Finite Group Databasebeta

← Group #14304917

Character table — Group #14304917

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222444444555588888888810101010101012121616161616161616202020202020202020202020202024242424244040404040404040404848606060606060120120120
order1222344666510101012124444412121520203030302212121212882020606060606060444466121212121212121244040404026688242424242020888888488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11-1-1
χ311111111111111111111111111111111111-1-11111111111111111111111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-111
χ511111111111111111111-1-1-111111111111111-1-111-1-1-1-111111111111111-11111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1
χ611111111111111111111-1-1-111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1111111-1-111-1-1-1-1-111
χ711111111111111111111-1-1-1111111111111-1-1-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111
χ811111111111111111111-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111111111-1-111111-1-1
χ91111111111111111-1-1-1-1111111111-1-1-1-1-1-11111111111ii−i−i-1-1iiii−i−i−i−i11111-1-1-1i−iii−i−i11-1-1ii−i−i-1i−i
χ101111111111111111-1-1-1-1111111111-1-1-1-1-1-11111111111−i−iii-1-1−i−i−i−iiiii11111-1-1-1−ii−i−iii11-1-1−i−iii-1−ii
χ111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111ii−i−i-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-1i−iii−i−i-1-111−i−iii1−ii
χ121111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111−i−iii-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1−ii−i−iii-1-111ii−i−i1i−i
χ131111111111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1ii−i−i-1-1iiii−i−i−i−i-11111111−ii−i−iii-1-1-1-1ii−i−i1−ii
χ141111111111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1−i−iii-1-1−i−i−i−iiiii-11111111i−iii−i−i-1-1-1-1−i−iii1i−i
χ151111111111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i-1-1iiii−i−i−i−i1-1-1-1-1111−ii−i−iii1111−i−iii-1i−i
χ161111111111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1−i−iii-1-1−i−i−i−iiiii1-1-1-1-1111i−iii−i−i1111ii−i−i-1−ii
χ1722222-2-22222222-2-222220002-2-2222-2-222220000-2-200000000-2-2000000000000000000000000002-22-2000
χ1822222-2-22222222-2-222220002-2-2222-2-222220000-2-200000000-2-200000000000000000000000000-22-22000
χ1922222-2-22222222-2-2-2-2-2-20002-2-222222-2-2-2-20000-2-20000000022000000000000000000000000002i−2i−2i2i000
χ2022222-2-22222222-2-2-2-2-2-20002-2-222222-2-2-2-20000-2-2000000002200000000000000000000000000−2i2i2i−2i000
χ212222-122-1-1-12222-1-122222-1-1-122-1-1-122-1-1-1-10022-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000002-1-122-1-1-1-100000000000
χ222222-122-1-1-12222-1-122222-1-1-122-1-1-122-1-1-1-10022-1-1-1-1-1-1-2-2-2-2-1-111111111000002-1-1-2-2111100000000000
