Finite Group Databasebeta

← Group #10613161

Character table — Group #10613161

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size11112222222222444444444444444488888888888888888888810101010161616162020202020202020404040
order1222445510101010101024444488101010102020202044820202020202020202020404040404040404022442020202024444488248
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-111111111-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1
χ411111111111111111111-1-111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ51111111111111111-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-11
χ61111111111111111-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1
χ71111111111111111-1-1-1-1-1-11111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1
χ81111111111111111-1-1-1-1-1-11111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-11
χ911111111111111-1-111-1-111-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111111-1-1
χ1011111111111111-1-111-1-111-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111
χ1111111111111111-1-111-1-1-1-1-1-1-1-11111-111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-111
χ1211111111111111-1-111-1-1-1-1-1-1-1-11111-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1111-1-1
χ1311111111111111-1-1-1-11111-1-1-1-11111-11-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-111-11-1
χ1411111111111111-1-1-1-11111-1-1-1-11111-11-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11-11
χ1511111111111111-1-1-1-111-1-1-1-1-1-111111-11-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-11-11
χ1611111111111111-1-1-1-111-1-1-1-1-1-111111-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11111-11-1
χ17222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52222−1+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+52−1−52−1−520000−1+52−1−52−1+52−1−5200000000000
χ18222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52222222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2−1+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+5200001−521+521−521+5200000000000
χ19222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222-2-2-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-22−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200001−521+521−521+5200000000000
χ20222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222-2-2-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+520000−1+52−1−52−1+52−1−5200000000000
χ21222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-222-2-2221−521−521+521+52−1+52−1+52−1−52−1−522-2-21−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+5200001−521+52−1+52−1−5200000000000
χ22222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-222-2-2-2-21−521−521+521+52−1+52−1+52−1−52−1−52-2221−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−520000−1+52−1−521−521+5200000000000
χ23222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2-2-222221−521−521+521+52−1+52−1+52−1−52−1−52-22-21−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+520000−1+52−1−521−521+5200000000000
χ24222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2-2-222-2-21−521−521+521+52−1+52−1+52−1−52−1−522-221−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200001−521+52−1+52−1−5200000000000
χ25222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52222−1−52−1+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+520000−1−52−1+52−1−52−1+5200000000000
χ26222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52222222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−5200001+521−521+521−5200000000000
χ27222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222-2-2-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-22−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200001+521−521+521−5200000000000
χ28222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222-2-2-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222-2−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−520000−1−52−1+52−1−52−1+5200000000000
χ29222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-222-2-2221+521+521−521−52−1−52−1−52−1+52−1+522-2-21+521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−5200001+521−52−1−52−1+5200000000000
χ30222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-222-2-2-2-21+521+521−521−52−1−52−1−52−1+52−1+52-2221+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+520000−1−52−1+521+521−5200000000000
χ31222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2-2-222221+521+521−521−52−1−52−1−52−1+52−1+52-22-21+521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−520000−1−52−1+521+521−5200000000000
χ32222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2-2-222-2-21+521+521−521−52−1−52−1−52−1+52−1+522-221+521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+5200001+521−52−1−52−1+5200000000000
