Finite Group Databasebeta

← Group #13103728

Character table — Group #13103728

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size1122222444445555888888888101010101010101010101616161616162020202020202020202020202020202025254040404040404040405050505050100100100
order12455101025102020224455101010101010202488881010101010101010202024442020202040404040404040404410101020202020202028888444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-11-1-1
χ311111111111111-1-1111111111-11111111111111111-111-1-11111111111-1-111-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111-1-1111111111-11-1-1-1-111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-111
χ5111111111111-1-1111111111111-1ii−i−i-1-1-1-1111111-11i−i11-1-1iiii−i−i−i−i-1-1-1-1111ii−i−i-1ii−i−i-1i−i
χ6111111111111-1-1111111111111-1−i−iii-1-1-1-1111111-11−ii11-1-1−i−i−i−iiiii-1-1-1-1111−i−iii-1−i−iii-1−ii
χ7111111111111-1-1-1-1111111111-1-1ii−i−i-1-1-1-1111111-1-1i−i-1-1-1-1iiii−i−i−i−i11-1-1-1-1-1ii−i−i1−i−iii1−ii
χ8111111111111-1-1-1-1111111111-1-1−i−iii-1-1-1-1111111-1-1−ii-1-1-1-1−i−i−i−iiiii11-1-1-1-1-1−i−iii1ii−i−i1i−i
χ91111111-11111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-111111111111111-1-11-1-1-1-1-1-111111-1-1-1
χ101111111-11111111111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-11-1-111111-1-1-1-1-111
χ111111111-1111111-1-111-1-1-1-1111-1111111111-1-1-1-111-11-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1111
χ121111111-1111111-1-111-1-1-1-1111-11-1-1-1-11111-1-1-1-111-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111111-1-1
χ131111111-11111-1-11111-1-1-1-11111-1ii−i−i-1-1-1-1-1-1-1-1111-1−ii11-1-1iiii−i−i−i−i-1-1111-1-1−i−iii-1ii−i−i1−ii
χ141111111-11111-1-11111-1-1-1-11111-1−i−iii-1-1-1-1-1-1-1-1111-1i−i11-1-1−i−i−i−iiiii-1-1111-1-1ii−i−i-1−i−iii1i−i
χ151111111-11111-1-1-1-111-1-1-1-1111-1-1ii−i−i-1-1-1-1-1-1-1-11111−ii-1-1-1-1iiii−i−i−i−i1111-111−i−iii1−i−iii-1i−i
χ161111111-11111-1-1-1-111-1-1-1-1111-1-1−i−iii-1-1-1-1-1-1-1-11111i−i-1-1-1-1−i−i−i−iiiii1111-111ii−i−i1ii−i−i-1−ii
χ17222−1+52−1−52−1+52−1−52222−1+52−1−522200−1+52−1−52−1+52−1−5222−1+52−1−522022222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52202200−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200−1+52−1−52000−1+52−1−52−1+52−1−5200000000
χ18222−1+52−1−52−1+52−1−52222−1+52−1−522200−1+52−1−52−1+52−1−5222−1+52−1−52202-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5220-2-200−1+52−1−521−521−521+521+521−521−521+521+5200−1+52−1−520001−521+521−521+5200000000
χ19222−1+52−1−52−1+52−1−52222−1+52−1−52-2-200−1+52−1−52−1+52−1−5222−1+52−1−5220-22i2i−2i−2i1−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1−52-202i−2i001−521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14001−521+52000−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ1400000000
χ20222−1+52−1−52−1+52−1−52222−1+52−1−52-2-200−1+52−1−52−1+52−1−5222−1+52−1−5220-2−2i−2i2i2i1−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1−52-20−2i2i001−521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14001−521+52000ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ1400000000
χ21222−1+52−1−52−1+52−1−52-222−1+52−1−522200−1+52−1−521−521+52-2-2−1+52−1−522022222−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1−52-20-2-200−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52001−521+520001−521+521−521+5200000000
χ22222−1+52−1−52−1+52−1−52-222−1+52−1−522200−1+52−1−521−521+52-2-2−1+52−1−52202-2-2-2-2−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1−52-202200−1+52−1−521−521−521+521+521−521−521+521+52001−521+52000−1+52−1−52−1+52−1−5200000000
χ23222−1+52−1−52−1+52−1−52-222−1+52−1−52-2-200−1+52−1−521−521+52-2-2−1+52−1−5220-22i2i−2i−2i1−521+521−521+521−521−521+521+52−1+52−1−5220−2i2i001−521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ1400−1+52−1−52000ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ1400000000
