Finite Group Databasebeta

← Group #13104319

Character table — Group #13104319

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size111144444444444444444888888888888888820202020202020202525252540404040404040404040404040404040100100100100100
order12224555510101010101010101010101051010102020202020202020202020202222444422221010101010101010202020202020202044444
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-111-1-111111111-1-1-1-11111-1-1-1-11-1-1-1-1
χ31111111111111111111111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-111111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ51111-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1-1
χ61111-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-111
χ71111-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-111
χ81111-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-111-1-1
χ9222222222222222222222222222222222222200000000-2-2-2-20000000000000000-20000
χ102222-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-2-2000000000000000020000
χ1122-2-20222222-2-2-2-2-2-222-2-222-2-20000000000000000002i−2i22-2-20000000000002i2i−2i−2i00000
χ1222-2-20222222-2-2-2-2-2-222-2-222-2-2000000000000000000−2i2i22-2-2000000000000−2i−2i2i2i00000
χ1322-2-20222222-2-2-2-2-2-222-2-222-2-2000000000000002-20000-2-222000022-2-20000000000000
χ1422-2-20222222-2-2-2-2-2-222-2-222-2-200000000000000-220000-2-2220000-2-2220000000000000
χ152-22-202222-2-222-2-2-2-2-2-2222-22-200000000000000002i−2i002-22-2000000002i2i−2i−2i000000000
χ162-22-202222-2-222-2-2-2-2-2-2222-22-20000000000000000−2i2i002-22-200000000−2i−2i2i2i000000000
χ172-22-202222-2-222-2-2-2-2-2-2222-22-20000000000002-2000000-22-2222-2-200000000000000000
χ182-22-202222-2-222-2-2-2-2-2-2222-22-2000000000000-22000000-22-22-2-22200000000000000000
χ192-2-2202222-2-2-2-22222-2-2-2-22-2-22000000000000000000002-2-22000000000000000002-200
χ202-2-2202222-2-2-2-22222-2-2-2-22-2-22000000000000000000002-2-2200000000000000000-2200
χ212-2-2202222-2-2-2-22222-2-2-2-22-2-2200000000000000000000-222-200000000000000000002i−2i
χ222-2-2202222-2-2-2-22222-2-2-2-22-2-2200000000000000000000-222-20000000000000000000−2i2i
χ2344444−1+53−523+52−1−5−1+5−1−53−523+52−1+53−523+52−1−53−523+52−1+5−1−5-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−5-1-1-1-1220022000000−1+52−1−52−1+52−1−520000−1+52−1−52−1+52−1−52000000000
χ2444444−1+53−523+52−1−5−1+5−1−53−523+52−1+53−523+52−1−53−523+52−1+5−1−5-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−5-1-1-1-1-2-200-2-20000001−521+521−521+5200001−521+521−521+52000000000
χ25444443−52−1−5−1+53+523−523+52−1−5−1+53−52−1−5−1+53+52−1−5−1+53−523+52-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+52-1-1-1-10022002200000000−1+52−1−52−1+52−1−520000−1+52−1−52−1+52−1−5200000
χ26444443−52−1−5−1+53+523−523+52−1−5−1+53−52−1−5−1+53+52−1−5−1+53−523+52-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+52-1-1-1-100-2-200-2-2000000001−521+521−521+5200001−521+521−521+5200000
χ27444443+52−1+5−1−53−523+523−52−1+5−1−53+52−1+5−1−53−52−1+5−1−53+523−52-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−52-1-1-1-10022002200000000−1−52−1+52−1−52−1+520000−1−52−1+52−1−52−1+5200000
χ28444443+52−1+5−1−53−523+523−52−1+5−1−53+52−1+5−1−53−52−1+5−1−53+523−52-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−52-1-1-1-100-2-200-2-2000000001+521−521+521−5200001+521−521+521−5200000
χ2944444−1−53+523−52−1+5−1−5−1+53+523−52−1−53+523−52−1+53+523−52−1−5−1+5-1-1-1-1−1−5−1−53+523+523−523−52−1+5−1+5-1-1-1-1220022000000−1−52−1+52−1−52−1+520000−1−52−1+52−1−52−1+52000000000
χ3044444−1−53+523−52−1+5−1−5−1+53+523−52−1−53+523−52−1+53+523−52−1−5−1+5-1-1-1-1−1−5−1−53+523+523−523−52−1+5−1+5-1-1-1-1-2-200-2-20000001+521−521+521−5200001+521−521+521−52000000000
χ314444-4−1+53−523+52−1−5−1+5−1−53−523+52−1+53−523+52−1−53−523+52−1+5−1−5-1-1-1-11−51−5−3+52−3+52−3−52−3−521+51+511112200-2-2000000−1+52−1−52−1+52−1−5200001−521+521−521+52000000000
χ324444-4−1+53−523+52−1−5−1+5−1−53−523+52−1+53−523+52−1−53−523+52−1+5−1−5-1-1-1-11−51−5−3+52−3+52−3−52−3−521+51+51111-2-200220000001−521+521−521+520000−1+52−1−52−1+52−1−52000000000
