Finite Group Databasebeta

← Group #87778

Character table — Group #87778

Order 400.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11112222222222222222444444444444444410101010101010101010101010101010101010105050
order12225555101010101010101010101010555510101010101010101010101022441010101010101010202020202020202044
χ11111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ511-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1i−i1111-1-1-1-1iiii−i−i−i−ii−i
χ611-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1−ii1111-1-1-1-1−i−i−i−iiiii−ii
χ711-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11i−i-1-1-1-11111iiii−i−i−i−i−ii
χ811-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11−ii-1-1-1-11111−i−i−i−iiiiii−i
χ9222222−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522200−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000
χ10222222−1+52−1−522222−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2001−521−521+521+521−521−521+521+520000000000
χ11222222−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1−52−1+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+522200−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000000
χ12222222−1−52−1+522222−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1−52−1+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+52-2-2001+521+521−521−521+521+521−521−520000000000
χ132222−1+52−1−5222−1+52−1−52−1+52−1−52222222−1+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+52−1−52−1−52002200000000−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200
χ142222−1+52−1−5222−1+52−1−52−1+52−1−52222222−1+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+52−1−52−1−5200-2-2000000001−521−521+521+521−521−521+521+5200
χ152222−1−52−1+5222−1−52−1+52−1−52−1+52222222−1−52−1+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+52002200000000−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200
χ162222−1−52−1+5222−1−52−1+52−1−52−1+52222222−1−52−1+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+5200-2-2000000001+521+521−521−521+521+521−521−5200
χ1722-2-222−1+52−1−5222-2-2−1+52−1−521−521−521+521+52-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+522-200−1+52−1+52−1−52−1−521−521−521+521+520000000000
χ1822-2-222−1+52−1−5222-2-2−1+52−1−521−521−521+521+52-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52-22001−521−521+521+52−1+52−1+52−1−52−1−520000000000
χ1922-2-222−1−52−1+5222-2-2−1−52−1+521+521+521−521−52-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−522-200−1−52−1−52−1+52−1+521+521+521−521−520000000000
χ2022-2-222−1−52−1+5222-2-2−1−52−1+521+521+521−521−52-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52-22001+521+521−521−52−1−52−1−52−1+52−1+520000000000
χ2122-2-2−1+52−1−5222−1+52−1−521−521+5222-2-2-2-21−521+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52002i−2i00000000−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ700
χ2222-2-2−1+52−1−5222−1+52−1−521−521+5222-2-2-2-21−521+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+5200−2i2i00000000ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ700
χ2322-2-2−1−52−1+5222−1−52−1+521+521−5222-2-2-2-21+521−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52002i−2i00000000−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ1900
χ2422-2-2−1−52−1+5222−1−52−1+521+521−5222-2-2-2-21+521−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−5200−2i2i00000000ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ1900
χ252-22-22222-2-2-2-2-2-22-22-2222222-2-2-2-22-22-22-22-20000000000000000000000
χ262-22-222−1+52−1−52-2-2-2-21−521+52−1+521−52−1−521+5222−1+52−1+52−1−52−1−521−521−521+521+52−1+521−52−1+521−52−1−521+52−1−521+520000ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000000000
χ272-22-222−1+52−1−52-2-2-2-21−521+52−1+521−52−1−521+5222−1+52−1+52−1−52−1−521−521−521+521+52−1+521−52−1+521−52−1−521+52−1−521+520000−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ180000000000
χ282-22-222−1−52−1+52-2-2-2-21+521−52−1−521+52−1+521−5222−1−52−1−52−1+52−1+521+521+521−521−52−1−521+52−1−521+52−1+521−52−1+521−520000−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ140000000000
χ292-22-222−1−52−1+52-2-2-2-21+521−52−1−521+52−1+521−5222−1−52−1−52−1+52−1+521+521+521−521−52−1−521+52−1−521+52−1+521−52−1+521−520000ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ140000000000
χ302-22-2−1+52−1−52221−521+521−521+52-2-22-22-2−1+52−1−52−1+52−1−52−1+52−1−521−521+521−521+52−1+521−52−1−521+52−1+521−52−1−521+52000000000000ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ1800
