Finite Group Databasebeta

← Group #14285031

Character table — Group #14285031

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111222222222222444444444444444444444444444448888888888888888888888888888888888888888881010101010102020202020202020204040404040406060606060606060120120120120
order12222234466612121212456610101012121515202020203030303030306060606060606060246610101010101012122020202020203030303030303030303030306060606060606060606060604444444121212121212121224661212888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ5111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-111111111-1-1-1-1
χ6111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−iii
χ8111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiii−i−i
χ91111-1-11-1-1111-1-1-1-111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-11-111-1-11111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-11-1-111ii−i−iii−i−ii−ii−i
χ101111-1-11-1-1111-1-1-1-111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-11-111-1-11111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-11-1-111−i−iii−i−iii−ii−ii
χ111111-1-11-1-1111-1-1-1-111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-11-111-1-11111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111-111-1-111-1-1-1-1111-1-11
χ121111-1-11-1-1111-1-1-1-111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-11-111-1-11111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111-111-1-1-1-11111-1-1-111-1
χ131111-1-11-1-1111-1-1-1-111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111111-1-1-1-11-111-1-1ii−i−iii−i−i−ii−ii
χ141111-1-11-1-1111-1-1-1-111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111111-1-1-1-11-111-1-1−i−iii−i−iiii−ii−i
χ151111-1-11-1-1111-1-1-1-111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-11111-11-1-11111-1-1-1-111-111-1
χ161111-1-11-1-1111-1-1-1-111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-11111-11-1-111-1-11111-1-11-1-11
χ172222222-2-2222-2-2-2-2-2222222-2-222-2-2-2-2222222-2-2-2-2-2-2-2-2000022000000-2-20000222200000000-2-2-2-200000000222-2-22-222-2-222-2-2000000000000000000
χ182222222-2-2222-2-2-2-2-2222222-2-222-2-2-2-2222222-2-2-2-2-2-2-2-2000022000000-2-20000222200000000-2-2-2-200000000-2-2-222-22-2-222-2-222000000000000000000
χ19222222-122-1-1-1-1-1-1-122-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1222222-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ20222222-122-1-1-1-1-1-1-122-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1222222-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-211111111-2-21111000000000000
χ21222222-122-1-1-1-1-1-1-122-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21122-2-2-2-21122-2-2-2-2-1-1-1-111111111-1-1-1-1111111112222222-1-1-1-1-1-1-1-1-2-21111000000000000
χ22222222-122-1-1-1-1-1-1-122-1-1222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21122-2-2-2-21122-2-2-2-2-1-1-1-111111111-1-1-1-111111111-2-2-2-2-2-2-21111111122-1-1-1-1000000000000
χ23222222-1-2-2-1-1-11111-22-1-122211-1-1-2-2-2-2-1-1-1-1-1-11111111100−i3i3220000−i3i3-2-20000-1-1-1-1−i3−i3−i3−i3i3i3i3i31111−i3−i3−i3−i3i3i3i3i3222-2-22-2-1-111-1-11100−i3i3−i3i3000000000000
χ24222222-1-2-2-1-1-11111-22-1-122211-1-1-2-2-2-2-1-1-1-1-1-11111111100−i3i3220000−i3i3-2-20000-1-1-1-1−i3−i3−i3−i3i3i3i3i31111−i3−i3−i3−i3i3i3i3i3-2-2-222-2211-1-111-1-100i3−i3i3−i3000000000000
χ25222222-1-2-2-1-1-11111-22-1-122211-1-1-2-2-2-2-1-1-1-1-1-11111111100i3−i3220000i3−i3-2-20000-1-1-1-1i3i3i3i3−i3−i3−i3−i31111i3i3i3i3−i3−i3−i3−i3222-2-22-2-1-111-1-11100i3−i3i3−i3000000000000
χ26222222-1-2-2-1-1-11111-22-1-122211-1-1-2-2-2-2-1-1-1-1-1-11111111100i3−i3220000i3−i3-2-20000-1-1-1-1i3i3i3i3−i3−i3−i3−i31111i3i3i3i3−i3−i3−i3−i3-2-2-222-2211-1-111-1-100−i3i3−i3i3000000000000
χ272222-2-22222222222-22-2-2222-2-2222222222222222222220000-2-2000000-2-20000-2-2-2-200000000-2-2-2-20000000022-222-2-222-2-2-2-222000000000000000000
