Finite Group Databasebeta

← Group #14284692

Character table — Group #14284692

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111122224444466668888888810101010151515151616161616161616162020202020202020202020202424242424404040404040404040484860606060606060606080120
order12223666451010102244412152020303030444444441220206060606060608888888812121212410102020424242424242424242020488888888124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111
χ31111111111111111111111111-1-1-1-1-1-1-1-1111111111ii−i−iii−i−i-1-1-1-111111-1iiii−i−i−i−i11-1ii−i−iii−i−i-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1111111111−i−iii−i−iii-1-1-1-111111-1−i−i−i−iiiii11-1−i−iii−i−iii-1-1
χ511111111111111111-1111111111111111-1-1-111-1-1-1-11111-1-1-1-11111-11111-111-1-111-1-1-1-111111-1-1-1-1-1-1
χ611111111111111111-1111111111111111-1-1-111-1-1-1-1-1-1-1-111111111-11111-1-1-111-1-111-1-11-1-1-1-11111-1-1
χ711111111111111111-11111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i−i−iii-1-1-1-1-111111ii−i−i−i−iii-1-1-1ii−i−i−i−iii11
χ811111111111111111-11111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1−i−iiiii−i−i-1-1-1-1-111111−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
χ101111111111111-1-1-1-1111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1111111111-1
χ111111111111111-1-1-1-111111111-1-1-1-11111111111111ii−i−iii−i−i-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-11−i−iii−i−iii-11
χ121111111111111-1-1-1-111111111-1-1-1-11111111111111−i−iii−i−iii-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-11ii−i−iii−i−i-11
χ131111111111111-1-1-1-1-111111111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111-1-1-1-1-111-1-111-1-111-1-1-1-1-11111-11
χ141111111111111-1-1-1-1-111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-111-1-11111-11111-1-1-1-1-11
χ151111111111111-1-1-1-1-11111111-1-1-1-11111-1-1-111-1-1-1-1ii−i−i−i−iii-1-1-1-11-1-1-1-11ii−i−i−i−iii111−i−iiiii−i−i1-1
χ161111111111111-1-1-1-1-11111111-1-1-1-11111-1-1-111-1-1-1-1−i−iiiii−i−i-1-1-1-11-1-1-1-11−i−iiiii−i−i111ii−i−i−i−iii1-1
χ1722222222-2222222-2-20-22-2-22222-2-222222000-2-20000000000002-22-2022-2-200000000000-20000000000
χ1822222222-2222222-2-20-22-2-2222-222-2-2-2-2-2000-2-2000000000000-22-22022-2-20000000000020000000000
χ1922222222-22222-2-2220-22-2-22222-2-22-2-2-2-2000-2-20000000000002-22-20-2-2220000000000020000000000
χ2022222222-22222-2-2220-22-2-2222-222-22222000-2-2000000000000-22-220-2-22200000000000-20000000000
χ212222-1-1-1-12222200002-1-122-1-1-122220000-122-1-1-1-1-1-122222222-1-1-1-1000002-1-1-1-1-1-1-1-100000000000-10
χ222222-1-1-1-12222200002-1-122-1-1-122220000-122-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-10000021111111100000000000-10
χ232222-1-1-1-12222200002-1-122-1-1-1-2-2-2-20000-122-1-1-1-1-1-12i2i−2i−2i2i2i−2i−2i111100000-2−i−i−i−iiiii0000000000010
χ242222-1-1-1-12222200002-1-122-1-1-1-2-2-2-20000-122-1-1-1-1-1-1−2i−2i2i2i−2i−2i2i2i111100000-2iiii−i−i−i−i0000000000010
χ252222-1-1-1-1222220000-2-1-122-1-1-1222200001-2-2-1-111112222-2-2-2-2-1-1-1-100000-2-1-111-1-1110000000000010