χ232222-122-1-1-12222-1-12222-211-122-1-1-122-1-1-1-100-2-2-1-111112222-1-1-1-1-1-1-1-1-1-100000-211-2-2111100000000000
χ242222-122-1-1-12222-1-12222-211-122-1-1-122-1-1-1-100-2-2-1-11111-2-2-2-2-1-11111111100000-21122-1-1-1-100000000000
χ252222-122-1-1-12222-1-1-2-2-2-22-1-1-122-1-1-1-2-211110022-1-1-1-1-1-12i2i−2i−2i11−i−i−i−iiiii00000-2112i−2i−i−iii00000000000
χ262222-122-1-1-12222-1-1-2-2-2-22-1-1-122-1-1-1-2-211110022-1-1-1-1-1-1−2i−2i2i2i11iiii−i−i−i−i00000-211−2i2iii−i−i00000000000
χ272222-122-1-1-12222-1-1-2-2-2-2-211-122-1-1-1-2-2111100-2-2-1-111112i2i−2i−2i11−i−i−i−iiiii000002-1-1−2i2iii−i−i00000000000
χ282222-122-1-1-12222-1-1-2-2-2-2-211-122-1-1-1-2-2111100-2-2-1-11111−2i−2i2i2i11iiii−i−i−i−i000002-1-12i−2i−i−iii00000000000
χ292-22-222-2-2-222-22-22-222-2-200022-2-2-22-2222-2-22i−2i002-200000000-220000000002i2i−2i−2i000000000002i−2i0000000
χ302-22-222-2-2-222-22-22-222-2-200022-2-2-22-2222-2-2−2i2i002-200000000-22000000000−2i−2i2i2i00000000000−2i2i0000000
χ312-22-222-2-2-222-22-22-2-2-22200022-2-2-222-2-2-2222i−2i002-2000000002-20000000002i2i−2i−2i00000000000−2i2i0000000
χ322-22-222-2-2-222-22-22-2-2-22200022-2-2-222-2-2-222−2i2i002-2000000002-2000000000−2i−2i2i2i000000000002i−2i0000000
χ332-22-22-22-2-222-22-2-2222-2-20002-22-2-222-222-2-20000-2200002i−2i2i−2i2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000
χ342-22-22-22-2-222-22-2-2222-2-20002-22-2-222-222-2-20000-220000−2i2i−2i2i2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000
χ352-22-22-22-2-222-22-2-22-2-2220002-22-2-22-22-2-2220000-2200002-2-22-2222-2-2-2-2220000000000000000000000000
χ362-22-22-22-2-222-22-2-22-2-2220002-22-2-22-22-2-2220000-220000-222-2-22-2-22222-2-20000000000000000000000000
χ372-22-2-1-2211-12-22-21-122-2-20−i3i3-1-2211-12-2-1-11100001-1−i3−i3i3i32i−2i2i−2i-11−i−iii−i−iii000000−i3i3003−33−300000000000
χ382-22-2-1-2211-12-22-21-122-2-20−i3i3-1-2211-12-2-1-11100001-1−i3−i3i3i3−2i2i−2i2i-11ii−i−iii−i−i000000−i3i300−33−3300000000000
χ392-22-2-1-2211-12-22-21-122-2-20i3−i3-1-2211-12-2-1-11100001-1i3i3−i3−i32i−2i2i−2i-11−i−iii−i−iii000000i3−i300−33−3300000000000
χ402-22-2-1-2211-12-22-21-122-2-20i3−i3-1-2211-12-2-1-11100001-1i3i3−i3−i3−2i2i−2i2i-11ii−i−iii−i−i000000i3−i3003−33−300000000000
χ412-22-2-1-2211-12-22-21-1-2-2220−i3i3-1-2211-1-2211-1-100001-1−i3−i3i3i32-2-221-1-1-11111-1-1000000i3−i300−i3i3i3−i300000000000
χ422-22-2-1-2211-12-22-21-1-2-2220−i3i3-1-2211-1-2211-1-100001-1−i3−i3i3i3-222-21-111-1-1-1-111000000i3−i300i3−i3−i3i300000000000
χ432-22-2-1-2211-12-22-21-1-2-2220i3−i3-1-2211-1-2211-1-100001-1i3i3−i3−i32-2-221-1-1-11111-1-1000000−i3i300i3−i3−i3i300000000000
χ442-22-2-1-2211-12-22-21-1-2-2220i3−i3-1-2211-1-2211-1-100001-1i3i3−i3−i3-222-21-111-1-1-1-111000000−i3i300−i3i3i3−i300000000000
χ454444444444-1-1-1-1440000444-1-1-1-1-1-100000044-1-1-1-1-1-1-1-1000000000000004-1-1-1-1000000000-1-1000000000
