Finite Group Databasebeta

← Group #87777

Character table — Group #87777

Order 400.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size112222551122225522444410102244441010224444101022444410105510101010252555101010102525
order12551010442210101010445105510102020510551010202010101010101020201010101010102020442020202044442020202044
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111-1-1111111-1-1111111-1-1111111-1-1111111-1-1111111-1-1111111-1-1111111-1-1
χ31-111-1-1i−i1-111-1-1i−i1-111-1-1i−i1-111-1-1i−i1-111-1-1i−i1-111-1-1i−i1-111-1-1i−i1-111-1-1i−i
χ41-111-1-1−ii1-111-1-1−ii1-111-1-1−ii1-111-1-1−ii1-111-1-1−ii1-111-1-1−ii1-111-1-1−ii1-111-1-1−ii
χ522−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−5200
χ622−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+5200
χ72-2−1+52−1−521−521+52002-2−1+52−1−521−521+52002-2−1+52−1−521−521+52002-2−1+52−1−521−521+52002-2−1+52−1−521−521+52002-2−1+52−1−521−521+52002-2−1+52−1−521−521+52002-2−1+52−1−521−521+5200
χ82-2−1−52−1+521+521−52002-2−1−52−1+521+521−52002-2−1−52−1+521+521−52002-2−1−52−1+521+521−52002-2−1−52−1+521+521−52002-2−1−52−1+521+521−52002-2−1−52−1+521+521−52002-2−1−52−1+521+521−5200
χ9111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ10111111-1-1111111-1-1111111-1-1111111-1-1111111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ111-111-1-1i−i1-111-1-1i−i1-111-1-1i−i1-111-1-1i−i1-111-1-1i−i1-111-1-1i−i-11-1-111−ii-11-1-111−ii
χ121-111-1-1−ii1-111-1-1−ii1-111-1-1−ii1-111-1-1−ii1-111-1-1−ii1-111-1-1−ii-11-1-111i−i-11-1-111i−i
χ1322−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−5200-2-21−521+521−521+5200-2-21−521+521−521+5200
χ1422−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+5200-2-21+521−521+521−5200-2-21+521−521+521−5200
χ152-2−1+52−1−521−521+52002-2−1+52−1−521−521+52002-2−1+52−1−521−521+52002-2−1+52−1−521−521+52002-2−1+52−1−521−521+52002-2−1+52−1−521−521+5200-221−521+52−1+52−1−5200-221−521+52−1+52−1−5200
χ162-2−1−52−1+521+521−52002-2−1−52−1+521+521−52002-2−1−52−1+521+521−52002-2−1−52−1+521+521−52002-2−1−52−1+521+521−52002-2−1−52−1+521+521−5200-221+521−52−1−52−1+5200-221+521−52−1−52−1+5200
χ1711111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ18111111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111iiiiii−i−i−i−i−i−i−i−iii
χ191-111-1-1i−i-11-1-111−ii1-111-1-1i−i1-111-1-1i−i-11-1-111−ii-11-1-111−iii−iii−i−i-11−ii−i−iii1-1
χ201-111-1-1−ii-11-1-111i−i1-111-1-1−ii1-111-1-1−ii-11-1-111i−i-11-1-111i−ii−iii−i−i1-1−ii−i−iii-11
χ2122−1+52−1−52−1+52−1−5200-2-21−521+521−521+520022−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−5200-2-21−521+521−521+5200-2-21−521+521−521+52002i2i−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ700−2i−2iζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ700
χ2222−1−52−1+52−1−52−1+5200-2-21+521−521+521−520022−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+5200-2-21+521−521+521−5200-2-21+521−521+521−52002i2i−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ1900−2i−2iζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ1900
χ232-2−1+52−1−521−521+5200-221−521+52−1+52−1−52002-2−1+52−1−521−521+52002-2−1+52−1−521−521+5200-221−521+52−1+52−1−5200-221−521+52−1+52−1−52002i−2i−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ700−2i2iζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ700
χ242-2−1−52−1+521+521−5200-221+521−52−1−52−1+52002-2−1−52−1+521+521−52002-2−1−52−1+521+521−5200-221+521−52−1−52−1+5200-221+521−52−1−52−1+52002i−2i−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ1900−2i2iζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ1900
