Finite Group Databasebeta

← Group #10601857

Character table — Group #10601857

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size11112222222222224444444444488888888888888888888816161616162020202020204040404040
order1222444455101010101010444202020202020202048820202020202020202020404040404040404042020202044888844488
χ11111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1
χ41111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111
χ51111111111111111-1-1111111111-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11111111-1-1-1-1
χ61111111111111111-1-1111111111-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-111
χ81111111111111111-1-1111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-111-1-1
χ922222222−1+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+52−1−52222−1+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+52−1−52−1−52−1−52−1−522−1+52−1+52−1−52−1−5200000000000
χ1022222222−1+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+52−1−522-2-2−1+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+52-21−521−521+521+5200000000000
χ1122222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-22−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52-222−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-21−521−521+521+5200000000000
χ1222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-22−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52-2-2-2−1+52−1−521−521−521+521+521−521−521+521+521−521−521−521−521+521+521+521+522−1+52−1+52−1−52−1−5200000000000
χ1322222222−1−52−1+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+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+522−1−52−1−52−1+52−1+5200000000000
χ1422222222−1−52−1+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+522-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52-21+521+521−521−5200000000000
χ1522222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-22−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52-222−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-21+521+521−521−5200000000000
χ1622222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-22−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52-2-2-2−1−52−1+521+521+521−521−521+521+521−521−521+521+521+521+521−521−521−521−522−1−52−1−52−1+52−1+5200000000000
χ1722222-2-222222222200-22222-2-2-2-2000-2-2000000000000000000000220000-20000
χ1822222-2-222222222200-22222-2-2-2-2000-2-2000000000000000000000-2-2000020000
χ192222-222-22222222222-2-2-2-2-22222-200-2-22222-2-2-2-2000000000000000000000000
χ202222-222-222222222-2-2-2-2-2-2-22222200-2-2-2-2-2-22222000000000000000000000000
χ212222-222-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222-21−521−521+521+52−1+52−1−52−1+52−1−52-2001−521+52−1+52−1+52−1−52−1−521−521−521+521+52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ360ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ3600000000000
χ222222-222-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222-21−521−521+521+52−1+52−1−52−1+52−1−52-2001−521+52−1+52−1+52−1−52−1−521−521−521+521+52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ360−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ3600000000000
χ232222-222-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2-21−521−521+521+52−1+52−1−52−1+52−1−522001−521+521−521−521+521+52−1+52−1+52−1−52−1−52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ360−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ3600000000000
χ242222-222-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2-21−521−521+521+52−1+52−1−52−1+52−1−522001−521+521−521−521+521+52−1+52−1+52−1−52−1−52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ360ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ3600000000000
χ252222-222-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222-21+521+521−521−52−1−52−1+52−1−52−1+52-2001+521−52−1−52−1−52−1+52−1+521+521+521−521−52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ280−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ2800000000000
χ262222-222-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222-21+521+521−521−52−1−52−1+52−1−52−1+52-2001+521−52−1−52−1−52−1+52−1+521+521+521−521−52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ280ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ2800000000000
χ272222-222-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2-21+521+521−521−52−1−52−1+52−1−52−1+522001+521−521+521+521−521−52−1−52−1−52−1+52−1+52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ280ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ2800000000000
