Finite Group Databasebeta

← Group #13104318

Character table — Group #13104318

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size111144444444444444444888888888888888820202020202020202525252540404040404040404040404040404040100100100100100
order12224555510101010101010101010101051010102020202020202020202020202222224422221010101010101010101010102020202044444
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-1-1-1
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
χ51111-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-111-1-1
χ61111-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-111
χ71111-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-111
χ81111-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111-111-1-1
χ9222222222222222222222222222222222222200000000-2-2-2-20000000000000000-20000
χ102222-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-2-2000000000000000020000
χ1122-2-2022222222-2-2-2-2-2-2-2-222-2-20000000000000000002i−2i22-2-20000000000002i2i−2i−2i00000
χ1222-2-2022222222-2-2-2-2-2-2-2-222-2-2000000000000000000−2i2i22-2-2000000000000−2i−2i2i2i00000
χ1322-2-2022222222-2-2-2-2-2-2-2-222-2-200000000000000002-200-2-22222-2-200000000000000000
χ1422-2-2022222222-2-2-2-2-2-2-2-222-2-20000000000000000-2200-2-222-2-22200000000000000000
χ152-22-202222-2-2-2-222-2-2-2-2222-22-2000000000000000000002-22-200000000000000000002-2
χ162-22-202222-2-2-2-222-2-2-2-2222-22-2000000000000000000002-22-20000000000000000000-22
χ172-22-202222-2-2-2-222-2-2-2-2222-22-200000000000000000000-22-22000000000000000002-200
χ182-22-202222-2-2-2-222-2-2-2-2222-22-200000000000000000000-22-2200000000000000000-2200
χ192-2-2202222-2-2-2-2-2-22222-2-22-2-22000000000000002-20000-222-20000000022-2-2000000000
χ202-2-2202222-2-2-2-2-2-22222-2-22-2-2200000000000000-220000-222-200000000-2-222000000000
χ212-2-2202222-2-2-2-2-2-22222-2-22-2-220000000000002-20000002-2-22000022-2-20000000000000
χ222-2-2202222-2-2-2-2-2-22222-2-22-2-22000000000000-220000002-2-220000-2-2220000000000000
χ2344444−1+5−1−53−523+52−1+5−1−53−523+523−523+52−1+5−1−53−523+52−1+5−1−5-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−5-1-1-1-12222000000000000−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52000000000
χ2444444−1+5−1−53−523+52−1+5−1−53−523+523−523+52−1+5−1−53−523+52−1+5−1−5-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−5-1-1-1-1-2-2-2-20000000000001−521+521−521+521−521+521−521+52000000000
χ25444443−523+52−1−5−1+53−523+52−1−5−1+5−1−5−1+53−523+52−1−5−1+53−523+52-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+52-1-1-1-1000022220000−1+52−1−52−1+52−1−5200000000−1+52−1−52−1+52−1−5200000
χ26444443−523+52−1−5−1+53−523+52−1−5−1+5−1−5−1+53−523+52−1−5−1+53−523+52-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+52-1-1-1-10000-2-2-2-200001−521+521−521+52000000001−521+521−521+5200000
χ27444443+523−52−1+5−1−53+523−52−1+5−1−5−1+5−1−53+523−52−1+5−1−53+523−52-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−52-1-1-1-1000022220000−1−52−1+52−1−52−1+5200000000−1−52−1+52−1−52−1+5200000
χ28444443+523−52−1+5−1−53+523−52−1+5−1−5−1+5−1−53+523−52−1+5−1−53+523−52-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−52-1-1-1-10000-2-2-2-200001+521−521+521−52000000001+521−521+521−5200000
χ2944444−1−5−1+53+523−52−1−5−1+53+523−523+523−52−1−5−1+53+523−52−1−5−1+5-1-1-1-1−1−5−1−53+523+523−523−52−1+5−1+5-1-1-1-12222000000000000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52000000000
