Finite Group Databasebeta

← Group #72221307

Character table — Group #72221307

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size112224444444444444488888888888888888888161616161616161616161616161616161616161616161616161616161616161616161616252550505050505050100100100100100100100100200200200200200200
order12244245555551010101010102810101010101020202020202020202020202010101010101010101010101010101010101020202020202040404040404040404040404022244888824888888244888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
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χ3111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1ii−i−i-1-1iii−i−i−i-1i−i-1i−i
χ4111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1−i−iii-1-1−i−i−iiii-1−ii-1−ii
χ51111111111111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1
χ61111111111111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-111-111
χ71111111111111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1iii−i−i−i1−ii1−ii
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χ1011111-1-11111111111111-1111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-111-1111-1-1-111
χ1111111-1-11111111111111-1111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i11i−i−i−iii-1i−i1−ii
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χ1311111-1-1111111111111-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-11-1-11-1-1-1-1-1111
χ1411111-1-1111111111111-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-111-111-1111-1-1
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χ6844-4-44-44-14-1-1-1-1-14-1-1-1-1001-411111-41111-14-1-1-1-11-41111−5500−555−55−5−55-14-1-1-1-15−5005−5−55−555−500000000000000000000000
χ6944-4-44-44-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−500111−5−3+52−3−521+5111−5−3+52−3−521+5-1-1−1+53−523+52−1−5111−5−3+52−3−521+55−5−55005+52−5−52−5+525−5200-1-1−1+53−523+52−1−5−555−500−5−525+525−52−5+520000000000000000000000000
χ7044-4-44-44-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−500111−5−3+52−3−521+5111−5−3+52−3−521+5-1-1−1+53−523+52−1−5111−5−3+52−3−521+5−555−500−5−525+525−52−5+5200-1-1−1+53−523+52−1−55−5−55005+52−5−52−5+525−520000000000000000000000000
χ7144-4-44-44-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+520011−3+521+51−5−3−5211−3+521+51−5−3−52-1-13−52−1−5−1+53+5211−3+521+51−5−3−525−55−5−5−525+5200005−52−5+52-1-13−52−1−5−1+53+52−55−555+52−5−520000−5+525−5200000000000000000000000
χ7244-4-44-44-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+520011−3+521+51−5−3−5211−3+521+51−5−3−52-1-13−52−1−5−1+53+5211−3+521+51−5−3−52−55−555+52−5−520000−5+525−52-1-13−52−1−5−1+53+525−55−5−5−525+5200005−52−5+5200000000000000000000000
χ7344-4-44-44-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−520011−3−521−51+5−3+5211−3−521−51+5−3+52-1-13+52−1+5−1−53−5211−3−521−51+5−3+525−55−55−52−5+520000−5−525+52-1-13+52−1+5−1−53−52−55−55−5+525−5200005+52−5−5200000000000000000000000
χ7444-4-44-44-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−520011−3−521−51+5−3+5211−3−521−51+5−3+52-1-13+52−1+5−1−53−5211−3−521−51+5−3+52−55−55−5+525−5200005+52−5−52-1-13+52−1+5−1−53−525−55−55−52−5+520000−5−525+5200000000000000000000000
χ7544-4-44-44-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+500111+5−3−52−3+521−5111+5−3−52−3+521−5-1-1−1−53+523−52−1+5111+5−3−52−3+521−55−5−5500−5+525−525+52−5−5200-1-1−1−53+523−52−1+5−555−5005−52−5+52−5−525+520000000000000000000000000
χ7644-4-44-44-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+500111+5−3−52−3+521−5111+5−3−52−3+521−5-1-1−1−53+523−52−1+5111+5−3−52−3+521−5−555−5005−52−5+52−5−525+5200-1-1−1−53+523−52−1+55−5−5500−5+525−525+52−5−520000000000000000000000000
χ774-400000444444-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000004-40002i2−2i22i2−2i200000000000000
χ784-400000444444-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000004-4000−2i22i2−2i22i200000000000000
χ794-400000444444-4-4-4-4-4-400000000000000000000000000000000000000000000000000000000-4400022−22−222200000000000000
χ804-400000444444-4-4-4-4-4-400000000000000000000000000000000000000000000000000000000-44000−222222−2200000000000000
χ81888-8-8008-2-2-2-2-28-2-2-2-2-2008-2-2-2-2-2-822222-82222200000000000000000000000000000000000000000000000000000000000
χ82888-8-800-28-2-2-2-2-28-2-2-2-200-28-2-2-2-22-822222-8222200000000000000000000000000000000000000000000000000000000000
χ83888-8-800-2-2−2+253−53+5−2−25-2-2−2+253−53+5−2−2500-2-2−2+253−53+5−2−25222−25−3+5−3−52+25222−25−3+5−3−52+2500000000000000000000000000000000000000000000000000000000000
χ84888-8-800-2-23−5−2−25−2+253+5-2-23−5−2−25−2+253+500-2-23−5−2−25−2+253+522−3+52+252−25−3−522−3+52+252−25−3−500000000000000000000000000000000000000000000000000000000000
χ85888-8-800-2-23+5−2+25−2−253−5-2-23+5−2+25−2−253−500-2-23+5−2+25−2−253−522−3−52−252+25−3+522−3−52−252+25−3+500000000000000000000000000000000000000000000000000000000000
χ86888-8-800-2-2−2−253+53−5−2+25-2-2−2−253+53−5−2+2500-2-2−2−253+53−5−2+25222+25−3−5−3+52−25222+25−3−5−3+52−2500000000000000000000000000000000000000000000000000000000000
χ8788-88-8008-2-2-2-2-28-2-2-2-2-200-8222228-2-2-2-2-2-82222200000000000000000000000000000000000000000000000000000000000
χ8888-88-800-28-2-2-2-2-28-2-2-2-2002-82222-28-2-2-2-22-8222200000000000000000000000000000000000000000000000000000000000
χ8988-88-800-2-2−2+253−53+5−2−25-2-2−2+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
χ9088-88-800-2-23−5−2−25−2+253+5-2-23−5−2−25−2+253+50022−3+52+252−25−3−5-2-23−5−2−25−2+253+522−3+52+252−25−3−500000000000000000000000000000000000000000000000000000000000
χ9188-88-800-2-23+5−2+25−2−253−5-2-23+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
χ9288-88-800-2-2−2−253+53−5−2+25-2-2−2−253+53−5−2+2500222+25−3−5−3+52−25-2-2−2−253+53−5−2+25222+25−3−5−3+52−2500000000000000000000000000000000000000000000000000000000000
χ9316-160000016-4-4-4-4-4-16444440000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9416-1600000-416-4-4-4-44-1644440000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9516-1600000-4-4−4+456−256+25−4−45444−45−6+25−6−254+450000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9616-1600000-4-46−25−4−45−4+456+2544−6+254+454−45−6−250000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9716-1600000-4-46+25−4+45−4−456−2544−6−254−454+45−6+250000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9816-1600000-4-4−4−456+256−25−4+45444+45−6−25−6+254−450000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).