Finite Group Databasebeta

← Group #14278274

Character table — Group #14278274

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size11112222224444444444888888888888888888888882020202020202020242424242424242424244040404040404040404040404040120120120120120120
order12222236665661010101010101041212152020202030303030303030606060606060606022446666442020202020202020444412121212121212121212448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111ii−i−i-1-1iiii−i−i−i−i-1-1ii−i−i
χ61111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111−i−iii-1-1−i−i−i−iiiii-1-1−i−iii
χ71111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i11−i−iii
χ81111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii11ii−i−i
χ922222222222222222222-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-222-2-2222200000000000000-2-200000000000000
χ1022222222222222222222-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2000000000000002200000000000000
χ11222222-1-1-1-12-1-122222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-100000000002222-1-1-1-1-1-1-1-1-1-1000000
χ12222222-1-1-1-12-1-122222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-10000000000-2-2-2-2-1-111111111000000
χ13222222-1-1-1-12-1-122222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111100000000002i2i−2i−2i11−i−i−i−iiiii000000
χ14222222-1-1-1-12-1-122222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211110000000000−2i−2i2i2i11iiii−i−i−i−i000000
χ15222222-1-1-1-12-1-12222222-211-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-1-1-1-10000000000000011−i3−i3i3i3−i3−i3i3i3000000
χ16222222-1-1-1-12-1-12222222-211-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-1-1-1-10000000000000011i3i3−i3−i3i3i3−i3−i3000000
χ17222222-1-1-1-12-1-12222222-211-1-2-2-2-2-1-1-1-1-1-1-111111111-2-222111100000000000000-1-133−3−3−3−333000000
χ18222222-1-1-1-12-1-12222222-211-1-2-2-2-2-1-1-1-1-1-1-111111111-2-222111100000000000000-1-1−3−33333−3−3000000
χ1922-2-22-222-2-222-2222-2-2-2-200020000222-2-2-2-2000000002-20022-2-2000000000000000000000000002−22−2
χ2022-2-22-222-2-222-2222-2-2-2-200020000222-2-2-2-2000000002-20022-2-200000000000000000000000000−22−22
χ2122-2-22-222-2-222-2222-2-2-2-200020000222-2-2-2-200000000-2200-2-22200000000000000000000000000−i2i2i2−i2