χ3044444−1−5−1+53+523−52−1−5−1+53+523−523+523−52−1−5−1+53+523−52−1−5−1+5-1-1-1-1−1−5−1−53+523+523−523−52−1+5−1+5-1-1-1-1-2-2-2-20000000000001+521−521+521−521+521−521+521−52000000000
χ314444-4−1+5−1−53−523+52−1+5−1−53−523+523−523+52−1+5−1−53−523+52−1+5−1−5-1-1-1-11−51−5−3+52−3+52−3−52−3−521+51+5111122-2-2000000000000−1+52−1−52−1+52−1−521−521+521−521+52000000000
χ324444-4−1+5−1−53−523+52−1+5−1−53−523+523−523+52−1+5−1−53−523+52−1+5−1−5-1-1-1-11−51−5−3+52−3+52−3−52−3−521+51+51111-2-2220000000000001−521+521−521+52−1+52−1−52−1+52−1−52000000000
χ334444-43−523+52−1−5−1+53−523+52−1−5−1+5−1−5−1+53−523+52−1−5−1+53−523+52-1-1-1-1−3+52−3+521+51+51−51−5−3−52−3−521111000022-2-20000−1+52−1−52−1+52−1−52000000001−521+521−521+5200000
χ344444-43−523+52−1−5−1+53−523+52−1−5−1+5−1−5−1+53−523+52−1−5−1+53−523+52-1-1-1-1−3+52−3+521+51+51−51−5−3−52−3−5211110000-2-22200001−521+521−521+5200000000−1+52−1−52−1+52−1−5200000
χ354444-43+523−52−1+5−1−53+523−52−1+5−1−5−1+5−1−53+523−52−1+5−1−53+523−52-1-1-1-1−3−52−3−521−51−51+51+5−3+52−3+521111000022-2-20000−1−52−1+52−1−52−1+52000000001+521−521+521−5200000
χ364444-43+523−52−1+5−1−53+523−52−1+5−1−5−1+5−1−53+523−52−1+5−1−53+523−52-1-1-1-1−3−52−3−521−51−51+51+5−3+52−3+5211110000-2-22200001+521−521+521−5200000000−1−52−1+52−1−52−1+5200000
χ374444-4−1−5−1+53+523−52−1−5−1+53+523−523+523−52−1−5−1+53+523−52−1−5−1+5-1-1-1-11+51+5−3−52−3−52−3+52−3+521−51−5111122-2-2000000000000−1−52−1+52−1−52−1+521+521−521+521−52000000000
χ384444-4−1−5−1+53+523−52−1−5−1+53+523−523+523−52−1−5−1+53+523−52−1−5−1+5-1-1-1-11+51+5−3−52−3−52−3+52−3+521−51−51111-2-2220000000000001+521−521+521−52−1−52−1+52−1−52−1+52000000000
χ3944-4-403−523+52−1−5−1+53−523+52−1−5−1+51+51−5−3+52−3−521+51−5−3+52−3−52-1-1113ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ190000−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ19i5i5−i5−i500002-22i−2i0000−1+52−1−521−521+5200000000−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ700000
χ4044-4-403−523+52−1−5−1+53−523+52−1−5−1+51+51−5−3+52−3−521+51−5−3+52−3−52-1-1113ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ190000−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ19i5i5−i5−i50000-22−2i2i00001−521+52−1+52−1−5200000000ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ700000
χ4144-4-403−523+52−1−5−1+53−523+52−1−5−1+51+51−5−3+52−3−521+51−5−3+52−3−52-1-111−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ1900002ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ19−i5−i5i5i500002-2−2i2i0000−1+52−1−521−521+5200000000ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ700000
χ4244-4-403−523+52−1−5−1+53−523+52−1−5−1+51+51−5−3+52−3−521+51−5−3+52−3−52-1-111−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ1900002ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ19−i5−i5i5i50000-222i−2i00001−521+52−1+52−1−5200000000−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ700000
χ4344-4-403+523−52−1+5−1−53+523−52−1+5−1−51−51+5−3−52−3+521−51+5−3−52−3+52-1-111−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ1900003ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ19i5i5−i5−i500002-2−2i2i0000−1−52−1+521+521−5200000000ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ1900000
χ4444-4-403+523−52−1+5−1−53+523−52−1+5−1−51−51+5−3−52−3+521−51+5−3−52−3+52-1-111−2ζ3−2ζ7−3ζ11−3ζ192ζ3+2ζ7+3ζ11+3ζ1900003ζ3+3ζ7+2ζ11+2ζ19−3ζ3−3ζ7−2ζ11−2ζ19i5i5−i5−i50000-222i−2i00001+521−52−1−52−1+5200000000−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ1900000
