Finite Group Databasebeta

← Group #72221269

Character table — Group #72221269

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size112224444444444444488888888888888888888161616161616161616161616161616161616161616161616161616161616161616161616252550505050505050100100100100100100100100200200200200200200
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χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
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χ3111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1ii−i−ii−ii−i-1-1i−i-1i−i-1i−i
χ4111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1−i−iii−ii−ii-1-1−ii-1−ii-1−ii
χ51111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1
χ61111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-111-111
χ71111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−ii−ii−i-1-1i−i1−ii1−ii
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χ1411111111111-1-1111111-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1111-1-1
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χ65444-4-4-1-13−52−1−5−1+53+524i−4i-1-13−52−1−5−1+53+5200-1-13−52−1−5−1+53+5211−3+521+51−5−3−5211−3+521+51−5−3−525−55−5−5−525+5200005−52−5+52−i−iζ6+ζ14+2ζ22+2ζ38−2ζ6−2ζ14−2ζ22−2ζ382ζ6+2ζ14+ζ22+ζ38ii−ζ6−ζ14−2ζ22−2ζ382ζ6+2ζ142ζ22+2ζ38−2ζ6−2ζ14−ζ22−ζ38i5−i5i5−i5−3ζ6−3ζ14−2ζ22−2ζ383ζ6+3ζ14+2ζ22+2ζ3800002ζ6+2ζ14+3ζ22+3ζ38−2ζ6−2ζ14−3ζ22−3ζ3800000000000000000000000
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χ69444-4-4-1-13+52−1+5−1−53−524i−4i-1-13+52−1+5−1−53−5200-1-13+52−1+5−1−53−5211−3−521−51+5−3+5211−3−521−51+5−3+525−55−55−52−5+520000−5−525+52−i−i2ζ6+2ζ14+ζ22+ζ38−2ζ22−2ζ38−2ζ6−2ζ14ζ6+ζ14+2ζ22+2ζ38ii−2ζ6−2ζ14−ζ22−ζ382ζ22+2ζ382ζ6+2ζ14−ζ6−ζ14−2ζ22−2ζ38i5−i5i5−i52ζ6+2ζ14+3ζ22+3ζ38−2ζ6−2ζ14−3ζ22−3ζ380000−3ζ6−3ζ14−2ζ22−2ζ383ζ6+3ζ14+2ζ22+2ζ3800000000000000000000000
χ70444-4-4-1-13+52−1+5−1−53−524i−4i-1-13+52−1+5−1−53−5200-1-13+52−1+5−1−53−5211−3−521−51+5−3+5211−3−521−51+5−3+52−55−55−5+525−5200005+52−5−52−i−i2ζ6+2ζ14+ζ22+ζ38−2ζ22−2ζ38−2ζ6−2ζ14ζ6+ζ14+2ζ22+2ζ38ii−2ζ6−2ζ14−ζ22−ζ382ζ22+2ζ382ζ6+2ζ14−ζ6−ζ14−2ζ22−2ζ38−i5i5−i5i5−2ζ6−2ζ14−3ζ22−3ζ382ζ6+2ζ14+3ζ22+3ζ3800003ζ6+3ζ14+2ζ22+2ζ38−3ζ6−3ζ14−2ζ22−2ζ3800000000000000000000000
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χ73444-4-4-1-1−1−53+523−52−1+54i−4i-1-1−1−53+523−52−1+500-1-1−1−53+523−52−1+5111+5−3−52−3+521−5111+5−3−52−3+521−55−5−5500−5+525−525+52−5−5200−i−i−2ζ6−2ζ142ζ6+2ζ14+ζ22+ζ38ζ6+ζ14+2ζ22+2ζ38−2ζ22−2ζ38ii2ζ6+2ζ14−2ζ6−2ζ14−ζ22−ζ38−ζ6−ζ14−2ζ22−2ζ382ζ22+2ζ38i5−i5−i5i500−2ζ6−2ζ14−3ζ22−3ζ382ζ6+2ζ14+3ζ22+3ζ383ζ6+3ζ14+2ζ22+2ζ38−3ζ6−3ζ14−2ζ22−2ζ380000000000000000000000000
χ74444-4-4-1-1−1−53+523−52−1+54i−4i-1-1−1−53+523−52−1+500-1-1−1−53+523−52−1+5111+5−3−52−3+521−5111+5−3−52−3+521−5−555−5005−52−5+52−5−525+5200−i−i−2ζ6−2ζ142ζ6+2ζ14+ζ22+ζ38ζ6+ζ14+2ζ22+2ζ38−2ζ22−2ζ38ii2ζ6+2ζ14−2ζ6−2ζ14−ζ22−ζ38−ζ6−ζ14−2ζ22−2ζ382ζ22+2ζ38−i5i5i5−i5002ζ6+2ζ14+3ζ22+3ζ38−2ζ6−2ζ14−3ζ22−3ζ38−3ζ6−3ζ14−2ζ22−2ζ383ζ6+3ζ14+2ζ22+2ζ380000000000000000000000000
