Finite Group Databasebeta

← Group #13104154

Character table — Group #13104154

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11222444444448888888888888888888825254040404050505050505050505050508080808080808080
order12488555510101010510202020202020404040404040404040404040222244444448888881010101020202020
χ11111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-11-1-1-1-1-1111-1-1-1-111-1-111-1-1
χ311111111111111111111111111111111111-11-11-1-1-1-1111-1-1-1-1-1-111-1-111
χ411111111111111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1
χ5111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-1-1-1-1-11111-1-1-1-1
χ6111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-11-1-1111111-1-1-1-111
χ7111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-11-1-11111-1-11111-1-1
χ8111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1-1-11111
χ9222222222222222222222222222222222-2-200000000-2-2-2000000000000
χ10222-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000-222000000000000
χ1122-2002222222222-2-2-2-2-2-200000000000022000022-2-2-200000000000000
χ1222-2002222222222-2-2-2-2-2-2000000000000220000-2-222-200000000000000
χ1322-2002222222222-2-2-2-2-2-2000000000000-2-20000000020022-2-200000000
χ1422-2002222222222-2-2-2-2-2-2000000000000-2-200000000200-2-22200000000
χ152-20i2−i22222-2-2-2-22-2000000i2i2i2i2i2i2−i2−i2−i2−i2−i2−i22-20000002-20i2−i2i2−i2i2−i200000000
χ162-20i2−i22222-2-2-2-22-2000000i2i2i2i2i2i2−i2−i2−i2−i2−i2−i22-2000000-220i2−i2−i2i2−i2i200000000
χ172-20i2−i22222-2-2-2-22-2000000i2i2i2i2i2i2−i2−i2−i2−i2−i2−i2-2200002-2000−i2i2i2−i2−i2i200000000
χ182-20i2−i22222-2-2-2-22-2000000i2i2i2i2i2i2−i2−i2−i2−i2−i2−i2-220000-22000−i2i2−i2i2i2−i200000000
χ192-20−i2i22222-2-2-2-22-2000000−i2−i2−i2−i2−i2−i2i2i2i2i2i2i22-20000002-20−i2i2−i2i2−i2i200000000
χ202-20−i2i22222-2-2-2-22-2000000−i2−i2−i2−i2−i2−i2i2i2i2i2i2i22-2000000-220−i2i2i2−i2i2−i200000000
χ212-20−i2i22222-2-2-2-22-2000000−i2−i2−i2−i2−i2−i2i2i2i2i2i2i2-2200002-2000i2−i2−i2i2i2−i200000000
χ222-20−i2i22222-2-2-2-22-2000000−i2−i2−i2−i2−i2−i2i2i2i2i2i2i2-220000-22000i2−i2i2−i2−i2i200000000
χ2344444−1+53−523+52−1−5−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−50002020000000000000−1+52−1−5200−1+52−1−52
χ2444444−1+53−523+52−1−5−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5000-20-200000000000001−521+52001−521+52
χ25444443−52−1−5−1+53+523−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-1-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+5200202000000000000−1+52−1−5200−1+52−1−5200
χ26444443−52−1−5−1+53+523−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-1-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+5200-20-20000000000001−521+52001−521+5200
χ27444443+52−1+5−1−53−523+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-1-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−5200202000000000000−1−52−1+5200−1−52−1+5200