χ2222-2-22-222-2-222-2222-2-2-2-200020000222-2-2-2-200000000-2200-2-22200000000000000000000000000i2−i2−i2i2
χ2322-2-2-2222-2-22-222-2-2-2-222000200002-2-222-2-200000000002i−2i000000000000001+i−1−i1−i−1+i2i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000
χ2422-2-2-2222-2-22-222-2-2-2-222000200002-2-222-2-200000000002i−2i00000000000000−1−i1+i−1+i1−i2i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000
χ2522-2-2-2222-2-22-222-2-2-2-222000200002-2-222-2-20000000000−2i2i000000000000001−i−1+i1+i−1−i−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000
χ2622-2-2-2222-2-22-222-2-2-2-222000200002-2-222-2-20000000000−2i2i00000000000000−1+i1−i−1−i1+i−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000
χ2722-2-2-22-1-11121-12-2-2-2-22203−3-10000-111-1-1113333−3−3−3−3002i−2i−i3i3−i3i300000000001+i−1−i1−i−1+i−ii−ζ22+ζ44−ζ46+ζ68+ζ92−ζ94+ζ116−ζ118ζ22−ζ44+ζ46−ζ68−ζ92+ζ94−ζ116+ζ118ζ4−ζ14+ζ28−ζ38+ζ52−ζ62+ζ76−ζ86−ζ4+ζ14−ζ28+ζ38−ζ52+ζ62−ζ76+ζ86ζ22+ζ44+ζ46+ζ68+ζ92+ζ94+ζ116+ζ118−ζ22−ζ44−ζ46−ζ68−ζ92−ζ94−ζ116−ζ118ζ4+ζ14+ζ28+ζ38+ζ52+ζ62+ζ76+ζ86−ζ4−ζ14−ζ28−ζ38−ζ52−ζ62−ζ76−ζ86000000
χ2822-2-2-22-1-11121-12-2-2-2-22203−3-10000-111-1-1113333−3−3−3−3002i−2i−i3i3−i3i30000000000−1−i1+i−1+i1−i−iiζ22−ζ44+ζ46−ζ68−ζ92+ζ94−ζ116+ζ118−ζ22+ζ44−ζ46+ζ68+ζ92−ζ94+ζ116−ζ118−ζ4+ζ14−ζ28+ζ38−ζ52+ζ62−ζ76+ζ86ζ4−ζ14+ζ28−ζ38+ζ52−ζ62+ζ76−ζ86−ζ22−ζ44−ζ46−ζ68−ζ92−ζ94−ζ116−ζ118ζ22+ζ44+ζ46+ζ68+ζ92+ζ94+ζ116+ζ118−ζ4−ζ14−ζ28−ζ38−ζ52−ζ62−ζ76−ζ86ζ4+ζ14+ζ28+ζ38+ζ52+ζ62+ζ76+ζ86000000
χ2922-2-2-22-1-11121-12-2-2-2-22203−3-10000-111-1-1113333−3−3−3−300−2i2ii3−i3i3−i300000000001−i−1+i1+i−1−ii−iζ4+ζ14+ζ28+ζ38+ζ52+ζ62+ζ76+ζ86−ζ4−ζ14−ζ28−ζ38−ζ52−ζ62−ζ76−ζ86ζ22+ζ44+ζ46+ζ68+ζ92+ζ94+ζ116+ζ118−ζ22−ζ44−ζ46−ζ68−ζ92−ζ94−ζ116−ζ118ζ4−ζ14+ζ28−ζ38+ζ52−ζ62+ζ76−ζ86−ζ4+ζ14−ζ28+ζ38−ζ52+ζ62−ζ76+ζ86−ζ22+ζ44−ζ46+ζ68+ζ92−ζ94+ζ116−ζ118ζ22−ζ44+ζ46−ζ68−ζ92+ζ94−ζ116+ζ118000000
χ3022-2-2-22-1-11121-12-2-2-2-22203−3-10000-111-1-1113333−3−3−3−300−2i2ii3−i3i3−i30000000000−1+i1−i−1−i1+ii−i−ζ4−ζ14−ζ28−ζ38−ζ52−ζ62−ζ76−ζ86ζ4+ζ14+ζ28+ζ38+ζ52+ζ62+ζ76+ζ86−ζ22−ζ44−ζ46−ζ68−ζ92−ζ94−ζ116−ζ118ζ22+ζ44+ζ46+ζ68+ζ92+ζ94+ζ116+ζ118−ζ4+ζ14−ζ28+ζ38−ζ52+ζ62−ζ76+ζ86ζ4−ζ14+ζ28−ζ38+ζ52−ζ62+ζ76−ζ86ζ22−ζ44+ζ46−ζ68−ζ92+ζ94−ζ116+ζ118−ζ22+ζ44−ζ46+ζ68+ζ92−ζ94+ζ116−ζ118000000
