Finite Group Databasebeta

← Group #13104300

Character table — Group #13104300

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size111144444444444444444888888888888888840404040404040404040404040404040404040405050100100100100100
order12224555510101010101010101010101051010102020202020202020202020202444101010102020202020202020202020204428888
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1
χ31111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-111111111111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ51111-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-11111-1-1-1-111-111-1-1
χ61111-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-1111111-1-1-111
χ71111-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111-1-1-1-111-1-1-111
χ81111-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-1111111-111-1-1
χ9222222222222222222222222222222222222200000000000000000000-2-2-20000
χ102222-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000-2-220000
χ112-2-2202222-2-2-2-222-2-2-2-2222-2-22000000000000000000000000000000002-202i−2i00
χ122-2-2202222-2-2-2-222-2-2-2-2222-2-22000000000000000000000000000000002-20−2i2i00
χ132-2-2202222-2-2-2-222-2-2-2-2222-2-2200000000000000000000000000000000-220002-2
χ142-2-2202222-2-2-2-222-2-2-2-2222-2-2200000000000000000000000000000000-22000-22
χ1544444−1+5−1−53−523+52−1+5−1−53−523+523−523+52−1+5−1−53−523+52−1+5−1−5-1-1-1-13−523−523+523+52−1+5−1+5−1−5−1−5-1-1-1-12200−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000
χ1644444−1+5−1−53−523+52−1+5−1−53−523+523−523+52−1+5−1−53−523+52−1+5−1−5-1-1-1-13−523−523+523+52−1+5−1+5−1−5−1−5-1-1-1-1-2-2001−521−521+521+521−521−521+521+52000000000000000
χ17444443−523+52−1−5−1+53−523+52−1−5−1+5−1−5−1+53−523+52−1−5−1+53−523+52-1-1-1-1−1−5−1−5−1+5−1+53−523−523+523+52-1-1-1-1002200000000−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000
χ18444443−523+52−1−5−1+53−523+52−1−5−1+5−1−5−1+53−523+52−1−5−1+53−523+52-1-1-1-1−1−5−1−5−1+5−1+53−523−523+523+52-1-1-1-100-2-2000000001−521−521+521+521−521−521+521+520000000
χ19444443+523−52−1+5−1−53+523−52−1+5−1−5−1+5−1−53+523−52−1+5−1−53+523−52-1-1-1-1−1+5−1+5−1−5−1−53+523+523−523−52-1-1-1-1002200000000−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000
χ20444443+523−52−1+5−1−53+523−52−1+5−1−5−1+5−1−53+523−52−1+5−1−53+523−52-1-1-1-1−1+5−1+5−1−5−1−53+523+523−523−52-1-1-1-100-2-2000000001+521+521−521−521+521+521−521−520000000
χ2144444−1−5−1+53+523−52−1−5−1+53+523−523+523−52−1−5−1+53+523−52−1−5−1+5-1-1-1-13+523+523−523−52−1−5−1−5−1+5−1+5-1-1-1-12200−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000000
χ2244444−1−5−1+53+523−52−1−5−1+53+523−523+523−52−1−5−1+53+523−52−1−5−1+5-1-1-1-13+523+523−523−52−1−5−1−5−1+5−1+5-1-1-1-1-2-2001+521+521−521−521+521+521−521−52000000000000000
χ234444-4−1+5−1−53−523+52−1+5−1−53−523+523−523+52−1+5−1−53−523+52−1+5−1−5-1-1-1-1−3+52−3+52−3−52−3−521−51−51+51+511112-200−1+52−1+52−1−52−1−521−521−521+521+52000000000000000
χ244444-4−1+5−1−53−523+52−1+5−1−53−523+523−523+52−1+5−1−53−523+52−1+5−1−5-1-1-1-1−3+52−3+52−3−52−3−521−51−51+51+51111-22001−521−521+521+52−1+52−1+52−1−52−1−52000000000000000
χ254444-43−523+52−1−5−1+53−523+52−1−5−1+5−1−5−1+53−523+52−1−5−1+53−523+52-1-1-1-11+51+51−51−5−3+52−3+52−3−52−3−521111002-200000000−1+52−1+52−1−52−1−521−521−521+521+520000000
χ264444-43−523+52−1−5−1+53−523+52−1−5−1+5−1−5−1+53−523+52−1−5−1+53−523+52-1-1-1-11+51+51−51−5−3+52−3+52−3−52−3−52111100-22000000001−521−521+521+52−1+52−1+52−1−52−1−520000000
