1-2-2-2-2-1-100000-2-1-1-1-111110000000000010
χ262222-1-1-1-1222220000-2-1-122-1-1-1222200001-2-21111-1-1-2-2-2-2-1-12222-1-100000-21111-1-1-1-10000000000010
χ272222-1-1-1-1222220000-2-1-122-1-1-1-2-2-2-200001-2-21111-1-12i2i−2i−2i11−2i−2i2i2i11000002−i−iiiii−i−i00000000000-10
χ282222-1-1-1-1222220000-2-1-122-1-1-1-2-2-2-200001-2-21111-1-1−2i−2i2i2i112i2i−2i−2i11000002ii−i−i−i−iii00000000000-10
χ292-22-22-2-22022-2-2002i−2i002002-2-22-2002i2i−2i−2i0000000000000-222−22−2000002i−2i000002−22−20000000−i2i2−i2i200
χ302-22-22-2-22022-2-2002i−2i002002-2-22-2002i2i−2i−2i0000000000000-22−22−22000002i−2i00000−22−220000000i2−i2i2−i200
χ312-22-22-2-22022-2-2002i−2i002002-2-2-2200−2i−2i2i2i00000000000002-2−i2i2i2−i2000002i−2i00000−i2i2i2−i20000000−222−200
χ322-22-22-2-22022-2-2002i−2i002002-2-2-2200−2i−2i2i2i00000000000002-2i2−i2−i2i2000002i−2i00000i2−i2−i2i200000002−2−2200
χ332-22-22-2-22022-2-200−2i2i002002-2-22-200−2i−2i2i2i0000000000000-222−22−200000−2i2i000002−22−20000000i2−i2i2−i200
χ342-22-22-2-22022-2-200−2i2i002002-2-22-200−2i−2i2i2i0000000000000-22−22−2200000−2i2i00000−22−220000000−i2i2−i2i200
χ352-22-22-2-22022-2-200−2i2i002002-2-2-22002i2i−2i−2i00000000000002-2−i2i2i2−i200000−2i2i00000−i2i2i2−i200000002−2−2200
χ362-22-22-2-22022-2-200−2i2i002002-2-2-22002i2i−2i−2i00000000000002-2i2−i2−i2i200000−2i2i00000i2−i2−i2i20000000−222−200
χ372-2-2222-2-202-22-22i−2i0000200-22-2002i−2i2-22-20000000001+i−1−i1−i−1+i0000002i−2i02i−2i0001+i−1−i1−i−1+i00000001−i−1+i1+i−1−i000000
χ382-2-2222-2-202-22-22i−2i0000200-22-2002i−2i2-22-2000000000−1−i1+i−1+i1−i0000002i−2i02i−2i000−1−i1+i−1+i1−i0000000−1+i1−i−1−i1+i000000
χ392-2-2222-2-202-22-22i−2i0000200-22-200−2i2i-22-220000000001−i−1+i1+i−1−i000000−2i2i02i−2i0001−i−1+i1+i−1−i0000000−1−i1+i−1+i1−i000000
χ402-2-2222-2-202-22-22i−2i0000200-22-200−2i2i-22-22000000000−1+i1−i−1−i1+i000000−2i2i02i−2i000−1+i1−i−1−i1+i00000001+i−1−i1−i−1+i000000
χ412-2-2222-2-202-22-2−2i2i0000200-22-2002i−2i-22-220000000001+i−1−i1−i−1+i0000002i−2i0−2i2i0001+i−1−i1−i−1+i0000000−1+i1−i−1−i1+i000000
χ422-2-2222-2-202-22-2−2i2i0000200-22-2002i−2i-22-22000000000−1−i1+i−1+i1−i0000002i−2i0−2i2i000−1−i1+i−1+i1−i00000001−i−1+i1+i−1−i000000
χ432-2-2222-2-202-22-2−2i2i0000200-22-200−2i2i2-22-20000000001−i−1+i1+i−1−i000000−2i2i0−2i2i0001−i−1+i1+i−1−i00000001+i−1−i1−i−1+i000000
χ442-2-2222-2-202-22-2−2i2i0000200-22-200−2i2i2-22-2000000000−1+i1−i−1−i1+i000000−2i2i0−2i2i000−1+i1−i−1−i1+i0000000−1−i1+i−1+i1−i000000
χ45444444444-1-1-1-1444444-1-1-1-1-1-1000000004-1-1-1-1-1-1-1-10000000000004-1-1-1-1000000000-1-100000000000
χ46444444444-1-1-1-14444-44-1-1-1-1-1-100000000-4111111-1-1000000000000-4-1-1-1-10000000001100000000000
χ47444444444-1-1-1-1-4-4-4-444-1-1-1-1-1-1000000004-1-1-1-1-1-1-1-1000000000000-411110000000001100000000000
χ48444444444-1-1-1-1-4-4-4-4-44-1-1-1-1-1-100000000-4111111-1-100000000000041111000000000-1-100000000000
χ4944444444-4-1-1-1-144-4-40-4-111-1-1-1000000000−55−5−555110000000000000-1-111000000000−5500000000000
χ5044444444-4-1-1-1-144-4-40-4-111-1-1-10000000005−555−5−5110000000000000-1-1110000000005−500000000000
χ5144444444-4-1-1-1-1-4-4440-4-111-1-1-1000000000−55−5−55511000000000000011-1-10000000005−500000000000
χ5244444444-4-1-1-1-1-4-4440-4-111-1-1-10000000005−555−5−511000000000000011-1-1000000000−5500000000000
χ534444-2-2-2-2-44444000002-2-4-4-2-2-244-4-400000000000220000-2-2000022000000000000000000000000000