χ4544-4-403+523−52−1+5−1−53+523−52−1+5−1−51−51+5−3−52−3+521−51+5−3−52−3+52-1-1112ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ190000−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ19−i5−i5i5i500002-22i−2i0000−1−52−1+521+521−5200000000−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ1900000
χ4644-4-403+523−52−1+5−1−53+523−52−1+5−1−51−51+5−3−52−3+521−51+5−3−52−3+52-1-1112ζ3+2ζ7+3ζ11+3ζ19−2ζ3−2ζ7−3ζ11−3ζ190000−3ζ3−3ζ7−2ζ11−2ζ193ζ3+3ζ7+2ζ11+2ζ19−i5−i5i5i50000-22−2i2i00001+521−52−1−52−1+5200000000ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ1900000
χ474-4-440−1+5−1−53−523+521−51+5−3+52−3−52−3+52−3−52−1+5−1−53−523+521−51+5-111-1005+52−5−525−52−5+52005−55−52-22-2000000000000−1+52−1−521−521+52−1+52−1−521−521+52000000000
χ484-4-440−1+5−1−53−523+521−51+5−3+52−3−52−3+52−3−52−1+5−1−53−523+521−51+5-111-1005+52−5−525−52−5+52005−55−5-22-220000000000001−521+52−1+52−1−521−521+52−1+52−1−52000000000
χ494-4-440−1+5−1−53−523+521−51+5−3+52−3−52−3+52−3−52−1+5−1−53−523+521−51+5-111-100−5−525+52−5+525−5200−55−552-2-22000000000000−1+52−1−521−521+521−521+52−1+52−1−52000000000
χ504-4-440−1+5−1−53−523+521−51+5−3+52−3−52−3+52−3−52−1+5−1−53−523+521−51+5-111-100−5−525+52−5+525−5200−55−55-222-20000000000001−521+52−1+52−1−52−1+52−1−521−521+52000000000
χ514-4-440−1−5−1+53+523−521+51−5−3−52−3+52−3−52−3+52−1−5−1+53+523−521+51−5-111-1005−52−5+525+52−5−5200−55−552-22-2000000000000−1−52−1+521+521−52−1−52−1+521+521−52000000000
χ524-4-440−1−5−1+53+523−521+51−5−3−52−3+52−3−52−3+52−1−5−1+53+523−521+51−5-111-1005−52−5+525+52−5−5200−55−55-22-220000000000001+521−52−1−52−1+521+521−52−1−52−1+52000000000
χ534-4-440−1−5−1+53+523−521+51−5−3−52−3+52−3−52−3+52−1−5−1+53+523−521+51−5-111-100−5+525−52−5−525+52005−55−52-2-22000000000000−1−52−1+521+521−521+521−52−1−52−1+52000000000
χ544-4-440−1−5−1+53+523−521+51−5−3−52−3+52−3−52−3+52−1−5−1+53+523−521+51−5-111-100−5+525−52−5−525+52005−55−5-222-20000000000001+521−52−1−52−1+52−1−52−1+521+521−52000000000
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
χ5788-8-80-2-2-2-2-2-2-2-22222222233-3-32i5−2i500002i5−2i5−i5−i5i5i5000000000000000000000000000000000
χ5888-8-80-2-2-2-2-2-2-2-22222222233-3-3−2i52i50000−2i52i5i5i5−i5−i5000000000000000000000000000000000
χ5988-8-80−2+25−2−253−53+5−2+25−2−253−53+5−3+5−3−52−252+25−3+5−3−52−252+25-2-222000000000000000000000000000000000000000000000
χ6088-8-80−2−25−2+253+53−5−2−25−2+253+53−5−3−5−3+52+252−25−3−5−3+52+252−25-2-222000000000000000000000000000000000000000000000
χ618-88-80-2-2-2-22222-2-22222-2-23-33-3000000005i−5i−5i5i000000000000000000000000000000000
χ628-88-80-2-2-2-22222-2-22222-2-23-33-300000000−5i5i5i−5i000000000000000000000000000000000
χ638-88-80−2+25−2−253−53+52−252+25−3+5−3−53−53+52−252+25−3+5−3−5−2+25−2−25-22-22000000000000000000000000000000000000000000000
χ648-88-803−53+5−2−25−2+25−3+5−3−52+252−25−2−25−2+25−3+5−3−52+252−253−53+5-22-22000000000000000000000000000000000000000000000
χ658-88-803+53−5−2+25−2−25−3−5−3+52−252+25−2+25−2−25−3−5−3+52−252+253+53−5-22-22000000000000000000000000000000000000000000000
χ668-88-80−2−25−2+253+53−52+252−25−3−5−3+53+53−52+252−25−3−5−3+5−2−25−2+25-22-22000000000000000000000000000000000000000000000
χ678-8-880-2-2-2-2222222-2-2-2-2223-3-330025−25−252500−55−55000000000000000000000000000000000
χ688-8-880-2-2-2-2222222-2-2-2-2223-3-3300−252525−25005−55−5000000000000000000000000000000000
χ698-8-8803−53+5−2−25−2+25−3+5−3−52+252−252+252−253−53+5−2−25−2+25−3+5−3−5-222-2000000000000000000000000000000000000000000000
χ708-8-8803+53−5−2+25−2−25−3−5−3+52−252+252−252+253+53−5−2+25−2−25−3−5−3+5-222-2000000000000000000000000000000000000000000000

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