Finite Group Databasebeta

← Group #66091

Character table — Group #66091

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size112222222222222444444444444444448888888810101010202020202020
order1224455881010101010102222820202020404040404040404010101010101010102244224488
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ4111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ51111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-1-1
χ61111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1111
χ71111111-1-1111111-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-1
χ81111111-1-1111111-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-111
χ911-1-111111-1-1-1-1111-11-1-1-1-1111111-1-1-1-111-1-111-1-11-11-111-1-11-1
χ1011-1-111111-1-1-1-1111-11-1-1-1-1111111-1-1-1-111-1-111-1-1-11-11-1-111-11
χ1111-1-111111-1-1-1-111-11-11-1-1-1111111-1-1-1-1-1-111-1-1111-11-1-1-1111-1
χ1211-1-111111-1-1-1-111-11-11-1-1-1111111-1-1-1-1-1-111-1-111-11-1111-1-1-11
χ1311-1-1111-1-1-1-1-1-1111-1-111-1-111-1-1-1-1111111-1-1-1-1111-11-11-1-11-11
χ1411-1-1111-1-1-1-1-1-1111-1-111-1-111-1-1-1-1111111-1-1-1-111-11-11-111-11-1
χ1511-1-1111-1-1-1-1-1-111-111-11-1-111-1-1-1-11111-1-11111-1-11-11-1-111-1-11
χ1611-1-1111-1-1-1-1-1-111-111-11-1-111-1-1-1-11111-1-11111-1-1-11-111-1-111-1
χ1722222−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1−5222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−520000000000
χ1822222−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-22−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+521−521+521−521+520000000000
χ1922222−1+52−1−52-2-2−1+52−1+52−1−52−1−52−1+52−1−5222-2-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−521−521+521−521+520000000000
χ2022222−1+52−1−52-2-2−1+52−1+52−1−52−1−52−1+52−1−52-2-222-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521+521−521+52−1+52−1−52−1+52−1−520000000000
χ2122222−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1+5222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+520000000000
χ2222222−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-22−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−521+521−521+521−521+521−520000000000
χ2322222−1−52−1+52-2-2−1−52−1−52−1+52−1+52−1−52−1+5222-2-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+521+521−521+521−520000000000
χ2422222−1−52−1+52-2-2−1−52−1−52−1+52−1+52−1−52−1+52-2-222-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521−521+521−52−1−52−1+52−1−52−1+520000000000
χ25222-2-2220022222200000-2-2-2-200000000000000002-2-22000000
χ26222-2-2220022222200000-2-2-2-20000000000000000-222-2000000
χ2722-22-22200-2-2-2-2220000022-2-2000000000000000022-2-2000000
χ2822-22-22200-2-2-2-2220000022-2-20000000000000000-2-222000000
χ2922-2-22−1+52−1−52221−521−521+521+52−1+52−1−522-22-2-21−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521+52−1+52−1−521−521+520000000000
χ3022-2-22−1+52−1−52221−521−521+521+52−1+52−1−52-22-22-21−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521+52−1+52−1−521−521+52−1+52−1−520000000000
χ3122-2-22−1+52−1−52-2-21−521−521+521+52−1+52−1−522-2-2221−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+521−521+52−1+52−1−520000000000
χ3222-2-22−1+52−1−52-2-21−521−521+521+52−1+52−1−52-222-221−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521+52−1+52−1−52−1+52−1−521−521+520000000000
χ3322-2-22−1−52−1+52221+521+521−521−52−1−52−1+522-22-2-21+521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521−52−1−52−1+521+521−520000000000
χ3422-2-22−1−52−1+52221+521+521−521−52−1−52−1+52-22-22-21+521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521−52−1−52−1+521+521−52−1−52−1+520000000000
χ3522-2-22−1−52−1+52-2-21+521+521−521−52−1−52−1+522-2-2221+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+521+521−521+521−52−1−52−1+520000000000
χ3622-2-22−1−52−1+52-2-21+521+521−521−52−1−52−1+52-222-221+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521−52−1−52−1+52−1−52−1+521+521−520000000000
χ37444-4-4−1+5−1−500−1+5−1+5−1−5−1−5−1+5−1−5000001−51+51−51+500000000000000000000000000
χ38444-4-4−1−5−1+500−1−5−1−5−1+5−1+5−1−5−1+5000001+51−51+51−500000000000000000000000000
χ3944-44-4−1+5−1−5001−51−51+51+5−1+5−1−500000−1+5−1−51−51+500000000000000000000000000
χ4044-44-4−1−5−1+5001+51+51−51−5−1−5−1+500000−1−5−1+51+51−500000000000000000000000000
χ414-40004422−220000-4-400000000022−2222−220000000000000000000000
χ424-400044−22220000-4-4000000000−2222−22220000000000000000000000
χ434-4000−1+5−1−522−222ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ361−51+5000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000000
χ444-4000−1+5−1−522−22−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ361−51+5000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39000000000000000000
χ454-4000−1+5−1−5−22222ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ361−51+5000000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39000000000000000000
χ464-4000−1+5−1−5−2222−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ361−51+5000000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000000
χ474-4000−1−5−1+522−22−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ281+51−5000000000ζ21+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−ζ37000000000000000000
χ484-4000−1−5−1+522−222ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ281+51−5000000000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37000000000000000000
χ494-4000−1−5−1+5−2222−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ281+51−5000000000−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+ζ37000000000000000000
χ504-4000−1−5−1+5−22222ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ281+51−5000000000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37000000000000000000

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