χ24222−1+52−1−52−1+52−1−52-222−1+52−1−52-2-200−1+52−1−521−521+52-2-2−1+52−1−5220-2−2i−2i2i2i1−521+521−521+521−521−521+521+52−1+52−1−52202i−2i001−521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ1400−1+52−1−52000−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ1400000000
χ25222−1−52−1+52−1−52−1+52222−1−52−1+522200−1−52−1+52−1−52−1+5222−1−52−1+522022222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52202200−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200−1−52−1+52000−1−52−1+52−1−52−1+5200000000
χ26222−1−52−1+52−1−52−1+52222−1−52−1+522200−1−52−1+52−1−52−1+5222−1−52−1+52202-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5220-2-200−1−52−1+521+521+521−521−521+521+521−521−5200−1−52−1+520001+521−521+521−5200000000
χ27222−1−52−1+52−1−52−1+52222−1−52−1+52-2-200−1−52−1+52−1−52−1+5222−1−52−1+5220-22i2i−2i−2i1+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1+52-202i−2i001+521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38001+521−52000−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ3800000000
χ28222−1−52−1+52−1−52−1+52222−1−52−1+52-2-200−1−52−1+52−1−52−1+5222−1−52−1+5220-2−2i−2i2i2i1+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1+52-20−2i2i001+521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38001+521−52000ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ3800000000
χ29222−1−52−1+52−1−52−1+52-222−1−52−1+522200−1−52−1+521+521−52-2-2−1−52−1+522022222−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1+52-20-2-200−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52001+521−520001+521−521+521−5200000000
χ30222−1−52−1+52−1−52−1+52-222−1−52−1+522200−1−52−1+521+521−52-2-2−1−52−1+52202-2-2-2-2−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1+52-202200−1−52−1+521+521+521−521−521+521+521−521−52001+521−52000−1−52−1+52−1−52−1+5200000000
χ31222−1−52−1+52−1−52−1+52-222−1−52−1+52-2-200−1−52−1+521+521−52-2-2−1−52−1+5220-22i2i−2i−2i1+521−521+521−521+521+521−521−52−1−52−1+5220−2i2i001+521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ3800−1−52−1+52000ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ3800000000
χ32222−1−52−1+52−1−52−1+52-222−1−52−1+52-2-200−1−52−1+521+521−52-2-2−1−52−1+5220-2−2i−2i2i2i1+521−521+521−521+521+521−521−52−1−52−1+52202i−2i001+521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ3800−1−52−1+52000−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ3800000000
χ3322-22222022-2-2222222000022-2-2-2000022220000-2-2000022-2-2000000002200-2000000-20000000
χ3422-22222022-2-222-2-222000022-22-2000022220000-2-20000-2-2-2-200000000-2-200200000020000000
χ3522-22222022-2-2-2-22222000022-2-220000-2-2-2-20000-2-20000222200000000-2-200-200000020000000
χ3622-22222022-2-2-2-2-2-222000022-2220000-2-2-2-20000-2-20000-2-2220000000022002000000-20000000
χ372-2022-2-202-2002-22i−2i220000-2-20002−22−2-2-22200000000002i−2i002−22−22−22−22i−2i0000000000i2−i2i2−i2000
χ382-2022-2-202-2002-22i−2i220000-2-2000−22−22-2-22200000000002i−2i00−22−22−22−222i−2i0000000000−i2i2−i2i2000
χ392-2022-2-202-2002-2−2i2i220000-2-20002−22−2-2-2220000000000−2i2i002−22−22−22−2−2i2i0000000000−i2i2−i2i2000
χ402-2022-2-202-2002-2−2i2i220000-2-2000−22−22-2-2220000000000−2i2i00−22−22−22−22−2i2i0000000000i2−i2i2−i2000
χ412-2022-2-202-200-222i−2i220000-2-2000i2−i2−i2i222-2-200000000002i−2i00i2−i2i2−i2−i2i2−i2i2−2i2i0000000000−222−2000
χ422-2022-2-202-200-222i−2i220000-2-2000−i2i2i2−i222-2-200000000002i−2i00−i2i2−i2i2i2−i2i2−i2−2i2i00000000002−2−22000
χ432-2022-2-202-200-22−2i2i220000-2-2000i2−i2−i2i222-2-20000000000−2i2i00i2−i2i2−i2−i2i2−i2i22i−2i00000000002−2−22000
χ442-2022-2-202-200-22−2i2i220000-2-2000−i2i2i2−i222-2-20000000000−2i2i00−i2i2−i2i2i2−i2i2−i22i−2i0000000000−222−2000
χ4544444444-1-1440044-1-144-1-1-1-1-14000000000-1-1-1-1-1-10400-1-100000000000000-1-1-1000000000000
χ4644444444-1-14400-4-4-1-144-1-1-1-1-1-4000000000-1-1-1-1-1-10-4001100000000000000111000000000000
χ474444444-4-1-1440044-1-1-4-411-1-1-140000000001111-1-10-400-1-100000000000000-111000000000000
