Finite Group Databasebeta

← Group #13104205

Character table — Group #13104205

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size11222444444444444444488888888888888882020202020202020252540404040404040404040404040404040505050100100100100
order12244555510101010202020202020202051010101010101020202020202020202244888822101010102020202040404040404040402444444
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ5111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1ii−i−i-1-111-1-111-1-1iiii−i−i−i−i-111ii−i−i
χ6111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1−i−iii-1-111-1-111-1-1−i−i−i−iiiii-111−i−iii
χ7111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11ii−i−i-1-1-1-111-1-111iiii−i−i−i−i-111−i−iii
χ8111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11−i−iii-1-1-1-111-1-111−i−i−i−iiiii-111ii−i−i
χ911-11-1111111111111-1-1-1-11-1-1-1-1-1-1111-1-111-1-11-1-11i−ii−i-1-111-1-1-1-111ii−i−iii−i−i11-1i−ii−i
χ1011-11-1111111111111-1-1-1-11-1-1-1-1-1-1111-1-111-1-11-1-11−ii−ii-1-111-1-1-1-111−i−iii−i−iii11-1−ii−ii
χ1111-11-1111111111111-1-1-1-11-1-1-1-1-1-1111-1-111-1-1-111-1i−ii−i-1-1-1-11111-1-1ii−i−iii−i−i11-1−ii−ii
χ1211-11-1111111111111-1-1-1-11-1-1-1-1-1-1111-1-111-1-1-111-1−ii−ii-1-1-1-11111-1-1−i−iii−i−iii11-1i−ii−i
χ1311-1-1111111111-1-1-1-111111-1-1-1-1-1-11-1-111-1-11111-1-11-1-11111111-1-1-1-111-1-1-1-111-11-11-1-11
χ1411-1-1111111111-1-1-1-111111-1-1-1-1-1-11-1-111-1-11111-1-1-111-1111111-1-1-1-1-1-11111-1-1-11-1-111-1
χ1511-1-1111111111-1-1-1-111111-1-1-1-1-1-11-1-111-1-111-1-1111-1-1111-1-1-1-1111111-1-1-1-111-11-1-111-1
χ1611-1-1111111111-1-1-1-111111-1-1-1-1-1-11-1-111-1-111-1-111-111-111-1-1-1-11111-1-11111-1-1-11-11-1-11
χ17222222222222222222222222222222222222200000000-2-20000000000000000-2-2-20000
χ18222-2-222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000002200000000000000002-2-20000
χ1922-22-2222222222222-2-2-2-22-2-2-2-2-2-2222-2-222-2-200000000220000000000000000-2-220000
χ2022-2-2222222222-2-2-2-222222-2-2-2-2-2-22-2-222-2-22200000000-2-200000000000000002-220000
χ2144444−1+5−1−53−523+52−1+5−1−53−523+523−523−523+523+52−1+5−1+5−1−5−1−5-1−1+5−1−53−523+52-1-1-1−1+5−1−53−523+52-1-1-1-12222000000−1+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+523−523−523+523+52−1+5−1+5−1−5−1−5-1−1+5−1−53−523+52-1-1-1−1+5−1−53−523+52-1-1-1-1-2-2-2-20000001−521+521−521+521−521+521−521+52000000000000000
χ23444443−523+52−1−5−1+53−523+52−1−5−1+5−1−5−1−5−1+5−1+53−523−523+523+52-13−523+52−1−5−1+5-1-1-13−523+52−1−5−1+5-1-1-1-1000022220000000000−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−520000000
χ24444443−523+52−1−5−1+53−523+52−1−5−1+5−1−5−1−5−1+5−1+53−523−523+523+52-13−523+52−1−5−1+5-1-1-13−523+52−1−5−1+5-1-1-1-10000-2-2-2-200000000001−521+521−521+521−521+521−521+520000000
χ25444443+523−52−1+5−1−53+523−52−1+5−1−5−1+5−1+5−1−5−1−53+523+523−523−52-13+523−52−1+5−1−5-1-1-13+523−52−1+5−1−5-1-1-1-1000022220000000000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+520000000
χ26444443+523−52−1+5−1−53+523−52−1+5−1−5−1+5−1+5−1−5−1−53+523+523−523−52-13+523−52−1+5−1−5-1-1-13+523−52−1+5−1−5-1-1-1-10000-2-2-2-200000000001+521−521+521−521+521−521+521−520000000
χ2744444−1−5−1+53+523−52−1−5−1+53+523−523+523+523−523−52−1−5−1−5−1+5−1+5-1−1−5−1+53+523−52-1-1-1−1−5−1+53+523−52-1-1-1-12222000000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52000000000000000