χ334444-43−52−1−5−1+53+523−523+52−1−5−1+53−52−1−5−1+53+52−1−5−1+53−523+52-1-1-1-1−3+52−3+521+51+51−51−5−3−52−3−521111002200-2-200000000−1+52−1−52−1+52−1−5200001−521+521−521+5200000
χ344444-43−52−1−5−1+53+523−523+52−1−5−1+53−52−1−5−1+53+52−1−5−1+53−523+52-1-1-1-1−3+52−3+521+51+51−51−5−3−52−3−52111100-2-20022000000001−521+521−521+520000−1+52−1−52−1+52−1−5200000
χ354444-43+52−1+5−1−53−523+523−52−1+5−1−53+52−1+5−1−53−52−1+5−1−53+523−52-1-1-1-1−3−52−3−521−51−51+51+5−3+52−3+521111002200-2-200000000−1−52−1+52−1−52−1+5200001+521−521+521−5200000
χ364444-43+52−1+5−1−53−523+523−52−1+5−1−53+52−1+5−1−53−52−1+5−1−53+523−52-1-1-1-1−3−52−3−521−51−51+51+5−3+52−3+52111100-2-20022000000001+521−521+521−520000−1−52−1+52−1−52−1+5200000
χ374444-4−1−53+523−52−1+5−1−5−1+53+523−52−1−53+523−52−1+53+523−52−1−5−1+5-1-1-1-11+51+5−3−52−3−52−3+52−3+521−51−511112200-2-2000000−1−52−1+52−1−52−1+5200001+521−521+521−52000000000
χ384444-4−1−53+523−52−1+5−1−5−1+53+523−52−1−53+523−52−1+53+523−52−1−5−1+5-1-1-1-11+51+5−3−52−3−52−3+52−3+521−51−51111-2-200220000001+521−521+521−520000−1−52−1+52−1−52−1+52000000000
χ3944-4-403−52−1−5−1+53+523−523+521+51−5−3+521+51−5−3−52−1−5−1+5−3+52−3−52-1-1113ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ190000−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ19i5i5−i5−i5002-2002i−2i00000000−1+52−1−521−521+520000−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ700000
χ4044-4-403−52−1−5−1+53+523−523+521+51−5−3+521+51−5−3−52−1−5−1+5−3+52−3−52-1-1113ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ190000−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ19i5i5−i5−i500-2200−2i2i000000001−521+52−1+52−1−520000ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ700000
χ4144-4-403−52−1−5−1+53+523−523+521+51−5−3+521+51−5−3−52−1−5−1+5−3+52−3−52-1-111−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ1900002ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ19−i5−i5i5i5002-200−2i2i00000000−1+52−1−521−521+520000ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ700000
χ4244-4-403−52−1−5−1+53+523−523+521+51−5−3+521+51−5−3−52−1−5−1+5−3+52−3−52-1-111−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ1900002ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ19−i5−i5i5i500-22002i−2i000000001−521+52−1+52−1−520000−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ700000
χ4344-4-403+52−1+5−1−53−523+523−521−51+5−3−521−51+5−3+52−1+5−1−5−3−52−3+52-1-111−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ1900003ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ19i5i5−i5−i5002-200−2i2i00000000−1−52−1+521+521−520000ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ1900000
χ4444-4-403+52−1+5−1−53−523+523−521−51+5−3−521−51+5−3+52−1+5−1−5−3−52−3+52-1-111−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ1900003ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ19i5i5−i5−i500-22002i−2i000000001+521−52−1−52−1+520000−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ1900000
χ4544-4-403+52−1+5−1−53−523+523−521−51+5−3−521−51+5−3+52−1+5−1−5−3−52−3+52-1-1112ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ190000−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ19−i5−i5i5i5002-2002i−2i00000000−1−52−1+521+521−520000−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ1900000
χ4644-4-403+52−1+5−1−53−523+523−521−51+5−3−521−51+5−3+52−1+5−1−5−3−52−3+52-1-1112ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ190000−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ19−i5−i5i5i500-2200−2i2i000000001+521−52−1−52−1+520000ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ1900000
χ474-44-40−1+53−523+52−1−51−51+53−523+521−5−3+52−3−521+5−3+52−3−52−1+5−1−5-11-11003ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ19−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ1900i5−i5i5−i52-2002i−2i000000−1+52−1−521−521+520000−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7000000000