χ464444444444-1-1-1-1440000444-1-1-1-1-1-1000000-4-4-1-1-1-1-1-1-1-100000000000000-4111100000000011000000000
χ474444444444-1-1-1-1440000-4-4-4-1-1-1-1-1-10000004411-1-1111100000000000000-4-1-1-1-100000000011000000000
χ484444444444-1-1-1-1440000-4-4-4-1-1-1-1-1-1000000-4-411-1-111110000000000000041111000000000-1-1000000000
χ494444-2-4-4-2-2-24444224444000-2-4-4-2-2-2-4-4-2-2-2-20000220000000022000000000000000000000000000000000
χ504444-2-4-4-2-2-2444422-4-4-4-4000-2-4-4-2-2-244222200002200000000-2-2000000000000000000000000000000000
χ5144-4-44004-4-44-4-44004i−4i4i−4i0004004-4-4004i−4i4i−4i0000000000000000000000000000000000000000000000000
χ5244-4-44004-4-44-4-4400−4i4i−4i4i0004004-4-400−4i4i−4i4i0000000000000000000000000000000000000000000000000
χ5344-4-4-200-2224-4-44004i−4i4i−4i000-200-22200−2i2i−2i2i0000000000000000−ζ4+ζ14−ζ22−ζ28+ζ38+ζ44−ζ46−ζ52+ζ62+ζ68−ζ76+ζ86+ζ92−ζ94+ζ116−ζ118ζ4−ζ14+ζ22+ζ28−ζ38−ζ44+ζ46+ζ52−ζ62−ζ68+ζ76−ζ86−ζ92+ζ94−ζ116+ζ118−ζ4+ζ14−ζ22−ζ28+ζ38+ζ44−ζ46−ζ52+ζ62+ζ68−ζ76+ζ86+ζ92−ζ94+ζ116−ζ118ζ4−ζ14+ζ22+ζ28−ζ38−ζ44+ζ46+ζ52−ζ62−ζ68+ζ76−ζ86−ζ92+ζ94−ζ116+ζ118−ζ4−ζ14+ζ22−ζ28−ζ38+ζ44+ζ46−ζ52−ζ62+ζ68−ζ76−ζ86+ζ92+ζ94+ζ116+ζ118ζ4+ζ14−ζ22+ζ28+ζ38−ζ44−ζ46+ζ52+ζ62−ζ68+ζ76+ζ86−ζ92−ζ94−ζ116−ζ118−ζ4−ζ14+ζ22−ζ28−ζ38+ζ44+ζ46−ζ52−ζ62+ζ68−ζ76−ζ86+ζ92+ζ94+ζ116+ζ118ζ4+ζ14−ζ22+ζ28+ζ38−ζ44−ζ46+ζ52+ζ62−ζ68+ζ76+ζ86−ζ92−ζ94−ζ116−ζ1180000000000000000000000000
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χ738888-4-8-8-4-4-4-2-2-2-24400000001221110000000000-1-1i15−i15−i15i15000000000000000000000000000000000000000
χ7488-8-88008-8-8-222-2000000000-200-2220000000000000000000000000000000i10−i10i10−i1000000000000000000000
χ7588-8-88008-8-8-222-2000000000-200-2220000000000000000000000000000000−i10i10−i10i1000000000000000000000
χ768-88-88-88-8-88-22-22-880000000-22-222-200000000002-20000000000000000000000000000000000000000000
χ778-88-8-48-844-4-22-22-4400000001-22-1-1100000000−25251-15−55−5000000000000000000000000000000000000000
χ788-88-8-48-844-4-22-22-4400000001-22-1-110000000025−251-1−55−55000000000000000000000000000000000000000
χ798-88-8-4-8844-4-22-224-400000−4i34i312-2-1-110000000000-11i3i3−i3−i3000000000000000000000000000000000000000
χ808-88-8-4-8844-4-22-224-4000004i3−4i312-2-1-110000000000-11−i3−i3i3i3000000000000000000000000000000000000000
χ818-8-88800-88-8-2-222000000000-2002-22000000000000000000000000000000010−10−101000000000000000000000
χ828-8-88800-88-8-2-222000000000-2002-220000000000000000000000000000000−101010−1000000000000000000000
χ831616-16-16-800-888-444-40000000002002-2-20000000000000000000000000000000000000000000000000000000
χ8416-16-1616-8008-88-4-444000000000200-22-20000000000000000000000000000000000000000000000000000000

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