χ282222-222-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2-21+521+521−521−52−1−52−1+52−1−52−1+522001+521−521+521+521−521−52−1−52−1−52−1+52−1+52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ280−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ2800000000000
χ292222-2-2-2-222222222002-2-2-2-2-2-2-2-20002200000000000000000000000000002-200
χ302222-2-2-2-222222222002-2-2-2-2-2-2-2-2000220000000000000000000000000000-2200
χ3122-2-2200-22222-2-2-2-20002-22-2000002−200000000002−22−22−22−2000002-222−2−200000
χ3222-2-2200-22222-2-2-2-20002-22-2000002−200000000002−22−22−22−200000-22−2−22200000
χ3322-2-2200-22222-2-2-2-20002-22-200000−220000000000−22−22−22−22000002-2−2−22200000
χ3422-2-2200-22222-2-2-2-20002-22-200000−220000000000−22−22−22−2200000-2222−2−200000
χ352-2-2202-2022-2-2-2-2222i−2i0000022-2-2000002i−2i2i−2i00000000000000000002−22−2000i2−i2
χ362-2-2202-2022-2-2-2-2222i−2i0000022-2-2000002i−2i2i−2i0000000000000000000−22−22000−i2i2
χ372-2-2202-2022-2-2-2-222−2i2i0000022-2-200000−2i2i−2i2i00000000000000000002−22−2000−i2i2
χ382-2-2202-2022-2-2-2-222−2i2i0000022-2-200000−2i2i−2i2i0000000000000000000−22−22000i2−i2
χ3944444-4-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500-4−1+5−1+5−1−5−1−51−51+51−51+50001−51+500000000000000000000000000000000
χ4044444-4-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+500-4−1−5−1−5−1+5−1+51+51−51+51−50001+51−500000000000000000000000000000000
χ414444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−50041−51−51+51+51−51+51−51+5000−1+5−1−500000000000000000000000000000000
χ424444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+50041+51+51−51−51+51−51+51−5000−1−5−1+500000000000000000000000000000000
χ4344-4-4400-4−1+5−1−5−1+5−1−51−51+51−51+5000−1+51−5−1−51+50000022−220000000000−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+ζ390000000000000000
χ4444-4-4400-4−1+5−1−5−1+5−1−51−51+51−51+5000−1+51−5−1−51+500000−22220000000000ζ7−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−ζ390000000000000000
χ4544-4-4400-4−1−5−1+5−1−5−1+51+51−51+51−5000−1−51+5−1+51−50000022−220000000000ζ21+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−ζ370000000000000000
χ4644-4-4400-4−1−5−1+5−1−5−1+51+51−51+51−5000−1−51+5−1+51−500000−22220000000000−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+ζ370000000000000000
χ4744-4-4-40044444-4-4-4-4000-44-4400000000000000000000000000000000000000000
χ4844-4-4-4004−1+5−1−5−1+5−1−51−51+51−51+50001−5−1+51+5−1−500000000000000000−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+ζ390000000000000000
χ4944-4-4-4004−1+5−1−5−1+5−1−51−51+51−51+50001−5−1+51+5−1−500000000000000000ζ7+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−ζ390000000000000000
χ5044-4-4-4004−1−5−1+5−1−5−1+51+51−51+51−50001+5−1−51−5−1+500000000000000000−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+ζ370000000000000000
χ5144-4-4-4004−1−5−1+5−1−5−1+51+51−51+51−50001+5−1−51−5−1+500000000000000000ζ21−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−ζ370000000000000000
χ524-44-4000044-4-444-4-40000000000000000000000000000000000000002-2-2200000
χ534-44-4000044-4-444-4-4000000000000000000000000000000000000000-222-200000
χ544-4-4404-40−1+5−1−51−51+51−51+5−1+5−1−54i−4i00000−1+5−1−51−51+500000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ140000000000000000000000000000
χ554-4-4404-40−1+5−1−51−51+51−51+5−1+5−1−5−4i4i00000−1+5−1−51−51+5000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ140000000000000000000000000000
χ564-4-4404-40−1−5−1+51+51−51+51−5−1−5−1+54i−4i00000−1−5−1+51+51−500000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ380000000000000000000000000000
χ574-4-4404-40−1−5−1+51+51−51+51−5−1−5−1+5−4i4i00000−1−5−1+51+51−5000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ380000000000000000000000000000
χ584-4-440-44044-4-4-4-4440000000-4-4440000000000000000000000000000000000000
χ594-4-440-440−1+5−1−51−51+51−51+5−1+5−1−500000001−51+5−1+5−1−50000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36000000000000000000000000
χ604-4-440-440−1+5−1−51−51+51−51+5−1+5−1−500000001−51+5−1+5−1−5000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36000000000000000000000000
χ614-4-440-440−1−5−1+51+51−51+51−5−1−5−1+500000001+51−5−1−5−1+5000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28000000000000000000000000
χ624-4-440-440−1−5−1+51+51−51+51−5−1−5−1+500000001+51−5−1−5−1+50000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28000000000000000000000000
χ638-88-80000−2+25−2−252−252+25−2+25−2−252−252+25000000000000000000000000000000000000000000000000
χ648-88-80000−2−25−2+252+252−25−2−25−2+252+252−25000000000000000000000000000000000000000000000000

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