χ484-44-40−1+53−523+52−1−51−51+53−523+521−5−3+52−3−521+5−3+52−3−52−1+5−1−5-11-11003ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ19−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ1900i5−i5i5−i5-2200−2i2i0000001−521+52−1+52−1−520000ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7000000000
χ494-44-40−1+53−523+52−1−51−51+53−523+521−5−3+52−3−521+5−3+52−3−52−1+5−1−5-11-1100−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ192ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ1900−i5i5−i5i52-200−2i2i000000−1+52−1−521−521+520000ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7000000000
χ504-44-40−1+53−523+52−1−51−51+53−523+521−5−3+52−3−521+5−3+52−3−52−1+5−1−5-11-1100−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ192ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ1900−i5i5−i5i5-22002i−2i0000001−521+52−1+52−1−520000−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7000000000
χ514-44-40−1−53+523−52−1+51+51−53+523−521+5−3−52−3+521−5−3−52−3+52−1−5−1+5-11-1100−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ193ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ1900i5−i5i5−i52-200−2i2i000000−1−52−1+521+521−520000ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19000000000
χ524-44-40−1−53+523−52−1+51+51−53+523−521+5−3−52−3+521−5−3−52−3+52−1−5−1+5-11-1100−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ193ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ1900i5−i5i5−i5-22002i−2i0000001+521−52−1−52−1+520000−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19000000000
χ534-44-40−1−53+523−52−1+51+51−53+523−521+5−3−52−3+521−5−3−52−3+52−1−5−1+5-11-11002ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ19−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ1900−i5i5−i5i52-2002i−2i000000−1−52−1+521+521−520000−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19000000000
χ544-44-40−1−53+523−52−1+51+51−53+523−521+5−3−52−3+521−5−3−52−3+52−1−5−1+5-11-11002ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ19−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ1900−i5i5−i5i5-2200−2i2i0000001+521−52−1−52−1+520000ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19000000000
χ5588888-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-23333-2-2-2-2-2-2-2-23333000000000000000000000000000000000
χ568888-8-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2333322222222-3-3-3-3000000000000000000000000000000000
χ5788-8-80-2-2-2-2-2-2222222-2-22233-3-32i5−2i500002i5−2i5−i5−i5i5i5000000000000000000000000000000000
χ5888-8-80-2-2-2-2-2-2222222-2-22233-3-3−2i52i50000−2i52i5i5i5−i5−i5000000000000000000000000000000000
χ5988-8-80−2+253−53+5−2−25−2+25−2−25−3+5−3−52−25−3+5−3−52+253−53+52−252+25-2-222000000000000000000000000000000000000000000000
χ6088-8-80−2−253+53−5−2+25−2−25−2+25−3−5−3+52+25−3−5−3+52−253+53−52+252−25-2-222000000000000000000000000000000000000000000000
χ618-88-80-2-2-2-222-2-2222222-2-23-33-3002i5−2i52i5−2i500−i5i5−i5i5000000000000000000000000000000000
χ628-88-80-2-2-2-222-2-2222222-2-23-33-300−2i52i5−2i52i500i5−i5i5−i5000000000000000000000000000000000
χ638-88-803−5−2−25−2+253+5−3+5−3−5−2−25−2+25−3+52+252−25−3−52+252−253−53+5-22-22000000000000000000000000000000000000000000000
χ648-88-803+5−2+25−2−253−5−3−5−3+5−2+25−2−25−3−52−252+25−3+52−252+253+53−5-22-22000000000000000000000000000000000000000000000
χ658-8-880-2-2-2-22222-2-2-2-222223-3-33000000005-5-55000000000000000000000000000000000
χ668-8-880-2-2-2-22222-2-2-2-222223-3-3300000000-555-5000000000000000000000000000000000
χ678-8-880−2+253−53+5−2−252−252+25−3+5−3−5−2+253−53+5−2−25−3+5−3−52−252+25-222-2000000000000000000000000000000000000000000000
χ688-8-8803−5−2−25−2+253+5−3+5−3−52+252−253−5−2−25−2+253+52+252−25−3+5−3−5-222-2000000000000000000000000000000000000000000000
χ698-8-8803+5−2+25−2−253−5−3−5−3+52−252+253+5−2+25−2−253−52−252+25−3−5−3+5-222-2000000000000000000000000000000000000000000000
χ708-8-880−2−253+53−5−2+252+252−25−3−5−3+5−2−253+53−5−2+25−3−5−3+52+252−25-222-2000000000000000000000000000000000000000000000

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