χ544444-2-2-2-2-44444000002-2-4-4-2-2-2-4-44400000000000220000220000-2-2000000000000000000000000000
χ5544-4-44-44-404-4-44000000400-4-4400004i−4i−4i4i000000000000000000000000000000000000000000000000
χ5644-4-44-44-404-4-44000000400-4-440000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ574-44-4-222-2044-4-4000000-200-2224-400000000000000000002-222−2222−22000000000000−22−220000000000000
χ584-44-4-222-2044-4-4000000-200-2224-400000000000000000002-2−2222−22220000000000002−22−20000000000000
χ594-44-4-222-2044-4-4000000-200-222-440000000000000000000-22−2i22i22i2−2i2000000000000i2−i2−i2i20000000000000
χ604-44-4-222-2044-4-4000000-200-222-440000000000000000000-222i2−2i2−2i22i2000000000000−i2i2i2−i20000000000000
χ614-4-44-2-22204-44-4000000-2002-22004i−4i00000000000002+2i−2−2i2−2i−2+2i000000−2i2i000000−1−i1+i−1+i1−i00000000000000000
χ624-4-44-2-22204-44-4000000-2002-22004i−4i0000000000000−2−2i2+2i−2+2i2−2i000000−2i2i0000001+i−1−i1−i−1+i00000000000000000
χ634-4-44-2-22204-44-4000000-2002-2200−4i4i00000000000002−2i−2+2i2+2i−2−2i0000002i−2i000000−1+i1−i−1−i1+i00000000000000000
χ644-4-44-2-22204-44-4000000-2002-2200−4i4i0000000000000−2+2i2−2i−2−2i2+2i0000002i−2i0000001−i−1+i1+i−1−i00000000000000000
χ658888-4-4-4-48-2-2-2-200008-41-2-211100000000-4-2-2111111000000000000000000000000000000000000000
χ668888-4-4-4-48-2-2-2-20000-8-41-2-211100000000422-1-1-1-111000000000000000000000000000000000000000
χ678888-4-4-4-4-8-2-2-2-2000004122111000000000−252555−5−5-1-1000000000000000000000000000000000000000
χ688888-4-4-4-4-8-2-2-2-200000412211100000000025−25−5−555-1-1000000000000000000000000000000000000000
χ6988-8-88-88-80-222-2000000-2−252522-2000000000000000−2525000000000000000000000000000000000000000
χ7088-8-88-88-80-222-2000000-225−2522-200000000000000025−25000000000000000000000000000000000000000
χ7188-8-8-44-4408-8-88000000-40044-400000000000000000000000000000000000000000000000000000000
χ7288-8-8-44-440-222-20000001−2525-1-1100000000000ζ4+ζ28−ζ44−ζ52−ζ68−ζ76+ζ92+ζ116−ζ4−ζ28+ζ44+ζ52+ζ68+ζ76−ζ92−ζ116−ζ4+ζ28+ζ44−ζ52−ζ68+ζ76+ζ92−ζ116ζ4−ζ28−ζ44+ζ52+ζ68−ζ76−ζ92+ζ1165−5000000000000000000000000000000000000000
χ7388-8-8-44-440-222-20000001−2525-1-1100000000000−ζ4−ζ28+ζ44+ζ52+ζ68+ζ76−ζ92−ζ116ζ4+ζ28−ζ44−ζ52−ζ68−ζ76+ζ92+ζ116ζ4−ζ28−ζ44+ζ52+ζ68−ζ76−ζ92+ζ116−ζ4+ζ28+ζ44−ζ52−ζ68+ζ76+ζ92−ζ1165−5000000000000000000000000000000000000000
χ7488-8-8-44-440-222-2000000125−25-1-1100000000000−ζ4+ζ28+ζ44−ζ52−ζ68+ζ76+ζ92−ζ116ζ4−ζ28−ζ44+ζ52+ζ68−ζ76−ζ92+ζ116−ζ4−ζ28+ζ44+ζ52+ζ68+ζ76−ζ92−ζ116ζ4+ζ28−ζ44−ζ52−ζ68−ζ76+ζ92+ζ116−55000000000000000000000000000000000000000
χ7588-8-8-44-440-222-2000000125−25-1-1100000000000ζ4−ζ28−ζ44+ζ52+ζ68−ζ76−ζ92+ζ116−ζ4+ζ28+ζ44−ζ52−ζ68+ζ76+ζ92−ζ116ζ4+ζ28−ζ44−ζ52−ζ68−ζ76+ζ92+ζ116−ζ4−ζ28+ζ44+ζ52+ζ68+ζ76−ζ92−ζ116−55000000000000000000000000000000000000000
χ768-88-88-8-880-2-222008i−8i00-200-22200000000000000000000000000000000−2i2i0000000000000000000000
χ778-88-88-8-880-2-22200−8i8i00-200-222000000000000000000000000000000002i−2i0000000000000000000000
χ788-8-8888-8-80-22-228i−8i0000-2002-22000000000000000000000000000000−2i2i000000000000000000000000
χ798-8-8888-8-80-22-22−8i8i0000-2002-220000000000000000000000000000002i−2i000000000000000000000000
χ8016-1616-16-888-80-4-4440000002002-2-200000000000000000000000000000000000000000000000000000000
χ8116-16-1616-8-8880-44-44000000200-22-200000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.