χ3122-2-2-22-1-11121-12-2-2-2-2220−33-10000-111-1-111−3−3−3−33333002i−2ii3−i3i3−i300000000001+i−1−i1−i−1+i−iiζ4−ζ14+ζ28−ζ38+ζ52−ζ62+ζ76−ζ86−ζ4+ζ14−ζ28+ζ38−ζ52+ζ62−ζ76+ζ86−ζ22+ζ44−ζ46+ζ68+ζ92−ζ94+ζ116−ζ118ζ22−ζ44+ζ46−ζ68−ζ92+ζ94−ζ116+ζ118ζ4+ζ14+ζ28+ζ38+ζ52+ζ62+ζ76+ζ86−ζ4−ζ14−ζ28−ζ38−ζ52−ζ62−ζ76−ζ86ζ22+ζ44+ζ46+ζ68+ζ92+ζ94+ζ116+ζ118−ζ22−ζ44−ζ46−ζ68−ζ92−ζ94−ζ116−ζ118000000
χ3222-2-2-22-1-11121-12-2-2-2-2220−33-10000-111-1-111−3−3−3−33333002i−2ii3−i3i3−i30000000000−1−i1+i−1+i1−i−ii−ζ4+ζ14−ζ28+ζ38−ζ52+ζ62−ζ76+ζ86ζ4−ζ14+ζ28−ζ38+ζ52−ζ62+ζ76−ζ86ζ22−ζ44+ζ46−ζ68−ζ92+ζ94−ζ116+ζ118−ζ22+ζ44−ζ46+ζ68+ζ92−ζ94+ζ116−ζ118−ζ4−ζ14−ζ28−ζ38−ζ52−ζ62−ζ76−ζ86ζ4+ζ14+ζ28+ζ38+ζ52+ζ62+ζ76+ζ86−ζ22−ζ44−ζ46−ζ68−ζ92−ζ94−ζ116−ζ118ζ22+ζ44+ζ46+ζ68+ζ92+ζ94+ζ116+ζ118000000
χ3322-2-2-22-1-11121-12-2-2-2-2220−33-10000-111-1-111−3−3−3−3333300−2i2i−i3i3−i3i300000000001−i−1+i1+i−1−ii−iζ22+ζ44+ζ46+ζ68+ζ92+ζ94+ζ116+ζ118−ζ22−ζ44−ζ46−ζ68−ζ92−ζ94−ζ116−ζ118ζ4+ζ14+ζ28+ζ38+ζ52+ζ62+ζ76+ζ86−ζ4−ζ14−ζ28−ζ38−ζ52−ζ62−ζ76−ζ86−ζ22+ζ44−ζ46+ζ68+ζ92−ζ94+ζ116−ζ118ζ22−ζ44+ζ46−ζ68−ζ92+ζ94−ζ116+ζ118ζ4−ζ14+ζ28−ζ38+ζ52−ζ62+ζ76−ζ86−ζ4+ζ14−ζ28+ζ38−ζ52+ζ62−ζ76+ζ86000000
χ3422-2-2-22-1-11121-12-2-2-2-2220−33-10000-111-1-111−3−3−3−3333300−2i2i−i3i3−i3i30000000000−1+i1−i−1−i1+ii−i−ζ22−ζ44−ζ46−ζ68−ζ92−ζ94−ζ116−ζ118ζ22+ζ44+ζ46+ζ68+ζ92+ζ94+ζ116+ζ118−ζ4−ζ14−ζ28−ζ38−ζ52−ζ62−ζ76−ζ86ζ4+ζ14+ζ28+ζ38+ζ52+ζ62+ζ76+ζ86ζ22−ζ44+ζ46−ζ68−ζ92+ζ94−ζ116+ζ118−ζ22+ζ44−ζ46+ζ68+ζ92−ζ94+ζ116−ζ118−ζ4+ζ14−ζ28+ζ38−ζ52+ζ62−ζ76+ζ86ζ4−ζ14+ζ28−ζ38+ζ52−ζ62+ζ76−ζ86000000
χ354444444444-144-1-1-1-1-1-1-1444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000044-1-1-1-1-1-1-1-100000000000000000000
χ364444444444-144-1-1-1-1-1-1-1444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-4-41111111100000000000000000000
χ374444444444-144-1-1-1-1-1-1-1-4-4-4-11111-1-1-1-1-1-1-1111111110000000000−5−5−5−5555500000000000000000000
χ384444444444-144-1-1-1-1-1-1-1-4-4-4-11111-1-1-1-1-1-1-11111111100000000005555−5−5−5−500000000000000000000
χ394444-4-444444-4-44-4-444-4-4000400004-4-4-4-4440000000000000000000000000000000000000000000000
χ404444-4-44444-1-4-4-111-1-111000-1−5−555-11111-1-1−5−555−5−5550000000000ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ11800000000000000000000