χ28444443+52−1+5−1−53−523+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-1-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−5200-20-20000000000001+521−52001+521−5200
χ2944444−1−53+523−52−1+5−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+50002020000000000000−1−52−1+5200−1−52−1+52
χ3044444−1−53+523−52−1+5−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5000-20-200000000000001+521−52001+521−52
χ31444-4-4−1+53−523+52−1−5−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1111−5−3+52−3−521+5111−5−3+52−3−521+500020-20000000000000−1+52−1−52001−521+52
χ32444-4-4−1+53−523+52−1−5−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1111−5−3+52−3−521+5111−5−3+52−3−521+5000-20200000000000001−521+5200−1+52−1−52
χ33444-4-43−52−1−5−1+53+523−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-111−3+521+51−5−3−5211−3+521+51−5−3−520020-2000000000000−1+52−1−52001−521+5200
χ34444-4-43−52−1−5−1+53+523−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-111−3+521+51−5−3−5211−3+521+51−5−3−5200-2020000000000001−521+5200−1+52−1−5200
χ35444-4-43+52−1+5−1−53−523+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-111−3−521−51+5−3+5211−3−521−51+5−3+520020-2000000000000−1−52−1+52001+521−5200
χ36444-4-43+52−1+5−1−53−523+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-111−3−521−51+5−3+5211−3−521−51+5−3+5200-2020000000000001+521−5200−1−52−1+5200
χ37444-4-4−1−53+523−52−1+5−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1111+5−3−52−3+521−5111+5−3−52−3+521−500020-20000000000000−1−52−1+52001+521−52
χ38444-4-4−1−53+523−52−1+5−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1111+5−3−52−3+521−5111+5−3−52−3+521−5000-20200000000000001+521−5200−1−52−1+52
χ3988888-2-2-2-2-2-2-2-233-2-2-2-23333-2-2-2-233-2-2-2-20000000000000000000000000
χ40888-8-8-2-2-2-2-2-2-2-233-2-2-2-233-3-32222-3-322220000000000000000000000000
χ4188-800-2-2-2-2-2-2-2-2332222-3-35i−5i00005i−5i00000000000000000000000000000
χ4288-800-2-2-2-2-2-2-2-2332222-3-3−5i5i0000−5i5i00000000000000000000000000000
χ4388-800−2+253−53+5−2−25−2+253−53+5−2−25-2-22−25−3+5−3−52+25220000000000000000000000000000000000000
χ4488-8003−5−2−25−2+253+53−5−2−25−2+253+5-2-2−3+52+252−25−3−5220000000000000000000000000000000000000
χ4588-8003+5−2+25−2−253−53+5−2+25−2−253−5-2-2−3−52−252+25−3+5220000000000000000000000000000000000000
χ4688-800−2−253+53−5−2+25−2−253+53−5−2+25-2-22+25−3−5−3+52−25220000000000000000000000000000000000000
χ478-804i2−4i2-2-2-2-222223-300005i−5iζ7−4ζ13−4ζ21+ζ23−4ζ29+ζ31−4ζ37+ζ39−4ζ7+ζ13+ζ21−4ζ23+ζ29−4ζ31+ζ37−4ζ39−i2−i2−i2−i2−ζ7+4ζ13+4ζ21−ζ23+4ζ29−ζ31+4ζ37−ζ394ζ7−ζ13−ζ21+4ζ23−ζ29+4ζ31−ζ37+4ζ39i2i2i2i20000000000000000000000000
χ488-804i2−4i2-2-2-2-222223-30000−5i5i−4ζ7+ζ13+ζ21−4ζ23+ζ29−4ζ31+ζ37−4ζ39ζ7−4ζ13−4ζ21+ζ23−4ζ29+ζ31−4ζ37+ζ39−i2−i2−i2−i24ζ7−ζ13−ζ21+4ζ23−ζ29+4ζ31−ζ37+4ζ39−ζ7+4ζ13+4ζ21−ζ23+4ζ29−ζ31+4ζ37−ζ39i2i2i2i20000000000000000000000000