χ274444-43+523−52−1+5−1−53+523−52−1+5−1−5−1+5−1−53+523−52−1+5−1−53+523−52-1-1-1-11−51−51+51+5−3−52−3−52−3+52−3+521111002-200000000−1−52−1−52−1+52−1+521+521+521−521−520000000
χ284444-43+523−52−1+5−1−53+523−52−1+5−1−5−1+5−1−53+523−52−1+5−1−53+523−52-1-1-1-11−51−51+51+5−3−52−3−52−3+52−3+52111100-22000000001+521+521−521−52−1−52−1−52−1+52−1+520000000
χ294444-4−1−5−1+53+523−52−1−5−1+53+523−523+523−52−1−5−1+53+523−52−1−5−1+5-1-1-1-1−3−52−3−52−3+52−3+521+51+51−51−511112-200−1−52−1−52−1+52−1+521+521+521−521−52000000000000000
χ304444-4−1−5−1+53+523−52−1−5−1+53+523−523+523−52−1−5−1+53+523−52−1−5−1+5-1-1-1-1−3−52−3−52−3+52−3+521+51+51−51−51111-22001+521+521−521−52−1−52−1−52−1+52−1+52000000000000000
χ3144-4-4044444444-4-4-4-4-4-4-4-444-4-4000000000000000000000000000000000000000
χ3244-4-40−1+5−1−53−523+52−1+5−1−53−523+52−3+52−3−521−51+5−3+52−3−521−51+5-1-1113ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ19−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ190000i5i5−i5−i50000ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000000000000
χ3344-4-40−1+5−1−53−523+52−1+5−1−53−523+52−3+52−3−521−51+5−3+52−3−521−51+5-1-1113ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ19−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ190000i5i5−i5−i50000−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000000000000
χ3444-4-40−1+5−1−53−523+52−1+5−1−53−523+52−3+52−3−521−51+5−3+52−3−521−51+5-1-111−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ192ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ190000−i5−i5i5i50000ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000000000000
χ3544-4-40−1+5−1−53−523+52−1+5−1−53−523+52−3+52−3−521−51+5−3+52−3−521−51+5-1-111−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ192ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ190000−i5−i5i5i50000−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000000000000
χ3644-4-40−1−5−1+53+523−52−1−5−1+53+523−52−3−52−3+521+51−5−3−52−3+521+51−5-1-111−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ193ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ190000i5i5−i5−i50000−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000000000000
χ3744-4-40−1−5−1+53+523−52−1−5−1+53+523−52−3−52−3+521+51−5−3−52−3+521+51−5-1-111−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ193ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ190000i5i5−i5−i50000ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000000000000
χ3844-4-40−1−5−1+53+523−52−1−5−1+53+523−52−3−52−3+521+51−5−3−52−3+521+51−5-1-1112ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ19−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ190000−i5−i5i5i50000−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000000000000
χ3944-4-40−1−5−1+53+523−52−1−5−1+53+523−52−3−52−3+521+51−5−3−52−3+521+51−5-1-1112ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ19−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ190000−i5−i5i5i50000ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000000000000
χ404-44-404444-4-4-4-4-4-44444-4-44-44-4000000000000000000000000000000000000000
χ414-44-403−523+52−1−5−1+5−3+52−3−521+51−51+51−53−523+52−1−5−1+5−3+52−3−52-11-1100003ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ19−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ19i5−i5i5−i5000000000000ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ70000000
χ424-44-403−523+52−1−5−1+5−3+52−3−521+51−51+51−53−523+52−1−5−1+5−3+52−3−52-11-1100003ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ19−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ19i5−i5i5−i5000000000000−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ70000000
