Finite Group Databasebeta

← Group #12012403

Character table — Group #12012403

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222444444888888888888161616161616161616161616161616161616161616161616161616161616164040404040408080808080
order1222225510101010101022101010104444101010102020202044488202020202020202020202020202020202020404040404040404022444444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-11-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1
χ411111111111111111111111111111111-11-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-111111111111-11-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-111-1-1
χ611111111111111111111-1-111111111111-11-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111
χ711111111111111111111-1-11111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-111
χ811111111111111111111-1-11111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-1-1
χ92222222222222222222200-2-22222-2-2-2-200000-2-20000000000000000000000002200-2-200000
χ102222222222222222222200-2-22222-2-2-2-200000-2-2000000000000000000000000-2-2002200000
χ1122222222222222-2-2222200-22-2-2-2-2-2-2-2-20000022000000000000000000000000002200-20000
χ1222222222222222-2-2222200-22-2-2-2-2-2-2-2-2000002200000000000000000000000000-2-20020000
χ1322222222222222-2-22222222-2-2-2-2-222220-2000-2-20000-2-2-2-2000022220000000000000000000
χ1422222222222222-2-22222-2-22-2-2-2-2-2222202000-2-2000022220000-2-2-2-20000000000000000000
χ15222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−522222−1+52−1+52−1−52−1−52−1+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+52−1+52−1+52−1−52−1−52−1−52−1−5200000000000
χ16222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-22-2-2-2−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+5200000000000
χ17222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522-22-2-2−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+5200000000000
χ18222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−52-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-222−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200000000000
χ19222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52222-21−521−521+521+52−1+52−1+52−1−52−1−520-20001−521+52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ361−521−521+521+52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−1+52−1+52−1−52−1−52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ3600000000000
χ20222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52222-21−521−521+521+52−1+52−1+52−1−52−1−520-20001−521+52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ361−521−521+521+52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−1+52−1+52−1−52−1−52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ3600000000000
χ21222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52-2-22-21−521−521+521+52−1+52−1+52−1−52−1−52020001−521+52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−1+52−1+52−1−52−1−52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ361−521−521+521+52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ3600000000000
χ22222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52-2-22-21−521−521+521+52−1+52−1+52−1−52−1−52020001−521+52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−1+52−1+52−1−52−1−52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ361−521−521+521+52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ3600000000000
χ23222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+522222−1−52−1−52−1+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200000000000
χ24222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-22-2-2-2−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−5200000000000
χ25222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522-22-2-2−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−5200000000000
χ26222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-222−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200000000000
χ27222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52222-21+521+521−521−52−1−52−1−52−1+52−1+520-20001+521−52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ281+521+521−521−52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−1−52−1−52−1+52−1+52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ2800000000000
χ28222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52222-21+521+521−521−52−1−52−1−52−1+52−1+520-20001+521−52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ281+521+521−521−52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−1−52−1−52−1+52−1+52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ2800000000000
χ29222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52-2-22-21+521+521−521−52−1−52−1−52−1+52−1+52020001+521−52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−1−52−1−52−1+52−1+52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ281+521+521−521−52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ2800000000000
χ30222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52-2-22-21+521+521−521−52−1−52−1−52−1+52−1+52020001+521−52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−1−52−1−52−1+52−1+52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ281+521+521−521−52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ2800000000000
χ312-2-222-22222-2-2-2-2-2222-2-200002-22-200000002−20000000000000000002−22−22−22−200002i−2i000i2−i2
χ322-2-222-22222-2-2-2-2-2222-2-200002-22-200000002−20000000000000000002−22−22−22−20000−2i2i000−i2i2
χ332-2-222-22222-2-2-2-2-2222-2-200002-22-20000000−22000000000000000000−22−22−22−2200002i−2i000−i2i2
χ342-2-222-22222-2-2-2-2-2222-2-200002-22-20000000−22000000000000000000−22−22−22−220000−2i2i000i2−i2
χ35444444−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−544−1+5−1−5−1+5−1−500-4-4−1+5−1+5−1−5−1−51−51−51+51+5000001−51+500000000000000000000000000000000000