χ498-804i2−4i2−2+253−53+5−2−252−25−3+5−3−52+25-22000000−i2−i22ζ7+2ζ13+2ζ23+2ζ37−2ζ7−2ζ13−ζ21−2ζ23−ζ29−ζ31−2ζ37−ζ39−ζ7−ζ13−2ζ21−ζ23−2ζ29−2ζ31−ζ37−2ζ392ζ21+2ζ29+2ζ31+2ζ39i2i2−2ζ7−2ζ13−2ζ23−2ζ372ζ7+2ζ13+ζ21+2ζ23+ζ29+ζ31+2ζ37+ζ39ζ7+ζ13+2ζ21+ζ23+2ζ29+2ζ31+ζ37+2ζ39−2ζ21−2ζ29−2ζ31−2ζ390000000000000000000000000
χ508-804i2−4i23−5−2−25−2+253+5−3+52+252−25−3−5-22000000−i2−i2−2ζ7−2ζ13−ζ21−2ζ23−ζ29−ζ31−2ζ37−ζ392ζ21+2ζ29+2ζ31+2ζ392ζ7+2ζ13+2ζ23+2ζ37−ζ7−ζ13−2ζ21−ζ23−2ζ29−2ζ31−ζ37−2ζ39i2i22ζ7+2ζ13+ζ21+2ζ23+ζ29+ζ31+2ζ37+ζ39−2ζ21−2ζ29−2ζ31−2ζ39−2ζ7−2ζ13−2ζ23−2ζ37ζ7+ζ13+2ζ21+ζ23+2ζ29+2ζ31+ζ37+2ζ390000000000000000000000000
χ518-804i2−4i23+5−2+25−2−253−5−3−52−252+25−3+5-22000000−i2−i2−ζ7−ζ13−2ζ21−ζ23−2ζ29−2ζ31−ζ37−2ζ392ζ7+2ζ13+2ζ23+2ζ372ζ21+2ζ29+2ζ31+2ζ39−2ζ7−2ζ13−ζ21−2ζ23−ζ29−ζ31−2ζ37−ζ39i2i2ζ7+ζ13+2ζ21+ζ23+2ζ29+2ζ31+ζ37+2ζ39−2ζ7−2ζ13−2ζ23−2ζ37−2ζ21−2ζ29−2ζ31−2ζ392ζ7+2ζ13+ζ21+2ζ23+ζ29+ζ31+2ζ37+ζ390000000000000000000000000
χ528-804i2−4i2−2−253+53−5−2+252+25−3−5−3+52−25-22000000−i2−i22ζ21+2ζ29+2ζ31+2ζ39−ζ7−ζ13−2ζ21−ζ23−2ζ29−2ζ31−ζ37−2ζ39−2ζ7−2ζ13−ζ21−2ζ23−ζ29−ζ31−2ζ37−ζ392ζ7+2ζ13+2ζ23+2ζ37i2i2−2ζ21−2ζ29−2ζ31−2ζ39ζ7+ζ13+2ζ21+ζ23+2ζ29+2ζ31+ζ37+2ζ392ζ7+2ζ13+ζ21+2ζ23+ζ29+ζ31+2ζ37+ζ39−2ζ7−2ζ13−2ζ23−2ζ370000000000000000000000000
χ538-80−4i24i2-2-2-2-222223-300005i−5i−ζ7+4ζ13+4ζ21−ζ23+4ζ29−ζ31+4ζ37−ζ394ζ7−ζ13−ζ21+4ζ23−ζ29+4ζ31−ζ37+4ζ39i2i2i2i2ζ7−4ζ13−4ζ21+ζ23−4ζ29+ζ31−4ζ37+ζ39−4ζ7+ζ13+ζ21−4ζ23+ζ29−4ζ31+ζ37−4ζ39−i2−i2−i2−i20000000000000000000000000
χ548-80−4i24i2-2-2-2-222223-30000−5i5i4ζ7−ζ13−ζ21+4ζ23−ζ29+4ζ31−ζ37+4ζ39−ζ7+4ζ13+4ζ21−ζ23+4ζ29−ζ31+4ζ37−ζ39i2i2i2i2−4ζ7+ζ13+ζ21−4ζ23+ζ29−4ζ31+ζ37−4ζ39ζ7−4ζ13−4ζ21+ζ23−4ζ29+ζ31−4ζ37+ζ39−i2−i2−i2−i20000000000000000000000000
χ558-80−4i24i2−2+253−53+5−2−252−25−3+5−3−52+25-22000000i2i2−2ζ7−2ζ13−2ζ23−2ζ372ζ7+2ζ13+ζ21+2ζ23+ζ29+ζ31+2ζ37+ζ39ζ7+ζ13+2ζ21+ζ23+2ζ29+2ζ31+ζ37+2ζ39−2ζ21−2ζ29−2ζ31−2ζ39−i2−i22ζ7+2ζ13+2ζ23+2ζ37−2ζ7−2ζ13−ζ21−2ζ23−ζ29−ζ31−2ζ37−ζ39−ζ7−ζ13−2ζ21−ζ23−2ζ29−2ζ31−ζ37−2ζ392ζ21+2ζ29+2ζ31+2ζ390000000000000000000000000
χ568-80−4i24i23−5−2−25−2+253+5−3+52+252−25−3−5-22000000i2i22ζ7+2ζ13+ζ21+2ζ23+ζ29+ζ31+2ζ37+ζ39−2ζ21−2ζ29−2ζ31−2ζ39−2ζ7−2ζ13−2ζ23−2ζ37ζ7+ζ13+2ζ21+ζ23+2ζ29+2ζ31+ζ37+2ζ39−i2−i2−2ζ7−2ζ13−ζ21−2ζ23−ζ29−ζ31−2ζ37−ζ392ζ21+2ζ29+2ζ31+2ζ392ζ7+2ζ13+2ζ23+2ζ37−ζ7−ζ13−2ζ21−ζ23−2ζ29−2ζ31−ζ37−2ζ390000000000000000000000000
χ578-80−4i24i23+5−2+25−2−253−5−3−52−252+25−3+5-22000000i2i2ζ7+ζ13+2ζ21+ζ23+2ζ29+2ζ31+ζ37+2ζ39−2ζ7−2ζ13−2ζ23−2ζ37−2ζ21−2ζ29−2ζ31−2ζ392ζ7+2ζ13+ζ21+2ζ23+ζ29+ζ31+2ζ37+ζ39−i2−i2−ζ7−ζ13−2ζ21−ζ23−2ζ29−2ζ31−ζ37−2ζ392ζ7+2ζ13+2ζ23+2ζ372ζ21+2ζ29+2ζ31+2ζ39−2ζ7−2ζ13−ζ21−2ζ23−ζ29−ζ31−2ζ37−ζ390000000000000000000000000
χ588-80−4i24i2−2−253+53−5−2+252+25−3−5−3+52−25-22000000i2i2−2ζ21−2ζ29−2ζ31−2ζ39ζ7+ζ13+2ζ21+ζ23+2ζ29+2ζ31+ζ37+2ζ392ζ7+2ζ13+ζ21+2ζ23+ζ29+ζ31+2ζ37+ζ39−2ζ7−2ζ13−2ζ23−2ζ37−i2−i22ζ21+2ζ29+2ζ31+2ζ39−ζ7−ζ13−2ζ21−ζ23−2ζ29−2ζ31−ζ37−2ζ39−2ζ7−2ζ13−ζ21−2ζ23−ζ29−ζ31−2ζ37−ζ392ζ7+2ζ13+2ζ23+2ζ370000000000000000000000000

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