Finite Group Databasebeta

← Group #14512486

Character table — Group #14512486

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111224444444455556688888888101012161616161616161616161616161616162424242430304040404040404040606060606060606060120120120120
order1222225101010101010104444443666666644415153030303030303030303030303030202020204412121212121212124888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111-1-1-1-11111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ411111111111111-1-1-1-11111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ51111-1-1111-1-1-1-11111111111-1-1-1-11-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-111-1-111-1-11-11-1
χ61111-1-1111-1-1-1-11111111111-1-1-1-11-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-111-1-111-11-11
χ71111-1-1111-1-1-1-11-1-1-1-111111-1-1-1-1111-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111ii−i−i−i−iiii−i−ii
χ81111-1-1111-1-1-1-11-1-1-1-111111-1-1-1-1111-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111−i−iiiii−i−i−iii−i
χ922222222222222222222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-12000000000000
χ1022222222222222-2-2-2-222-1-1-1-1-1-1-1-1-2-22-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-211111111-2000000000000
χ112222-2-2222-2-2-2-22222222-1-1-11111-1-2-2-2-1-1-1-1-1-1-1-11111111122-2-222-1-1-1-11111-2000000000000
χ122222-2-2222-2-2-2-22-2-2-2-222-1-1-11111-122-2-1-1-1-1-1-1-1-11111111122-2-2-2-21111-1-1-1-12000000000000
χ1322-2-2002-2-2000022i−2i2i−2i2-222-20000-20002222-2-2-2-2000000002-2002i−2i2i2i−2i−2i00000000000000000
χ1422-2-2002-2-2000022i−2i2i−2i2-2-1-11−i3−i3i3i31000-1-1-1-11111−i3−i3−i3−i3i3i3i3i32-2002i−2i−i−iii33−3−30000000000000
χ1522-2-2002-2-2000022i−2i2i−2i2-2-1-11i3i3−i3−i31000-1-1-1-11111i3i3i3i3−i3−i3−i3−i32-2002i−2i−i−iii−3−3330000000000000
χ1622-2-2002-2-200002−2i2i−2i2i2-222-20000-20002222-2-2-2-2000000002-200−2i2i−2i−2i2i2i00000000000000000
χ1722-2-2002-2-200002−2i2i−2i2i2-2-1-11−i3−i3i3i31000-1-1-1-11111−i3−i3−i3−i3i3i3i3i32-200−2i2iii−i−i−3−3330000000000000
χ1822-2-2002-2-200002−2i2i−2i2i2-2-1-11i3i3−i3−i31000-1-1-1-11111i3i3i3i3−i3−i3−i3−i32-200−2i2iii−i−i33−3−30000000000000
χ192-22-22-222-222-2-2-222-2-200-1111-11-1-12-20-1-11111-1-111-1-111-1-10000001-11-11-11-102−22−22−22−20000
χ202-22-22-222-222-2-2-222-2-200-1111-11-1-12-20-1-11111-1-111-1-111-1-10000001-11-11-11-10−22−22−22−220000
χ212-22-22-222-222-2-2-2-2-22200-1111-11-1-1-220-1-11111-1-111-1-111-1-1000000-11-11-11-110−i2i2−i2i2i2−i2i2−i20000
χ222-22-22-222-222-2-2-2-2-22200-1111-11-1-1-220-1-11111-1-111-1-111-1-1000000-11-11-11-110i2−i2i2−i2−i2i2−i2i20000
χ232-22-2-2222-2-2-222-222-2-200-111-11-11-1-220-1-11111-1-1-1-111-1-1110000001-11-1-11-1102−2−222−2−220000
χ242-22-2-2222-2-2-222-222-2-200-111-11-11-1-220-1-11111-1-1-1-111-1-1110000001-11-1-11-110−222−2−222−20000
χ252-22-2-2222-2-2-222-2-2-22200-111-11-11-12-20-1-11111-1-1-1-111-1-111000000-11-111-11-10−i2i2i2−i2i2−i2−i2i20000
χ262-22-2-2222-2-2-222-2-2-22200-111-11-11-12-20-1-11111-1-1-1-111-1-111000000-11-111-11-10i2−i2−i2i2−i2i2i2−i20000