χ2511111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ26111111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111−i−i−i−i−i−iiiiiiiii−i−i
χ271-111-1-1i−i-11-1-111−ii1-111-1-1i−i1-111-1-1i−i-11-1-111−ii-11-1-111−ii−ii−i−iii1-1i−iii−i−i-11
χ281-111-1-1−ii-11-1-111i−i1-111-1-1−ii1-111-1-1−ii-11-1-111i−i-11-1-111i−i−ii−i−iii-11i−iii−i−i1-1
χ2922−1+52−1−52−1+52−1−5200-2-21−521+521−521+520022−1+52−1−52−1+52−1−520022−1+52−1−52−1+52−1−5200-2-21−521+521−521+5200-2-21−521+521−521+5200−2i−2iζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7002i2i−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ700
χ3022−1−52−1+52−1−52−1+5200-2-21+521−521+521−520022−1−52−1+52−1−52−1+520022−1−52−1+52−1−52−1+5200-2-21+521−521+521−5200-2-21+521−521+521−5200−2i−2iζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19002i2i−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ1900
χ312-2−1+52−1−521−521+5200-221−521+52−1+52−1−52002-2−1+52−1−521−521+52002-2−1+52−1−521−521+5200-221−521+52−1+52−1−5200-221−521+52−1+52−1−5200−2i2iζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7002i−2i−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ700
χ322-2−1−52−1+521+521−5200-221+521−52−1−52−1+52002-2−1−52−1+521+521−52002-2−1−52−1+521+521−5200-221+521−52−1−52−1+5200-221+521−52−1−52−1+5200−2i2iζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19002i−2i−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ1900
χ332222222222222222−1+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+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−520000000000000000
χ34222222-2-2222222-2-2−1+52−1+52−1+52−1+52−1+52−1+521−521−52−1−52−1−52−1−52−1−52−1−52−1−521+521+52−1+52−1+52−1+52−1+52−1+52−1+521−521−52−1−52−1−52−1−52−1−52−1−52−1−521+521+520000000000000000
χ352-222-2-22i−2i2-222-2-22i−2i−1+521−52−1+52−1+521−521−52−ζ11−ζ19ζ11+ζ19−1−521+52−1−52−1−521+521+52−ζ3−ζ7ζ3+ζ7−1+521−52−1+52−1+521−521−52−ζ11−ζ19ζ11+ζ19−1−521+52−1−52−1−521+521+52−ζ3−ζ7ζ3+ζ70000000000000000
χ362-222-2-2−2i2i2-222-2-2−2i2i−1+521−52−1+52−1+521−521−52ζ11+ζ19−ζ11−ζ19−1−521+52−1−52−1−521+521+52ζ3+ζ7−ζ3−ζ7−1+521−52−1+52−1+521−521−52ζ11+ζ19−ζ11−ζ19−1−521+52−1−52−1−521+521+52ζ3+ζ7−ζ3−ζ70000000000000000
χ3744−1+5−1−5−1+5−1−50044−1+5−1−5−1+5−1−500−1+5−1+53−52-13−52-100−1−5−1−5-13+52-13+5200−1+5−1+53−52-13−52-100−1−5−1−5-13+52-13+52000000000000000000
χ3844−1−5−1+5−1−5−1+50044−1−5−1+5−1−5−1+500−1+5−1+5-13−52-13−5200−1−5−1−53+52-13+52-100−1+5−1+5-13−52-13−5200−1−5−1−53+52-13+52-1000000000000000000
χ394-4−1+5−1−51−51+5004-4−1+5−1−51−51+500−1+51−53−52-1−3+52100−1−51+5-13+521−3−5200−1+51−53−52-1−3+52100−1−51+5-13+521−3−52000000000000000000
χ404-4−1−5−1+51+51−5004-4−1−5−1+51+51−500−1+51−5-13−521−3+5200−1−51+53+52-1−3−52100−1+51−5-13−521−3+5200−1−51+53+52-1−3−521000000000000000000
χ412222222222222222−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+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+52−1+52−1+52−1+52−1+52−1+52−1+520000000000000000
χ42222222-2-2222222-2-2−1−52−1−52−1−52−1−52−1−52−1−521+521+52−1+52−1+52−1+52−1+52−1+52−1+521−521−52−1−52−1−52−1−52−1−52−1−52−1−521+521+52−1+52−1+52−1+52−1+52−1+52−1+521−521−520000000000000000
χ432-222-2-22i−2i2-222-2-22i−2i−1−521+52−1−52−1−521+521+52−ζ3−ζ7ζ3+ζ7−1+521−52−1+52−1+521−521−52−ζ11−ζ19ζ11+ζ19−1−521+52−1−52−1−521+521+52−ζ3−ζ7ζ3+ζ7−1+521−52−1+52−1+521−521−52−ζ11−ζ19ζ11+ζ190000000000000000