χ36444444−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4-4−1+5−1−5−1+5−1−500-441−51−51+51+51−51−51+51+500000−1+5−1−500000000000000000000000000000000000
χ37444444−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+544−1−5−1+5−1−5−1+500-4-4−1−5−1−5−1+5−1+51+51+51−51−5000001+51−500000000000000000000000000000000000
χ38444444−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-4-4−1−5−1+5−1−5−1+500-441+51+51−51−51+51+51−51−500000−1−5−1+500000000000000000000000000000000000
χ394444-4-44444444400-4-4-4-400000000000020-2000022220000-2-2-2-200000000000000000000000
χ404444-4-44444444400-4-4-4-4000000000000-2020000-2-2-2-20000222200000000000000000000000
χ414444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5001−51+51−51+5000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3620-20000−2ζ28−2ζ12−2ζ4−2ζ3600002ζ282ζ122ζ42ζ3600000000000000000000000
χ424444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5001−51+51−51+5000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36-20200002ζ282ζ122ζ42ζ360000−2ζ28−2ζ12−2ζ4−2ζ3600000000000000000000000
χ434444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5001−51+51−51+500000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3620-20000−2ζ12−2ζ28−2ζ36−2ζ400002ζ122ζ282ζ362ζ400000000000000000000000
χ444444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5001−51+51−51+500000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36-20200002ζ122ζ282ζ362ζ40000−2ζ12−2ζ28−2ζ36−2ζ400000000000000000000000
χ454444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5001+51−51+51−500000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2820-20000−2ζ4−2ζ36−2ζ12−2ζ2800002ζ42ζ362ζ122ζ2800000000000000000000000
χ464444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5001+51−51+51−500000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28-20200002ζ42ζ362ζ122ζ280000−2ζ4−2ζ36−2ζ12−2ζ2800000000000000000000000
χ474444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5001+51−51+51−5000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2820-20000−2ζ36−2ζ4−2ζ28−2ζ1200002ζ362ζ42ζ282ζ1200000000000000000000000
χ484444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5001+51−51+51−5000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28-20200002ζ362ζ42ζ282ζ120000−2ζ36−2ζ4−2ζ28−2ζ1200000000000000000000000
χ4944-4-40044-4-444-4-40000002i−2i000000000000000000000000000002i−2i2i−2i000000002-22i−2i0000000
χ5044-4-40044-4-444-4-40000002i−2i000000000000000000000000000002i−2i2i−2i00000000-22−2i2i0000000
χ5144-4-40044-4-444-4-4000000−2i2i00000000000000000000000000000−2i2i−2i2i000000002-2−2i2i0000000
χ5244-4-40044-4-444-4-4000000−2i2i00000000000000000000000000000−2i2i−2i2i00000000-222i−2i0000000
χ534-4-444-44444-4-4-4-44-444-4-40000-44-440000000000000000000000000000000000000000000000
χ544-4-444-4−1+5−1−5−1+5−1−51−51+51−51+54-4−1+5−1−51−51+500001−5−1+51+5−1−5000000000000000000000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ3900000000000
χ554-4-444-4−1+5−1−5−1+5−1−51−51+51−51+54-4−1+5−1−51−51+500001−5−1+51+5−1−5000000000000000000000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ3900000000000
χ564-4-444-4−1+5−1−5−1+5−1−51−51+51−51+5-44−1+5−1−51−51+50000−1+51−5−1−51+5000000022−22000000000000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ3900000000000
χ574-4-444-4−1+5−1−5−1+5−1−51−51+51−51+5-44−1+5−1−51−51+50000−1+51−5−1−51+50000000−2222000000000000000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ3900000000000
χ584-4-444-4−1−5−1+5−1−5−1+51+51−51+51−54-4−1−5−1+51+51−500001+5−1−51−5−1+5000000000000000000000000000−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ3700000000000
χ594-4-444-4−1−5−1+5−1−5−1+51+51−51+51−54-4−1−5−1+51+51−500001+5−1−51−5−1+5000000000000000000000000000ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ3700000000000
χ604-4-444-4−1−5−1+5−1−5−1+51+51−51+51−5-44−1−5−1+51+51−50000−1−51+5−1+51−5000000022−22000000000000000000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ3700000000000
χ614-4-444-4−1−5−1+5−1−5−1+51+51−51+51−5-44−1−5−1+51+51−50000−1−51+5−1+51−50000000−2222000000000000000000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ3700000000000
χ624-4-44-444444-4-4-4-400-4-444000000000000000000000000000000000000000000000000002i−2i00
χ634-4-44-444444-4-4-4-400-4-44400000000000000000000000000000000000000000000000000−2i2i00
χ6488-8-800−2+25−2−252−252+25−2+25−2−252−252+250000004i−4i00000000000000000000000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ140000000000000000000
χ6588-8-800−2+25−2−252−252+25−2+25−2−252−252+25000000−4i4i000000000000000000000000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ140000000000000000000
χ6688-8-800−2−25−2+252+252−25−2−25−2+252+252−250000004i−4i00000000000000000000000000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ380000000000000000000
χ6788-8-800−2−25−2+252+252−25−2−25−2+252+252−25000000−4i4i000000000000000000000000000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ380000000000000000000
χ688-88-80088-8-8-8-888000000000000000000000000000000000000000000000000000000000000
χ698-88-800−2+25−2−252−252+252−252+25−2+25−2−25000000000000000000000000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36000000000000000000000000000
χ708-88-800−2+25−2−252−252+252−252+25−2+25−2−2500000000000000000000000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36000000000000000000000000000
χ718-88-800−2−25−2+252+252−252+252−25−2−25−2+2500000000000000000000000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28000000000000000000000000000
χ728-88-800−2−25−2+252+252−252+252−25−2−25−2+25000000000000000000000000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28000000000000000000000000000
χ738-8-88-88−2+25−2−25−2+25−2−252−252+252−252+25002−252+25−2+25−2−25000000000000000000000000000000000000000000000000000000
χ748-8-88-88−2−25−2+25−2−25−2+252+252−252+252−25002+252−25−2−25−2+25000000000000000000000000000000000000000000000000000000

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