χ484444444-4-1-14400-4-4-1-1-4-411-1-1-1-40000000001111-1-1040011000000000000001-1-1000000000000
χ4944-444440-1-1-4-40044-1-1005−5-1-11-40000000005−55−5110000-1-10000000000000015−5000000000000
χ5044-444440-1-1-4-40044-1-100−55-1-11-4000000000−55−55110000-1-1000000000000001−55000000000000
χ5144-444440-1-1-4-400-4-4-1-1005−5-1-1140000000005−55−51100001100000000000000-1−55000000000000
χ5244-444440-1-1-4-400-4-4-1-100−55-1-114000000000−55−551100001100000000000000-15−5000000000000
χ5344-4−1+5−1−5−1+5−1−50441−51+54400−1+5−1−50000−1+5−1−5-40-40000−1+5−1−5−1+5−1−500001−51+50000001−51+5000000000000000000000000000
χ5444-4−1+5−1−5−1+5−1−50441−51+5-4-400−1+5−1−50000−1+5−1−5-40400001−51+51−51+500001−51+5000000−1+5−1−5000000000000000000000000000
χ5544-4−1−5−1+5−1−5−1+50441+51−54400−1−5−1+50000−1−5−1+5-40-40000−1−5−1+5−1−5−1+500001+51−50000001+51−5000000000000000000000000000
χ5644-4−1−5−1+5−1−5−1+50441+51−5-4-400−1−5−1+50000−1−5−1+5-40400001+51−51+51−500001+51−5000000−1−5−1+5000000000000000000000000000
χ574-40−1+5−1−51−51+504-4004-400−1+5−1−500001−51+500022−2222−221−51+5−1+5−1−500000000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ390000000000000000000
χ584-40−1+5−1−51−51+504-4004-400−1+5−1−500001−51+5000−2222−22221−51+5−1+5−1−500000000000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ390000000000000000000
χ594-40−1+5−1−51−51+504-400-4400−1+5−1−500001−51+50002i2−2i2−2i22i2−1+5−1−51−51+500000000000000ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ390000000000000000000
χ604-40−1+5−1−51−51+504-400-4400−1+5−1−500001−51+5000−2i22i22i2−2i2−1+5−1−51−51+500000000000000−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ390000000000000000000
χ614-40−1−5−1+51+51−504-4004-400−1−5−1+500001+51−500022−2222−221+51−5−1−5−1+500000000000000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ370000000000000000000
χ624-40−1−5−1+51+51−504-4004-400−1−5−1+500001+51−5000−2222−22221+51−5−1−5−1+500000000000000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ370000000000000000000
χ634-40−1−5−1+51+51−504-400-4400−1−5−1+500001+51−50002i2−2i2−2i22i2−1−5−1+51+51−500000000000000ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ370000000000000000000
χ644-40−1−5−1+51+51−504-400-4400−1−5−1+500001+51−5000−2i22i22i2−2i2−1−5−1+51+51−500000000000000−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ370000000000000000000
χ65888−2+25−2−25−2+25−2−258-2-2−2+25−2−2500001−521+52−2+25−2−25-2-21−521+52-200000000001−521−521+521+521−521+5200000000000000000000000000000000000
χ66888−2+25−2−25−2+25−2−25-8-2-2−2+25−2−2500001−521+522−252+25221−521+52-20000000000−1+52−1+52−1−52−1−521−521+5200000000000000000000000000000000000
χ67888−2−25−2+25−2−25−2+258-2-2−2−25−2+2500001+521−52−2−25−2+25-2-21+521−52-200000000001+521+521−521−521+521−5200000000000000000000000000000000000
χ68888−2−25−2+25−2−25−2+25-8-2-2−2−25−2+2500001+521−522+252−25221+521−52-20000000000−1−52−1−52−1+52−1+521+521−5200000000000000000000000000000000000
χ6988-8−2+25−2−25−2+25−2−250-2-22−252+2500001−521+520025−251−521+52200000000005−52−5+52−5−525+52−1+52−1−5200000000000000000000000000000000000
χ7088-8−2+25−2−25−2+25−2−250-2-22−252+2500001−521+5200−25251−521+5220000000000−5+525−525+52−5−52−1+52−1−5200000000000000000000000000000000000
χ7188-8−2−25−2+25−2−25−2+250-2-22+252−2500001+521−520025−251+521−5220000000000−5−525+525−52−5+52−1−52−1+5200000000000000000000000000000000000
χ7288-8−2−25−2+25−2−25−2+250-2-22+252−2500001+521−5200−25251+521−52200000000005+52−5−52−5+525−52−1−52−1+5200000000000000000000000000000000000
χ738-8088-8-80-2200008i−8i-2-2000022000000000000000000000−2i2i00000000000000000000000000000
χ748-8088-8-80-220000−8i8i-2-20000220000000000000000000002i−2i00000000000000000000000000000
χ7516-160−4+45−4−454−454+450-440000001−51+50000−1+5−1−50000000000000000000000000000000000000000000000000000
χ7616-160−4−45−4+454+454−450-440000001+51−50000−1−5−1+50000000000000000000000000000000000000000000000000000

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