χ442-222-2-2−2i2i2-222-2-2−2i2i−1−521+52−1−52−1−521+521+52ζ3+ζ7−ζ3−ζ7−1+521−52−1+52−1+521−521−52ζ11+ζ19−ζ11−ζ19−1−521+52−1−52−1−521+521+52ζ3+ζ7−ζ3−ζ7−1+521−52−1+52−1+521−521−52ζ11+ζ19−ζ11−ζ190000000000000000
χ4544−1+5−1−5−1+5−1−50044−1+5−1−5−1+5−1−500−1−5−1−5-13+52-13+5200−1+5−1+53−52-13−52-100−1−5−1−5-13+52-13+5200−1+5−1+53−52-13−52-1000000000000000000
χ4644−1−5−1+5−1−5−1+50044−1−5−1+5−1−5−1+500−1−5−1−53+52-13+52-100−1+5−1+5-13−52-13−5200−1−5−1−53+52-13+52-100−1+5−1+5-13−52-13−52000000000000000000
χ474-4−1+5−1−51−51+5004-4−1+5−1−51−51+500−1−51+5-13+521−3−5200−1+51−53−52-1−3+52100−1−51+5-13+521−3−5200−1+51−53−52-1−3+521000000000000000000
χ484-4−1−5−1+51+51−5004-4−1−5−1+51+51−500−1−51+53+52-1−3−52100−1+51−5-13−521−3+5200−1−51+53+52-1−3−52100−1+51−5-13−521−3+52000000000000000000
χ4922222222-2-2-2-2-2-2-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521−521−521−521−521−521−521−521−521+521+521+521+521+521+521+521+520000000000000000
χ50222222-2-2-2-2-2-2-2-222−1+52−1+52−1+52−1+52−1+52−1+521−521−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521−521−521−521−521−521−52−1+52−1+521+521+521+521+521+521+52−1−52−1−520000000000000000
χ512-222-2-22i−2i-22-2-222−2i2i−1+521−52−1+52−1+521−521−52−ζ11−ζ19ζ11+ζ19−1−521+52−1−52−1−521+521+52−ζ3−ζ7ζ3+ζ71−52−1+521−521−52−1+52−1+52ζ11+ζ19−ζ11−ζ191+52−1−521+521+52−1−52−1−52ζ3+ζ7−ζ3−ζ70000000000000000
χ522-222-2-2−2i2i-22-2-2222i−2i−1+521−52−1+52−1+521−521−52ζ11+ζ19−ζ11−ζ19−1−521+52−1−52−1−521+521+52ζ3+ζ7−ζ3−ζ71−52−1+521−521−52−1+52−1+52−ζ11−ζ19ζ11+ζ191+52−1−521+521+52−1−52−1−52−ζ3−ζ7ζ3+ζ70000000000000000
χ5344−1+5−1−5−1+5−1−500-4-41−51+51−51+500−1+5−1+53−52-13−52-100−1−5−1−5-13+52-13+52001−51−5−3+521−3+521001+51+51−3−521−3−52000000000000000000
χ5444−1−5−1+5−1−5−1+500-4-41+51−51+51−500−1+5−1+5-13−52-13−5200−1−5−1−53+52-13+52-1001−51−51−3+521−3+52001+51+5−3−521−3−521000000000000000000
χ554-4−1+5−1−51−51+500-441−51+5−1+5−1−500−1+51−53−52-1−3+52100−1−51+5-13+521−3−52001−5−1+5−3+5213−52-1001+5−1−51−3−52-13+52000000000000000000
χ564-4−1−5−1+51+51−500-441+51−5−1−5−1+500−1+51−5-13−521−3+5200−1−51+53+52-1−3−521001−5−1+51−3+52-13−52001+5−1−5−3−5213+52-1000000000000000000
χ5722222222-2-2-2-2-2-2-2-2−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521+521+521+521+521+521+521+521+521−521−521−521−521−521−521−521−520000000000000000
χ58222222-2-2-2-2-2-2-2-222−1−52−1−52−1−52−1−52−1−52−1−521+521+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521+521+521+521+521+521+52−1−52−1−521−521−521−521−521−521−52−1+52−1+520000000000000000
χ592-222-2-22i−2i-22-2-222−2i2i−1−521+52−1−52−1−521+521+52−ζ3−ζ7ζ3+ζ7−1+521−52−1+52−1+521−521−52−ζ11−ζ19ζ11+ζ191+52−1−521+521+52−1−52−1−52ζ3+ζ7−ζ3−ζ71−52−1+521−521−52−1+52−1+52ζ11+ζ19−ζ11−ζ190000000000000000
χ602-222-2-2−2i2i-22-2-2222i−2i−1−521+52−1−52−1−521+521+52ζ3+ζ7−ζ3−ζ7−1+521−52−1+52−1+521−521−52ζ11+ζ19−ζ11−ζ191+52−1−521+521+52−1−52−1−52−ζ3−ζ7ζ3+ζ71−52−1+521−521−52−1+52−1+52−ζ11−ζ19ζ11+ζ190000000000000000
χ6144−1+5−1−5−1+5−1−500-4-41−51+51−51+500−1−5−1−5-13+52-13+5200−1+5−1+53−52-13−52-1001+51+51−3−521−3−52001−51−5−3+521−3+521000000000000000000
χ6244−1−5−1+5−1−5−1+500-4-41+51−51+51−500−1−5−1−53+52-13+52-100−1+5−1+5-13−52-13−52001+51+5−3−521−3−521001−51−51−3+521−3+52000000000000000000
χ634-4−1+5−1−51−51+500-441−51+5−1+5−1−500−1−51+5-13+521−3−5200−1+51−53−52-1−3+521001+5−1−51−3−52-13+52001−5−1+5−3+5213−52-1000000000000000000
χ644-4−1−5−1+51+51−500-441+51−5−1−5−1+500−1−51+53+52-1−3−52100−1+51−5-13−521−3+52001+5−1−5−3−5213+52-1001−5−1+51−3+52-13−52000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.