χ414444-4-44444-1-4-4-111-1-111000-1−5−555-11111-1-1−5−555−5−5550000000000−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ11800000000000000000000
χ424444-4-44444-1-4-4-111-1-111000-155−5−5-11111-1-155−5−555−5−50000000000ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ11800000000000000000000
χ434444-4-44444-1-4-4-111-1-111000-155−5−5-11111-1-155−5−555−5−50000000000−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ11800000000000000000000
χ444444-4-4-2-2-2-24224-4-444-4-4000-20000-22222-2-2000000000000−2i32i32i3−2i3000000000000000000000000000000
χ454444-4-4-2-2-2-24224-4-444-4-4000-20000-22222-2-20000000000002i3−2i3−2i32i3000000000000000000000000000000
χ4644-4-44-4-2-2224-22444-4-4-4-4000-20000-2-2-22222000000004-400-2-222000000000000000000000000000000
χ4744-4-44-4-2-2224-22444-4-4-4-4000-20000-2-2-2222200000000-440022-2-2000000000000000000000000000000
χ484-44-4004-4-44400-4004-40000040000-400004-400000000000000002i−2i2i−2i2i−2i2i−2i2i−2i00000000000000000000
χ494-44-4004-4-44400-4004-40000040000-400004-40000000000000000−2i2i−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ504-44-4004-4-44-1001−55-11−55000-1ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ1181−55−55-11ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118000000002i−2i−ζ14−ζ28−ζ46+ζ52−ζ68−ζ86+ζ92−ζ94ζ14+ζ28+ζ46−ζ52+ζ68+ζ86−ζ92+ζ94−ζ14+ζ28−ζ46−ζ52+ζ68−ζ86−ζ92−ζ94ζ14−ζ28+ζ46+ζ52−ζ68+ζ86+ζ92+ζ94ζ4−ζ22−ζ38+ζ44−ζ62−ζ76−ζ116−ζ118−ζ4+ζ22+ζ38−ζ44+ζ62+ζ76+ζ116+ζ118−ζ4−ζ22−ζ38−ζ44−ζ62+ζ76+ζ116−ζ118ζ4+ζ22+ζ38+ζ44+ζ62−ζ76−ζ116+ζ11800000000000000000000
χ514-44-4004-4-44-1001−55-11−55000-1ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ1181−55−55-11ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ118ζ14+ζ22−ζ38−ζ46+ζ62−ζ86+ζ94−ζ118−ζ14−ζ22+ζ38+ζ46−ζ62+ζ86−ζ94+ζ118ζ14−ζ22+ζ38−ζ46−ζ62−ζ86+ζ94+ζ118−ζ14+ζ22−ζ38+ζ46+ζ62+ζ86−ζ94−ζ11800000000−2i2iζ14+ζ28+ζ46−ζ52+ζ68+ζ86−ζ92+ζ94−ζ14−ζ28−ζ46+ζ52−ζ68−ζ86+ζ92−ζ94ζ14−ζ28+ζ46+ζ52−ζ68+ζ86+ζ92+ζ94−ζ14+ζ28−ζ46−ζ52+ζ68−ζ86−ζ92−ζ94−ζ4+ζ22+ζ38−ζ44+ζ62+ζ76+ζ116+ζ118ζ4−ζ22−ζ38+ζ44−ζ62−ζ76−ζ116−ζ118ζ4+ζ22+ζ38+ζ44+ζ62−ζ76−ζ116+ζ118−ζ4−ζ22−ζ38−ζ44−ζ62+ζ76+ζ116−ζ11800000000000000000000
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Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.