χ27333333333333333333-1-10000000033-10000000000000000-1-1-1-1-1-100000000-111111111-1-1-1-1
χ28333333333333333333-1-10000000033-10000000000000000-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-11111
χ2933333333333333-3-3-3-3-1-100000000-3-3-10000000000000000-1-1-1-111000000001iiii−i−i−i−i−i−iii
χ3033333333333333-3-3-3-3-1-100000000-3-3-10000000000000000-1-1-1-111000000001−i−i−i−iiiiiii−i−i
χ313333-3-3333-3-3-3-333333-1-100000000-3-310000000000000000-1-111-1-100000000111-1-111-1-1-11-11
χ323333-3-3333-3-3-3-333333-1-100000000-3-310000000000000000-1-111-1-1000000001-1-111-1-1111-11-1
χ333333-3-3333-3-3-3-33-3-3-3-3-1-1000000003310000000000000000-1-1111100000000-1ii−i−i−i−iii−iii−i
χ343333-3-3333-3-3-3-33-3-3-3-3-1-1000000003310000000000000000-1-1111100000000-1−i−iiiii−i−ii−i−ii
χ35444444-1-1-1-1-1-1-1-100004444444444004-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000
χ36444444-1-1-1-1-1-1-1-1000044-2-2-2-2-2-2-2-20041−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152-1-1-1-100000000000000000000000
χ37444444-1-1-1-1-1-1-1-1000044-2-2-2-2-2-2-2-20041+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152-1-1-1-100000000000000000000000
χ384444-4-4-1-1-11111-1000044444-4-4-4-4400-4-1-1-1-1-1-1-1-111111111-1-11100000000000000000000000
χ394444-4-4-1-1-11111-1000044-2-2-22222-200-41−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152-1-11100000000000000000000000
χ404444-4-4-1-1-11111-1000044-2-2-22222-200-41+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152-1-11100000000000000000000000
χ4144-4-400-111−55−55-100004-444-40000-4000-1-1-1-11111−55−555−55−5-11−5500000000000000000000000
χ4244-4-400-111−55−55-100004-4-2-22−2i3−2i32i32i320001+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116-11−5500000000000000000000000
χ4344-4-400-111−55−55-100004-4-2-222i32i3−2i3−2i320001−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92-11−5500000000000000000000000
χ4444-4-400-1115−55−5-100004-444-40000-4000-1-1-1-111115−55−5−55−55-115−500000000000000000000000
χ4544-4-400-1115−55−5-100004-4-2-22−2i3−2i32i32i320001−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92-115−500000000000000000000000
χ4644-4-400-1115−55−5-100004-4-2-222i32i3−2i3−2i320001+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116-115−500000000000000000000000
χ474-44-44-444-444-4-4-444-4-4001-1-1-11-1114-4011-1-1-1-111-1-111-1-111000000-11-11-11-110000000000000
χ484-44-44-444-444-4-4-4-4-444001-1-1-11-111-44011-1-1-1-111-1-111-1-1110000001-11-11-11-10000000000000
χ494-44-4-4444-4-4-444-444-4-4001-1-11-11-11-44011-1-1-1-11111-1-111-1-1000000-11-111-11-10000000000000
χ504-44-4-4444-4-4-444-4-4-444001-1-11-11-114-4011-1-1-1-11111-1-111-1-10000001-11-1-11-110000000000000
χ514-4-44004-440000-44i−4i−4i4i001-11−i3i3i3−i3-100011-1-111-1-1−i3−i3i3i3i3i3−i3−i3000000−iii−i3−3−330000000000000
χ524-4-44004-440000-44i−4i−4i4i001-11i3−i3−i3i3-100011-1-111-1-1i3i3−i3−i3−i3−i3i3i3000000−iii−i−333−30000000000000