χ434-44-403−523+52−1−5−1+5−3+52−3−521+51−51+51−53−523+52−1−5−1+5−3+52−3−52-11-110000−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ192ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ19−i5i5−i5i5000000000000ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ70000000
χ444-44-403−523+52−1−5−1+5−3+52−3−521+51−51+51−53−523+52−1−5−1+5−3+52−3−52-11-110000−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ192ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ19−i5i5−i5i5000000000000−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ70000000
χ454-44-403+523−52−1+5−1−5−3−52−3+521−51+51−51+53+523−52−1+5−1−5−3−52−3+52-11-110000−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ193ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ19i5−i5i5−i5000000000000−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ190000000
χ464-44-403+523−52−1+5−1−5−3−52−3+521−51+51−51+53+523−52−1+5−1−5−3−52−3+52-11-110000−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ193ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ19i5−i5i5−i5000000000000ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ190000000
χ474-44-403+523−52−1+5−1−5−3−52−3+521−51+51−51+53+523−52−1+5−1−5−3−52−3+52-11-1100002ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ19−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ19−i5i5−i5i5000000000000−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ190000000
χ484-44-403+523−52−1+5−1−5−3−52−3+521−51+51−51+53+523−52−1+5−1−5−3−52−3+52-11-1100002ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ19−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ19−i5i5−i5i5000000000000ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ190000000
χ4988888-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-23333-2-2-2-2-2-2-2-23333000000000000000000000000000
χ508888-8-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2333322222222-3-3-3-3000000000000000000000000000
χ5188-8-80-2-2-2-2-2-2-2-22222222233-3-32i5−2i52i5−2i50000−i5−i5i5i5000000000000000000000000000
χ5288-8-80-2-2-2-2-2-2-2-22222222233-3-3−2i52i5−2i52i50000i5i5−i5−i5000000000000000000000000000
χ5388-8-803−53+5−2−25−2+253−53+5−2−25−2+252+252−25−3+5−3−52+252−25−3+5−3−5-2-222000000000000000000000000000000000000000
χ5488-8-803+53−5−2+25−2−253+53−5−2+25−2−252−252+25−3−5−3+52−252+25−3−5−3+5-2-222000000000000000000000000000000000000000
χ558-88-80-2-2-2-2222222-2-2-2-2223-33-300002i5−2i52i5−2i5−i5i5−i5i5000000000000000000000000000
χ568-88-80-2-2-2-2222222-2-2-2-2223-33-30000−2i52i5−2i52i5i5−i5i5−i5000000000000000000000000000
χ578-88-80−2+25−2−253−53+52−252+25−3+5−3−5−3+5−3−5−2+25−2−253−53+52−252+25-22-22000000000000000000000000000000000000000
χ588-88-80−2−25−2+253+53−52+252−25−3−5−3+5−3−5−3+5−2−25−2+253+53−52+252−25-22-22000000000000000000000000000000000000000
χ598-8-880-2-2-2-22222-2-22222-2-23-3-33000000005-5-55000000000000000000000000000
χ608-8-880-2-2-2-22222-2-22222-2-23-3-3300000000-555-5000000000000000000000000000
χ618-8-880−2+25−2−253−53+52−252+25−3+5−3−53−53+52−252+25−3+5−3−5−2+25−2−25-222-2000000000000000000000000000000000000000
χ628-8-8803−53+5−2−25−2+25−3+5−3−52+252−25−2−25−2+25−3+5−3−52+252−253−53+5-222-2000000000000000000000000000000000000000
χ638-8-8803+53−5−2+25−2−25−3−5−3+52−252+25−2+25−2−25−3−5−3+52−252+253+53−5-222-2000000000000000000000000000000000000000
χ648-8-880−2−25−2+253+53−52+252−25−3−5−3+53+53−52+252−25−3−5−3+5−2−25−2+25-222-2000000000000000000000000000000000000000

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