χ75444-4-4-1-1−1−53+523−52−1+5−4i4i-1-1−1−53+523−52−1+500-1-1−1−53+523−52−1+5111+5−3−52−3+521−5111+5−3−52−3+521−55−5−5500−5+525−525+52−5−5200ii2ζ6+2ζ14−2ζ6−2ζ14−ζ22−ζ38−ζ6−ζ14−2ζ22−2ζ382ζ22+2ζ38−i−i−2ζ6−2ζ142ζ6+2ζ14+ζ22+ζ38ζ6+ζ14+2ζ22+2ζ38−2ζ22−2ζ38−i5i5i5−i5002ζ6+2ζ14+3ζ22+3ζ38−2ζ6−2ζ14−3ζ22−3ζ38−3ζ6−3ζ14−2ζ22−2ζ383ζ6+3ζ14+2ζ22+2ζ380000000000000000000000000
χ76444-4-4-1-1−1−53+523−52−1+5−4i4i-1-1−1−53+523−52−1+500-1-1−1−53+523−52−1+5111+5−3−52−3+521−5111+5−3−52−3+521−5−555−5005−52−5+52−5−525+5200ii2ζ6+2ζ14−2ζ6−2ζ14−ζ22−ζ38−ζ6−ζ14−2ζ22−2ζ382ζ22+2ζ38−i−i−2ζ6−2ζ142ζ6+2ζ14+ζ22+ζ38ζ6+ζ14+2ζ22+2ζ38−2ζ22−2ζ38i5−i5−i5i500−2ζ6−2ζ14−3ζ22−3ζ382ζ6+2ζ14+3ζ22+3ζ383ζ6+3ζ14+2ζ22+2ζ38−3ζ6−3ζ14−2ζ22−2ζ380000000000000000000000000
χ774-400044444400-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000004-40002i2−2i22i2−2i200000000000000
χ784-400044444400-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000004-4000−2i22i2−2i22i200000000000000
χ794-400044444400-4-4-4-4-4-400000000000000000000000000000000000000000000000000000000-4400022−22−222200000000000000
χ804-400044444400-4-4-4-4-4-400000000000000000000000000000000000000000000000000000000-44000−222222−2200000000000000
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χ8288-88-8-28-2-2-2-200-28-2-2-2-2002-82222-28-2-2-2-22-8222200000000000000000000000000000000000000000000000000000000000
χ8388-88-8-2-2−2+253−53+5−2−2500-2-2−2+253−53+5−2−2500222−25−3+5−3−52+25-2-2−2+253−53+5−2−25222−25−3+5−3−52+2500000000000000000000000000000000000000000000000000000000000
χ8488-88-8-2-23−5−2−25−2+253+500-2-23−5−2−25−2+253+50022−3+52+252−25−3−5-2-23−5−2−25−2+253+522−3+52+252−25−3−500000000000000000000000000000000000000000000000000000000000
χ8588-88-8-2-23+5−2+25−2−253−500-2-23+5−2+25−2−253−50022−3−52−252+25−3+5-2-23+5−2+25−2−253−522−3−52−252+25−3+500000000000000000000000000000000000000000000000000000000000
χ8688-88-8-2-2−2−253+53−5−2+2500-2-2−2−253+53−5−2+2500222+25−3−5−3+52−25-2-2−2−253+53−5−2+25222+25−3−5−3+52−2500000000000000000000000000000000000000000000000000000000000
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χ8988-8-88-2-2−2+253−53+5−2−2500-2-2−2+253−53+5−2−2500222−25−3+5−3−52+25222−25−3+5−3−52+25-2-2−2+253−53+5−2−2500000000000000000000000000000000000000000000000000000000000
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χ9188-8-88-2-23+5−2+25−2−253−500-2-23+5−2+25−2−253−50022−3−52−252+25−3+522−3−52−252+25−3+5-2-23+5−2+25−2−253−500000000000000000000000000000000000000000000000000000000000
χ9288-8-88-2-2−2−253+53−5−2+2500-2-2−2−253+53−5−2+2500222+25−3−5−3+52−25222+25−3−5−3+52−25-2-2−2−253+53−5−2+2500000000000000000000000000000000000000000000000000000000000
χ9316-1600016-4-4-4-4-400-16444440000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9416-16000-416-4-4-4-4004-1644440000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9516-16000-4-4−4+456−256+25−4−4500444−45−6+25−6−254+450000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9616-16000-4-46−25−4−45−4+456+250044−6+254+454−45−6−250000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9716-16000-4-46+25−4+45−4−456−250044−6−254−454+45−6+250000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9816-16000-4-4−4−456+256−25−4+4500444+45−6−25−6+254−450000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.