χ282222-2-22222222222-22-2-2222-2-2222222222222222222220000-2-2000000-2-20000-2-2-2-200000000-2-2-2-200000000-2-22-2-222-2-22222-2-2000000000000000000
χ292222-2-2-122-1-1-1-1-1-1-1-221122211-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100−i3i3-2-20000i3−i3-2-200001111−i3−i3−i3−i3i3i3i3i31111i3i3i3i3−i3−i3−i3−i322-222-2-2-1-11111-1-100i3−i3−i3i3000000000000
χ302222-2-2-122-1-1-1-1-1-1-1-221122211-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100−i3i3-2-20000i3−i3-2-200001111−i3−i3−i3−i3i3i3i3i31111i3i3i3i3−i3−i3−i3−i3-2-22-2-22211-1-1-1-11100−i3i3i3−i3000000000000
χ312222-2-2-122-1-1-1-1-1-1-1-221122211-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100i3−i3-2-20000−i3i3-2-200001111i3i3i3i3−i3−i3−i3−i31111−i3−i3−i3−i3i3i3i3i322-222-2-2-1-11111-1-100−i3i3i3−i3000000000000
χ322222-2-2-122-1-1-1-1-1-1-1-221122211-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100i3−i3-2-20000−i3i3-2-200001111i3i3i3i3−i3−i3−i3−i31111−i3−i3−i3−i3i3i3i3i3-2-22-2-22211-1-1-1-11100i3−i3−i3i3000000000000
χ332222-2-2-1-2-2-1-1-111112211222-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111112-2-1-1-2-222221122-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-1-11111111122-2-2-2-22-1-1-1-11111-2211-1-1000000000000
χ342222-2-2-1-2-2-1-1-111112211222-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111112-2-1-1-2-222221122-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-1-111111111-2-22222-21111-1-1-1-12-2-1-111000000000000
χ352222-2-2-1-2-2-1-1-111112211222-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111-2211-2-2-2-2-2-2-1-1222222111111111111-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-22-1-1-1-111112-2-1-111000000000000
χ362222-2-2-1-2-2-1-1-111112211222-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111-2211-2-2-2-2-2-2-1-1222222111111111111-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-21111-1-1-1-1-2211-1-1000000000000
χ3722-2-20022i−2i2-2-22i2i−2i−2i02002-2-200222i2i−2i−2i22-2-2-2-22i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000002i−2i02-2002i−2i00002-20000002−2−i2i2−i2i22−20000
χ3822-2-20022i−2i2-2-22i2i−2i−2i02002-2-200222i2i−2i−2i22-2-2-2-22i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000002i−2i02-2002i−2i00002-2000000−22i2−i2i2−i2−220000
χ3922-2-20022i−2i2-2-22i2i−2i−2i02002-2-200222i2i−2i−2i22-2-2-2-22i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000−2i2i0-2200−2i2i0000-22000000−i2i2−222−2i2−i20000
χ4022-2-20022i−2i2-2-22i2i−2i−2i02002-2-200222i2i−2i−2i22-2-2-2-22i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000−2i2i0-2200−2i2i0000-22000000i2−i22−2−22−i2i20000
χ4122-2-2002−2i2i2-2-2−2i−2i2i2i02002-2-20022−2i−2i2i2i22-2-2-2-2−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000002i−2i0-22002i−2i0000-22000000−i2i22−2−22i2−i20000
χ4222-2-2002−2i2i2-2-2−2i−2i2i2i02002-2-20022−2i−2i2i2i22-2-2-2-2−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000002i−2i0-22002i−2i0000-22000000i2−i2−222−2−i2i20000
χ4322-2-2002−2i2i2-2-2−2i−2i2i2i02002-2-20022−2i−2i2i2i22-2-2-2-2−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000−2i2i02-200−2i2i00002-20000002−2i2−i2i2−i22−20000
χ4422-2-2002−2i2i2-2-2−2i−2i2i2i02002-2-20022−2i−2i2i2i22-2-2-2-2−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000−2i2i02-200−2i2i00002-2000000−22−i2i2−i2i2−220000
χ4544444444444444444-144-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-14444-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000
χ4644444444444444444-144-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-4-4-1-11111-4-4-1-11111-1-1-1-111111111-1-1-1-111111111000000000000000000000000000000000
χ474444444-4-4444-4-4-4-4-4-144-1-1-1-4-4-1-11111-1-1-1-1-1-1111111110000-1-1−5−5550011−5−555-1-1-1-1−5−555−5−5551111−5−555−5−555000000000000000000000000000000000
χ484444444-4-4444-4-4-4-4-4-144-1-1-1-4-4-1-11111-1-1-1-1-1-1111111110000-1-155−5−5001155−5−5-1-1-1-155−5−555−5−5111155−5−555−5−5000000000000000000000000000000000