χ312-22-2−1+52−1−52221−521+521−521+52-2-22-22-2−1+52−1−52−1+52−1−52−1+52−1−521−521+521−521+52−1+521−52−1−521+52−1+521−52−1−521+52000000000000−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ1800
χ322-22-2−1−52−1+52221+521−521+521−52-2-22-22-2−1−52−1+52−1−52−1+52−1−52−1+521+521−521+521−52−1−521+52−1+521−52−1−521+52−1+521−52000000000000−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ1400
χ332-22-2−1−52−1+52221+521−521+521−52-2-22-22-2−1−52−1+52−1−52−1+52−1−52−1+521+521−521+521−52−1−521+52−1+521−52−1−521+52−1+521−52000000000000ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ1400
χ342-2-222222-2-222-2-2-22-22-2-22222-2-2-2-2-22-22-22-220000000000000000000000
χ352-2-2222−1+52−1−52-2-2221−521+521−52−1+521+52−1−52-2-2−1+52−1+52−1−52−1−521−521−521+521+521−52−1+521−52−1+521+52−1−521+52−1−520000ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ180000000000
χ362-2-2222−1+52−1−52-2-2221−521+521−52−1+521+52−1−52-2-2−1+52−1+52−1−52−1−521−521−521+521+521−52−1+521−52−1+521+52−1−521+52−1−520000−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000000000
χ372-2-2222−1−52−1+52-2-2221+521−521+52−1−521−52−1+52-2-2−1−52−1−52−1+52−1+521+521+521−521−521+52−1−521+52−1−521−52−1+521−52−1+520000−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ140000000000
χ382-2-2222−1−52−1+52-2-2221+521−521+52−1−521−52−1+52-2-2−1−52−1−52−1+52−1+521+521+521−521−521+52−1−521+52−1−521−52−1+521−52−1+520000ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ140000000000
χ392-2-22−1+52−1−52221−521+52−1+52−1−52-2-2-22-221−521+52−1+52−1−52−1+52−1−521−521+521−521+521−52−1+521+52−1−521−52−1+521+52−1−52000000000000−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ700
χ402-2-22−1+52−1−52221−521+52−1+52−1−52-2-2-22-221−521+52−1+52−1−52−1+52−1−521−521+521−521+521−52−1+521+52−1−521−52−1+521+52−1−52000000000000ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ700
χ412-2-22−1−52−1+52221+521−52−1−52−1+52-2-2-22-221+521−52−1−52−1+52−1−52−1+521+521−521+521−521+52−1−521−52−1+521+52−1−521−52−1+52000000000000ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ1900
χ422-2-22−1−52−1+52221+521−52−1−52−1+52-2-2-22-221+521−52−1−52−1+52−1−52−1+521+521−521+521−521+52−1−521−52−1+521+52−1−521−52−1+52000000000000−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ1900
χ434444−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−53−52-1-13+523−52-1-13+523−523−52-1-1-1-13+523+520000000000000000000000
χ444444−1+5−1−5−1−5−1+5−1+5−1−5−1+5−1−5−1−5−1+5−1−5−1−5−1+5−1+5−1+5−1−5-13+523−52-1-13+523−52-1-1-13+523+523−523−52-1-10000000000000000000000
χ454444−1−5−1+5−1+5−1−5−1−5−1+5−1−5−1+5−1+5−1−5−1+5−1+5−1−5−1−5−1−5−1+5-13−523+52-1-13−523+52-1-1-13−523−523+523+52-1-10000000000000000000000
χ464444−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+53+52-1-13−523+52-1-13−523+523+52-1-1-1-13−523−520000000000000000000000
χ4744-4-4−1+5−1−5−1+5−1−5−1+5−1−51−51+5−1+5−1−51−51−51+51+51−51+53−52-1-13+523−52-1-13+52−3+52−3+521111−3−52−3−520000000000000000000000
χ4844-4-4−1+5−1−5−1−5−1+5−1+5−1−51−51+5−1−5−1+51+51+51−51−51−51+5-13+523−52-1-13+523−52-111−3−52−3−52−3+52−3+52110000000000000000000000
χ4944-4-4−1−5−1+5−1+5−1−5−1−5−1+51+51−5−1+5−1−51−51−51+51+51+51−5-13−523+52-1-13−523+52-111−3+52−3+52−3−52−3−52110000000000000000000000
χ5044-4-4−1−5−1+5−1−5−1+5−1−5−1+51+51−5−1−5−1+51+51+51−51−51+51−53+52-1-13−523+52-1-13−52−3−52−3−521111−3+52−3+520000000000000000000000
χ514-44-4−1+5−1−5−1+5−1−51−51+51−51+51−51+5−1+51−5−1−51+5−1+5−1−53−52-1-13+52−3+5211−3−523−52−3+52-11-113+52−3−520000000000000000000000
χ524-44-4−1+5−1−5−1−5−1+51−51+51−51+51+51−5−1−51+5−1+51−5−1+5−1−5-13+523−52-11−3−52−3+521-113+52−3−523−52−3+52-110000000000000000000000
χ534-44-4−1−5−1+5−1+5−1−51+51−51+51−51−51+5−1+51−5−1−51+5−1−5−1+5-13−523+52-11−3+52−3−521-113−52−3+523+52−3−52-110000000000000000000000
χ544-44-4−1−5−1+5−1−5−1+51+51−51+51−51+51−5−1−51+5−1+51−5−1−5−1+53+52-1-13−52−3−5211−3+523+52−3−52-11-113−52−3+520000000000000000000000
χ554-4-44−1+5−1−5−1+5−1−51−51+5−1+5−1−51−51+51−5−1+51+5−1−51−51+53−52-1-13+52−3+5211−3−52−3+523−521-11-1−3−523+520000000000000000000000
χ564-4-44−1+5−1−5−1−5−1+51−51+5−1+5−1−51+51−51+5−1−51−5−1+51−51+5-13+523−52-11−3−52−3+5211-1−3−523+52−3+523−521-10000000000000000000000
χ574-4-44−1−5−1+5−1+5−1−51+51−5−1−5−1+51−51+51−5−1+51+5−1−51+51−5-13−523+52-11−3+52−3−5211-1−3+523−52−3−523+521-10000000000000000000000
χ584-4-44−1−5−1+5−1−5−1+51+51−5−1−5−1+51+51−51+5−1−51−5−1+51+51−53+52-1-13−52−3−5211−3+52−3−523+521-11-1−3+523−520000000000000000000000

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