χ262222-1-1-1-1222220000-2-1-122-1-1-1222200001-2-2-1-11111-2-2-2-22222-1-1-1-100000-211-1-111-1-10000000000010
χ272222-1-1-1-1222220000-2-1-122-1-1-1-2-2-2-200001-2-2-1-111112i2i−2i−2i−2i−2i2i2i1111000002−i−iiiii−i−i00000000000-10
χ282222-1-1-1-1222220000-2-1-122-1-1-1-2-2-2-200001-2-2-1-11111−2i−2i2i2i2i2i−2i−2i1111000002ii−i−i−i−iii00000000000-10
χ292-22-222-2-2022-2-22-200002002-2-2200-222-2-20000000002−22−2000020-2002-20002−2002−2000002−22−2000000
χ302-22-222-2-2022-2-22-200002002-2-2200-222-2-2000000000−22−22000020-2002-2000−2200−2200000−22−22000000
χ312-22-222-2-2022-2-22-200002002-2-2-2002-2-222000000000−i2i2i2−i20000-202002-2000−i2i200i2−i200000−i2i2i2−i2000000
χ322-22-222-2-2022-2-22-200002002-2-2-2002-2-222000000000i2−i2−i2i20000-202002-2000i2−i200−i2i200000i2−i2−i2i2000000
χ332-22-222-2-2022-2-2-2200002002-2-2200-2-2-2220000000002−22−2000020-200-220002−2002−200000−22−22000000
χ342-22-222-2-2022-2-2-2200002002-2-2200-2-2-222000000000−22−22000020-200-22000−2200−22000002−22−2000000
χ352-22-222-2-2022-2-2-2200002002-2-2-200222-2-2000000000−i2i2i2−i20000-20200-22000−i2i200i2−i200000i2−i2−i2i2000000
χ362-22-222-2-2022-2-2-2200002002-2-2-200222-2-2000000000i2−i2−i2i20000-20200-22000i2−i200−i2i200000−i2i2i2−i2000000
χ372-2-222-22-202-22-2002i−2i00200-22-202-202i−2i2i−2i0000000000000−i2i2−i2i20-2020002i−2i000−i2i200−i2i200000002−22−200
χ382-2-222-22-202-22-2002i−2i00200-22-202-202i−2i2i−2i0000000000000i2−i2i2−i20-2020002i−2i000i2−i200i2−i20000000−22−2200
χ392-2-222-22-202-22-2002i−2i00200-22-20-220−2i2i−2i2i00000000000002−2−22020-20002i−2i0002−200−220000000i2−i2−i2i200
χ402-2-222-22-202-22-2002i−2i00200-22-20-220−2i2i−2i2i0000000000000−222−2020-20002i−2i000−22002−20000000−i2i2i2−i200
χ412-2-222-22-202-22-200−2i2i00200-22-202-20−2i2i−2i2i0000000000000−i2i2−i2i20-202000−2i2i000−i2i200−i2i20000000−22−2200
χ422-2-222-22-202-22-200−2i2i00200-22-202-20−2i2i−2i2i0000000000000i2−i2i2−i20-202000−2i2i000i2−i200i2−i200000002−22−200
χ432-2-222-22-202-22-200−2i2i00200-22-20-2202i−2i2i−2i00000000000002−2−22020-2000−2i2i0002−200−220000000−i2i2i2−i200
χ442-2-222-22-202-22-200−2i2i00200-22-20-2202i−2i2i−2i0000000000000−222−2020-2000−2i2i000−22002−20000000i2−i2−i2i200
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
χ46444444444-1-1-1-14444-44-1-1-1-1-1-100000000-411-1-11111000000000000-4-1-1-1-10000000001100000000000
χ47444444444-1-1-1-1-4-4-4-444-1-1-1-1-1-1000000004-1-1-1-1-1-1-1-1000000000000-411110000000001100000000000
χ48444444444-1-1-1-1-4-4-4-4-44-1-1-1-1-1-100000000-411-1-1111100000000000041111000000000-1-100000000000
χ4944444444-4-1-1-1-144-4-40-4-111-1-1-1000000000−5511−5−5550000000000000-1-111000000000−5500000000000
χ5044444444-4-1-1-1-144-4-40-4-111-1-1-10000000005−51155−5−50000000000000-1-1110000000005−500000000000
χ5144444444-4-1-1-1-1-4-4440-4-111-1-1-1000000000−5511−5−555000000000000011-1-10000000005−500000000000
χ5244444444-4-1-1-1-1-4-4440-4-111-1-1-10000000005−51155−5−5000000000000011-1-1000000000−5500000000000
χ534444-2-2-2-2-44444000002-2-4-4-2-2-24-4-44000000022000000000000-22-22000000000000000000000000000