χ332222-2-2222222222-20000002222-2-2-2-2000-2-2000000000000000022-2-20000-22000000000
χ342222-2-2222222222-20000002222-2-2-2-2000-2-20000000000000000-2-22200002-2000000000
χ352222-2-222222222-22000000-2-2-2-2-2-2-2-200022000000000000000022-2-200002-2000000000
χ362222-2-222222222-22000000-2-2-2-2-2-2-2-2000220000000000000000-2-2220000-22000000000
χ3722-2-22-222-2-22-22-200002i−2i0000002-22-20000000002i−2i2i−2i000000002-22-20000002i−2i0000000
χ3822-2-22-222-2-22-22-200002i−2i0000002-22-20000000002i−2i2i−2i00000000-22-22000000−2i2i0000000
χ3922-2-22-222-2-22-22-20000−2i2i0000002-22-2000000000−2i2i−2i2i000000002-22-2000000−2i2i0000000
χ4022-2-22-222-2-22-22-20000−2i2i0000002-22-2000000000−2i2i−2i2i00000000-22-220000002i−2i0000000
χ4122-2-2-2222-2-22-22-2002i−2i00000000-22-22000002i−2i2i−2i0000000000002-2-22000000002i−2i00000
χ4222-2-2-2222-2-22-22-2002i−2i00000000-22-22000002i−2i2i−2i000000000000-222-200000000−2i2i00000
χ4322-2-2-2222-2-22-22-200−2i2i00000000-22-2200000−2i2i−2i2i0000000000002-2-2200000000−2i2i00000
χ4422-2-2-2222-2-22-22-200−2i2i00000000-22-2200000−2i2i−2i2i000000000000-222-2000000002i−2i00000
χ454444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−54-4000000−1+5−1+5−1−5−1−51−51−51+51+50001−51+500000000000000000000000000000000000
χ464444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5-440000001−51−51+51+51−51−51+51+5000−1+5−1−500000000000000000000000000000000000
χ474444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+54-4000000−1−5−1−5−1+5−1+51+51+51−51−50001+51−500000000000000000000000000000000000
χ484444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5-440000001+51+51−51−51+51+51−51−5000−1−5−1+500000000000000000000000000000000000
χ4944-4-44-4−1+5−1−51−51+5−1+51−5−1−51+500004i−4i000000−1+51−5−1−51+5000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14000000000000000000000000000
χ5044-4-44-4−1+5−1−51−51+5−1+51−5−1−51+50000−4i4i000000−1+51−5−1−51+50000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ14000000000000000000000000000
χ5144-4-44-4−1−5−1+51+51−5−1−51+5−1+51−500004i−4i000000−1−51+5−1+51−5000000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ38000000000000000000000000000
χ5244-4-44-4−1−5−1+51+51−5−1−51+5−1+51−50000−4i4i000000−1−51+5−1+51−50000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ38000000000000000000000000000
χ5344-4-4-44−1+5−1−51−51+5−1+51−5−1−51+5004i−4i000000001−5−1+51+5−1−500000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ140000000000000000000000000000000
χ5444-4-4-44−1+5−1−51−51+5−1+51−5−1−51+500−4i4i000000001−5−1+51+5−1−5000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ140000000000000000000000000000000
χ5544-4-4-44−1−5−1+51+51−5−1−51+5−1+51−5004i−4i000000001+5−1−51−5−1+500000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ380000000000000000000000000000000
χ5644-4-4-44−1−5−1+51+51−5−1−51+5−1+51−500−4i4i000000001+5−1−51−5−1+5000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ380000000000000000000000000000000
χ574-44-40044-4-4-44-440000002i2−2i20000000000000000000002i2−2i22i2−2i200000000000000000000000
χ584-44-40044-4-4-44-44000000−2i22i2000000000000000000000−2i22i2−2i22i200000000000000000000000
χ594-44-400−1+5−1−51−51+51−5−1+51+5−1−50000002i2−2i22ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ390000000000000000000
χ604-44-400−1+5−1−51−51+51−5−1+51+5−1−50000002i2−2i2−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ390000000000000000000
χ614-44-400−1+5−1−51−51+51−5−1+51+5−1−5000000−2i22i22ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ390000000000000000000
χ624-44-400−1+5−1−51−51+51−5−1+51+5−1−5000000−2i22i2−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ390000000000000000000
χ634-44-400−1−5−1+51+51−51+5−1−51−5−1+50000002i2−2i2−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ370000000000000000000
χ644-44-400−1−5−1+51+51−51+5−1−51−5−1+50000002i2−2i22ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000ζ21+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
χ654-44-400−1−5−1+51+51−51+5−1−51−5−1+5000000−2i22i2−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ370000000000000000000
χ664-44-400−1−5−1+51+51−51+5−1−51−5−1+5000000−2i22i22ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000−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
χ674-4-44004444-4-4-4-40000000000000000000000000000000000000000000000000002i2−2i2000
χ684-4-44004444-4-4-4-4000000000000000000000000000000000000000000000000000−2i22i2000
χ698-8-8800−2+25−2−25−2+25−2−252−252−252+252+2500000000000000000000000000000000000000000000000000000000
χ708-8-8800−2−25−2+25−2−25−2+252+252+252−252−2500000000000000000000000000000000000000000000000000000000

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