χ534-4-44004-440000-44i−4i−4i4i00-22-200002000-2-222-2-222000000000000002i−2i−2i2i00000000000000000
χ544-4-44004-440000-4−4i4i4i−4i001-11−i3i3i3−i3-100011-1-111-1-1−i3−i3i3i3i3i3−i3−i3000000i−i−ii−333−30000000000000
χ554-4-44004-440000-4−4i4i4i−4i001-11i3−i3−i3i3-100011-1-111-1-1i3i3−i3−i3−i3−i3i3i3000000i−i−ii3−3−330000000000000
χ564-4-44004-440000-4−4i4i4i−4i00-22-200002000-2-222-2-22200000000000000−2i2i2i−2i00000000000000000
χ5766-6-6006-6-6000066i−6i6i−6i-22000000000000000000000000000-2200−2i2i000000000000000000000
χ5866-6-6006-6-600006−6i6i−6i6i-22000000000000000000000000000-22002i−2i000000000000000000000
χ598-88-88-8-2-22-2-22220000002-2-2-22-222000−1−i152−1+i1521+i1521−i1521+i1521−i152−1−i152−1+i1521+i1521−i152−1−i152−1+i1521+i1521−i152−1−i152−1+i152000000000000000000000000000
χ608-88-88-8-2-22-2-22220000002-2-2-22-222000−1+i152−1−i1521−i1521+i1521−i1521+i152−1+i152−1−i1521−i1521+i152−1+i152−1−i1521−i1521+i152−1+i152−1−i152000000000000000000000000000
χ618-88-88-8-2-22-2-2222000000-4444-44-4-400011-1-1-1-111-1-111-1-111000000000000000000000000000
χ628-88-8-88-2-2222-2-220000002-2-22-22-22000−1−i152−1+i1521+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i1521+i1521−i152−1−i152−1+i1521+i1521−i152000000000000000000000000000
χ638-88-8-88-2-2222-2-220000002-2-22-22-22000−1+i152−1−i1521−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i1521−i1521+i152−1+i152−1−i1521−i1521+i152000000000000000000000000000
χ648-88-8-88-2-2222-2-22000000-444-44-44-400011-1-1-1-11111-1-111-1-1000000000000000000000000000
χ658-8-8800-22-2−252525−2520000002-22−2i32i32i3−2i3-2000−1−i152−1+i1521+i1521−i152−1−i152−1+i1521+i1521−i152ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116000000000000000000000000000
χ668-8-8800-22-2−252525−2520000002-222i3−2i3−2i32i3-2000−1+i152−1−i1521−i1521+i152−1+i152−1−i1521−i1521+i152−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92000000000000000000000000000
χ678-8-8800-22-2−252525−252000000-44-40000400011-1-111-1-1−555−55−5−55000000000000000000000000000
χ688-8-8800-22-225−25−252520000002-22−2i32i32i3−2i3-2000−1+i152−1−i1521−i1521+i152−1+i152−1−i1521−i1521+i152ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ4+ζ68−ζ76+ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92000000000000000000000000000
χ698-8-8800-22-225−25−252520000002-222i3−2i3−2i32i3-2000−1−i152−1+i1521+i1521−i152−1−i152−1+i1521+i1521−i152−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ28−ζ44+ζ52−ζ116−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116000000000000000000000000000
χ708-8-8800-22-225−25−25252000000-44-40000400011-1-111-1-15−5−55−555−5000000000000000000000000000
χ71121212121212-3-3-3-3-3-3-3-30000-4-40000000000-40000000000000000111100000000000000000000000
χ7212121212-12-12-3-3-33333-30000-4-400000000004000000000000000011-1-100000000000000000000000
χ731212-12-1200-333−3535−3535-30000-440000000000000000000000000001-15−500000000000000000000000
χ741212-12-1200-33335−3535−35-30000-440000000000000000000000000001-1−5500000000000000000000000

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