Finite Group Databasebeta

← Group #10604057

Character table — Group #10604057

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size111122222244445555888888881010101010101010101010101010101010101010101016161616404040404040
order12224488885101010444444202040404040224444444488888888888820202020448888
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-111111111-1-1iiii−i−i−i−i-1-1-1-1iiii−i−i−i−i1111-1-1ii−i−i
χ611111111111111-1-1-1-111111111-1-1−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii1111-1-1−i−iii
χ711111111111111-1-1-1-1-1-1111111-1-1iiii−i−i−i−i-1-1-1-1iiii−i−i−i−i-1-1-1-111−i−iii
χ811111111111111-1-1-1-1-1-1111111-1-1−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii-1-1-1-111ii−i−i
χ9111111-1-1-1-1111111111-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-11-1
χ10111111-1-1-1-1111111111-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11-1-11-11
χ11111111-1-1-1-111111111-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-11-11
χ12111111-1-1-1-111111111-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-111-11-1
χ13111111-1-1-1-11111-1-1-1-11-111-1-1-1-1-1-1iiii−i−i−i−i1111−i−i−i−iiiii11-1-1-11i−i−ii
χ14111111-1-1-1-11111-1-1-1-11-111-1-1-1-1-1-1−i−i−i−iiiii1111iiii−i−i−i−i11-1-1-11−iii−i
χ15111111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-1iiii−i−i−i−i1111−i−i−i−iiiii-1-1111-1−iii−i
χ16111111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-1−i−i−i−iiiii1111iiii−i−i−i−i-1-1111-1i−i−ii
χ172222-2-200002222222200-2-20000-2-200000000000022-2-222-2-20000000000
χ182222-2-200002222222200-2-20000-2-2000000000000-2-222-2-2220000000000
χ192222-2-200002222-2-2-2-200-2-20000220000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ202222-2-200002222-2-2-2-200-2-2000022000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ2122-2-22-2000022-2-222-2-2002-20000-2222-2-222-2-20000000000000000000000
χ2222-2-22-2000022-2-222-2-2002-20000-22-2-222-2-2220000000000000000000000
χ2322-2-22-2000022-2-2-2-222002-200002-22i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ2422-2-22-2000022-2-2-2-222002-200002-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ2522-2-2-2222-2-222-2-222-2-200-2222-2-22-20000000022-2-2000000000000000000
χ2622-2-2-2222-2-222-2-2-2-22200-2222-2-2-2200000000-2-222000000000000000000
χ2722-2-2-22-2-22222-2-222-2-200-22-2-2222-200000000-2-222000000000000000000
χ2822-2-2-22-2-22222-2-2-2-22200-22-2-222-220000000022-2-2000000000000000000
χ292-22-200i2−i2i2−i22-22-22i−2i2i−2i0000i2−i2i2−i2001+i−1−i1+i−1−i1−i−1+i1−i−1+i2−22−200−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ302-22-200i2−i2i2−i22-22-22i−2i2i−2i0000i2−i2i2−i200−1−i1+i−1−i1+i−1+i1−i−1+i1−i2−22−2002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ312-22-200i2−i2i2−i22-22-2−2i2i−2i2i0000i2−i2i2−i2001−i−1+i1−i−1+i1+i−1−i1+i−1−i−22−2200−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ322-22-200i2−i2i2−i22-22-2−2i2i−2i2i0000i2−i2i2−i200−1+i1−i−1+i1−i−1−i1+i−1−i1+i−22−22002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ332-22-200−i2i2−i2i22-22-22i−2i2i−2i0000−i2i2−i2i2001+i−1−i1+i−1−i1−i−1+i1−i−1+i−22−22002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ342-22-200−i2i2−i2i22-22-22i−2i2i−2i0000−i2i2−i2i200−1−i1+i−1−i1+i−1+i1−i−1+i1−i−22−2200−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ352-22-200−i2i2−i2i22-22-2−2i2i−2i2i0000−i2i2−i2i2001−i−1+i1−i−1+i1+i−1−i1+i−1−i2−22−2002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ362-22-200−i2i2−i2i22-22-2−2i2i−2i2i0000−i2i2−i2i200−1+i1−i−1+i1−i−1−i1+i−1−i1+i2−22−200−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ372-2-2200i2−i2−i2i22-2-222i−2i−2i2i0000i2−i2−i2i2001+i−1−i−1−i1+i1−i−1+i−1+i1−i2−2−22−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ382-2-2200i2−i2−i2i22-2-222i−2i−2i2i0000i2−i2−i2i200−1−i1+i1+i−1−i−1+i1−i1−i−1+i2−2−222ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
χ392-2-2200i2−i2−i2i22-2-22−2i2i2i−2i0000i2−i2−i2i2001−i−1+i−1+i1−i1+i−1−i−1−i1+i−222−2−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ402-2-2200i2−i2−i2i22-2-22−2i2i2i−2i0000i2−i2−i2i200−1+i1−i1−i−1+i−1−i1+i1+i−1−i−222−22ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ412-2-2200−i2i2i2−i22-2-222i−2i−2i2i0000−i2i2i2−i2001+i−1−i−1−i1+i1−i−1+i−1+i1−i−222−22ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
χ422-2-2200−i2i2i2−i22-2-222i−2i−2i2i0000−i2i2i2−i200−1−i1+i1+i−1−i−1+i1−i1−i−1+i−222−2−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ432-2-2200−i2i2i2−i22-2-22−2i2i2i−2i0000−i2i2i2−i2001−i−1+i−1+i1−i1+i−1−i−1−i1+i2−2−222ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ442-2-2200−i2i2i2−i22-2-22−2i2i2i−2i0000−i2i2i2−i200−1+i1−i1−i−1+i−1−i1+i1+i−1−i2−2−22−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ454444444444-1-1-1-1000044-1-1-1-1-1-10000000000000000000000-1-1-1-1000000
χ464444444444-1-1-1-10000-4-4-1-1-1-1-1-100000000000000000000001111000000
χ47444444-4-4-4-4-1-1-1-100004-4-1-111110000000000000000000000-1-111000000
χ48444444-4-4-4-4-1-1-1-10000-44-1-11111000000000000000000000011-1-1000000
χ4944-4-4-4444-4-4-1-1110000001-1-1-1110000000000000000000000i5−i5i5−i5000000
χ5044-4-4-4444-4-4-1-1110000001-1-1-1110000000000000000000000−i5i5−i5i5000000
χ5144-4-4-44-4-444-1-1110000001-111-1-10000000000000000000000i5−i5−i5i5000000
χ5244-4-4-44-4-444-1-1110000001-111-1-10000000000000000000000−i5i5i5−i5000000
χ538888-8-80000-2-2-2-200000022000000000000000000000000000000000000
χ5488-8-88-80000-2-222000000-22000000000000000000000000000000000000
χ558-88-8004i2−4i24i2−4i2-22-2200000000−i2i2−i2i200000000000000000000000000000000
χ568-88-800−4i24i2−4i24i2-22-2200000000i2−i2i2−i200000000000000000000000000000000
χ578-8-88004i2−4i2−4i24i2-222-200000000−i2i2i2−i200000000000000000000000000000000
χ588-8-8800−4i24i24i2−4i2-222-200000000i2−i2−i2i200000000000000000000000000000000

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