χ544444-2-2-2-2-44444000002-2-4-4-2-2-2-444-40000000220000000000002-22-2000000000000000000000000000
χ5544-4-44-4-4404-4-44000000400-4-4400004i−4i−4i4i000000000000000000000000000000000000000000000000
χ5644-4-44-4-4404-4-44000000400-4-440000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ574-44-4-2-222044-4-4000000-200-222400-4000000000000022−2222−220000-2020000000−2200−22000000000000000
χ584-44-4-2-222044-4-4000000-200-222400-40000000000000−2222−22220000-20200000002−2002−2000000000000000
χ594-44-4-2-222044-4-4000000-200-222-40040000000000000−2i22i22i2−2i2000020-20000000i2−i200−i2i2000000000000000
χ604-44-4-2-222044-4-4000000-200-222-400400000000000002i2−2i2−2i22i2000020-20000000−i2i200i2−i2000000000000000
χ614-4-44-22-2204-44-4000000-2002-2204-4000000000000000000−2i22i2−2i22i2020-200000000i2−i200i2−i20000000000000
χ624-4-44-22-2204-44-4000000-2002-2204-40000000000000000002i2−2i22i2−2i2020-200000000−i2i200−i2i20000000000000
χ634-4-44-22-2204-44-4000000-2002-220-4400000000000000000022−22−22220-20200000000−22002−20000000000000
χ644-4-44-22-2204-44-4000000-2002-220-44000000000000000000−222222−220-202000000002−200−220000000000000
χ658888-4-4-4-48-2-2-2-200008-41-2-211100000000-4-2-2111111000000000000000000000000000000000000000
χ668888-4-4-4-48-2-2-2-20000-8-41-2-21110000000042211-1-1-1-1000000000000000000000000000000000000000
χ678888-4-4-4-4-8-2-2-2-2000004122111000000000−2525-1-155−5−5000000000000000000000000000000000000000
χ688888-4-4-4-4-8-2-2-2-200000412211100000000025−25-1-1−5−555000000000000000000000000000000000000000
χ6988-8-88-8-880-222-2000000-2−252522-200000000000−25250000000000000000000000000000000000000000000
χ7088-8-88-8-880-222-2000000-225−2522-20000000000025−250000000000000000000000000000000000000000000
χ7188-8-8-444-408-8-88000000-40044-400000000000000000000000000000000000000000000000000000000
χ7288-8-8-444-40-222-20000001−2525-1-11000000000005−5ζ4+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+ζ116000000000000000000000000000000000000000
χ7388-8-8-444-40-222-20000001−2525-1-11000000000005−5−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−ζ116000000000000000000000000000000000000000
χ7488-8-8-444-40-222-2000000125−25-1-1100000000000−55−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+ζ116000000000000000000000000000000000000000
χ7588-8-8-444-40-222-2000000125−25-1-1100000000000−55ζ4−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−ζ116000000000000000000000000000000000000000
χ768-88-888-8-80-2-2228-80000-200-222000000000000000000000000000000-22000000000000000000000000
χ778-88-888-8-80-2-222-880000-200-2220000000000000000000000000000002-2000000000000000000000000
χ788-8-888-88-80-22-22008i−8i00-2002-2200000000000000000000000000000000−2i2i0000000000000000000000
χ798-8-888-88-80-22-2200−8i8i00-2002-22000000000000000000000000000000002i−2i0000000000000000000000
χ8016-1616-16-8-8880-4-4440000002002-2-200000000000000000000000000000000000000000000000000000000
χ8116-16-1616-88-880-44-44000000200-22-200000000000000000000000000000000000000000000000000000000

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