χ49444444-244-2-2-2-2-2-2-24-1-2-2-1-1-1-2-21−i1521+i152-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i15244-2-2-1-1-1-1-1-1-2-2-1-1-1-1-1-11−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i152000000000000000000000000000000000
χ50444444-244-2-2-2-2-2-2-24-1-2-2-1-1-1-2-21−i1521+i152-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i1521+i152-4-422-1-1111122-1-111111−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i1521−i1521−i1521+i1521+i152−1+i152−1+i152−1−i152−1−i152−1−i152−1−i152−1+i152−1+i152000000000000000000000000000000000
χ51444444-244-2-2-2-2-2-2-24-1-2-2-1-1-1-2-21+i1521−i152-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i15244-2-2-1-1-1-1-1-1-2-2-1-1-1-1-1-11+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521−i1521−i1521+i1521+i152000000000000000000000000000000000
χ52444444-244-2-2-2-2-2-2-24-1-2-2-1-1-1-2-21+i1521−i152-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i1521−i152-4-422-1-1111122-1-111111+i1521+i1521−i1521−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i1521+i1521+i1521−i1521−i152−1−i152−1−i152−1+i152−1+i152−1+i152−1+i152−1−i152−1−i152000000000000000000000000000000000
χ53444444-2-4-4-2-2-22222-4-1-2-2-1-1-1221−i1521+i15211111−i1521+i1521−i1521+i1521−i1521+i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i15200−2i32i3-1-155−5−5−2i32i31155−5−51−i1521−i1521+i1521+i152ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116−1+i152−1+i152−1−i152−1−i152ζ28−ζ44+ζ52−ζ116ζ28−ζ44+ζ52−ζ116ζ4−ζ68+ζ76−ζ92ζ4−ζ68+ζ76−ζ92−ζ4+ζ68−ζ76+ζ92−ζ4+ζ68−ζ76+ζ92−ζ28+ζ44−ζ52+ζ116−ζ28+ζ44−ζ52+ζ116000000000000000000000000000000000
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χ11088-8-8008−8i8i8-8-8−8i−8i8i8i0-200-22200-2-22i2i−2i−2i-2-222222i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000000000000000000000000000000000000
χ11188-8-800-48i−8i-444−4i−4i4i4i0-200-222001−i151+i15−2i−2i2i2i1−i151+i15−1+i15−1−i15−1+i15−1−i152ζ14+2ζ22+2ζ86+2ζ1182ζ14+2ζ22+2ζ86+2ζ1182ζ38+2ζ46+2ζ62+2ζ942ζ38+2ζ46+2ζ62+2ζ94−2ζ14−2ζ22−2ζ86−2ζ118−2ζ14−2ζ22−2ζ86−2ζ118−2ζ38−2ζ46−2ζ62−2ζ94−2ζ38−2ζ46−2ζ62−2ζ94000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1158-88-800800-88-800000-2002-2200-2-2−2i52i52i5−2i522-2-222−2i52i52i5−2i5−2i52i52i5−2i5000000000000000000000000000000000000000000000000000000000000000000000000000
χ1168-88-800800-88-800000-2002-2200-2-22i5−2i5−2i52i522-2-2222i5−2i5−2i52i52i5−2i5−2i52i5000000000000000000000000000000000000000000000000000000000000000000000000000
χ1178-88-800-4004-4443−4343−430-2002-22001−i151+i152i5−2i5−2i52i5−1+i15−1−i151−i151+i15−1+i15−1−i152ζ14−2ζ22+2ζ86−2ζ118−2ζ14+2ζ22−2ζ86+2ζ1182ζ38−2ζ46+2ζ62−2ζ94−2ζ38+2ζ46−2ζ62+2ζ942ζ14−2ζ22+2ζ86−2ζ118−2ζ14+2ζ22−2ζ86+2ζ1182ζ38−2ζ46+2ζ62−2ζ94−2ζ38+2ζ46−2ζ62+2ζ94000000000000000000000000000000000000000000000000000000000000000000000000000
χ1188-88-800-4004-4443−4343−430-2002-22001+i151−i15−2i52i52i5−2i5−1−i15−1+i151+i151−i15−1−i15−1+i152ζ38−2ζ46+2ζ62−2ζ94−2ζ38+2ζ46−2ζ62+2ζ942ζ14−2ζ22+2ζ86−2ζ118−2ζ14+2ζ22−2ζ86+2ζ1182ζ38−2ζ46+2ζ62−2ζ94−2ζ38+2ζ46−2ζ62+2ζ942ζ14−2ζ22+2ζ86−2ζ118−2ζ14+2ζ22−2ζ86+2ζ118000000000000000000000000000000000000000000000000000000000000000000000000000
χ1198-88-800-4004-44−4343−43430-2002-22001−i151+i15−2i52i52i5−2i5−1+i15−1−i151−i151+i15−1+i15−1−i15−2ζ14+2ζ22−2ζ86+2ζ1182ζ14−2ζ22+2ζ86−2ζ118−2ζ38+2ζ46−2ζ62+2ζ942ζ38−2ζ46+2ζ62−2ζ94−2ζ14+2ζ22−2ζ86+2ζ1182ζ14−2ζ22+2ζ86−2ζ118−2ζ38+2ζ46−2ζ62+2ζ942ζ38−2ζ46+2ζ62−2ζ94000000000000000000000000000000000000000000000000000000000000000000000000000
χ1208-88-800-4004-44−4343−43430-2002-22001+i151−i152i5−2i5−2i52i5−1−i15−1+i151+i151−i15−1−i15−1+i15−2ζ38+2ζ46−2ζ62+2ζ942ζ38−2ζ46+2ζ62−2ζ94−2ζ14+2ζ22−2ζ86+2ζ1182ζ14−2ζ22+2ζ86−2ζ118−2ζ38+2ζ46−2ζ62+2ζ942ζ38−2ζ46+2ζ62−2ζ94−2ζ14+2ζ22−2ζ86+2ζ1182ζ14−2ζ22+2ζ86−2ζ118000000000000000000000000000000000000000000000000000000000000000000000000000

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