χ2844444−1−5−1+53+523−52−1−5−1+53+523−523+523+523−523−52−1−5−1−5−1+5−1+5-1−1−5−1+53+523−52-1-1-1−1−5−1+53+523−52-1-1-1-1-2-2-2-20000001+521−521+521−521+521−521+521−52000000000000000
χ29444-4-4−1+5−1−53−523+52−1+5−1−53−523+52−3+52−3+52−3−52−3−521−51−51+51+5-1−1+5−1−53−523+52-1-1-11−51+5−3+52−3−5211112-22-2000000−1+52−1−521−521+52−1+52−1−521−521+52000000000000000
χ30444-4-4−1+5−1−53−523+52−1+5−1−53−523+52−3+52−3+52−3−52−3−521−51−51+51+5-1−1+5−1−53−523+52-1-1-11−51+5−3+52−3−521111-22-220000001−521+52−1+52−1−521−521+52−1+52−1−52000000000000000
χ31444-4-43−523+52−1−5−1+53−523+52−1−5−1+51+51+51−51−5−3+52−3+52−3−52−3−52-13−523+52−1−5−1+5-1-1-1−3+52−3−521+51−5111100002i2i−2i−2i0000000000−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ70000000
χ32444-4-43−523+52−1−5−1+53−523+52−1−5−1+51+51+51−51−5−3+52−3+52−3−52−3−52-13−523+52−1−5−1+5-1-1-1−3+52−3−521+51−511110000−2i−2i2i2i0000000000ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ70000000
χ33444-4-43+523−52−1+5−1−53+523−52−1+5−1−51−51−51+51+5−3−52−3−52−3+52−3+52-13+523−52−1+5−1−5-1-1-1−3−52−3+521−51+5111100002i2i−2i−2i0000000000−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ190000000
χ34444-4-43+523−52−1+5−1−53+523−52−1+5−1−51−51−51+51+5−3−52−3−52−3+52−3+52-13+523−52−1+5−1−5-1-1-1−3−52−3+521−51+511110000−2i−2i2i2i0000000000ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ190000000
χ35444-4-4−1−5−1+53+523−52−1−5−1+53+523−52−3−52−3−52−3+52−3+521+51+51−51−5-1−1−5−1+53+523−52-1-1-11+51−5−3−52−3+5211112-22-2000000−1−52−1+521+521−52−1−52−1+521+521−52000000000000000
χ36444-4-4−1−5−1+53+523−52−1−5−1+53+523−52−3−52−3−52−3+52−3+521+51+51−51−5-1−1−5−1+53+523−52-1-1-11+51−5−3−52−3+521111-22-220000001+521−52−1−52−1+521+521−52−1−52−1+52000000000000000
χ3744-44-4−1+5−1−53−523+52−1+5−1−53−523+523−523−523+523+521−51−51+51+5-11−51+5−3+52−3−5211-1−1+5−1−5−3+52−3−52-1-1112-2-22000000−1+52−1−521−521+521−521+52−1+52−1−52000000000000000
χ3844-44-4−1+5−1−53−523+52−1+5−1−53−523+523−523−523+523+521−51−51+51+5-11−51+5−3+52−3−5211-1−1+5−1−5−3+52−3−52-1-111-222-20000001−521+52−1+52−1−52−1+52−1−521−521+52000000000000000
χ3944-44-43−523+52−1−5−1+53−523+52−1−5−1+5−1−5−1−5−1+5−1+5−3+52−3+52−3−52−3−52-1−3+52−3−521+51−511-13−523+521+51−5-1-11100002i−2i2i−2i0000000000−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ70000000
χ4044-44-43−523+52−1−5−1+53−523+52−1−5−1+5−1−5−1−5−1+5−1+5−3+52−3+52−3−52−3−52-1−3+52−3−521+51−511-13−523+521+51−5-1-1110000−2i2i−2i2i0000000000ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ70000000
χ4144-44-43+523−52−1+5−1−53+523−52−1+5−1−5−1+5−1+5−1−5−1−5−3−52−3−52−3+52−3+52-1−3−52−3+521−51+511-13+523−521−51+5-1-11100002i−2i2i−2i0000000000−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ190000000
χ4244-44-43+523−52−1+5−1−53+523−52−1+5−1−5−1+5−1+5−1−5−1−5−3−52−3−52−3+52−3+52-1−3−52−3+521−51+511-13+523−521−51+5-1-1110000−2i2i−2i2i0000000000ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ190000000
χ4344-44-4−1−5−1+53+523−52−1−5−1+53+523−523+523+523−523−521+51+51−51−5-11+51−5−3−52−3+5211-1−1−5−1+5−3−52−3+52-1-1112-2-22000000−1−52−1+521+521−521+521−52−1−52−1+52000000000000000
χ4444-44-4−1−5−1+53+523−52−1−5−1+53+523−523+523+523−523−521+51+51−51−5-11+51−5−3−52−3+5211-1−1−5−1+5−3−52−3+52-1-111-222-20000001+521−52−1−52−1+52−1−52−1+521+521−52000000000000000
χ4544-4-44−1+5−1−53−523+52−1+5−1−53−523+52−3+52−3+52−3−52−3−52−1+5−1+5−1−5−1−5-11−51+5−3+52−3−5211-11−51+53−523+5211-1-122-2-2000000−1+52−1−52−1+52−1−521−521+521−521+52000000000000000
χ4644-4-44−1+5−1−53−523+52−1+5−1−53−523+52−3+52−3+52−3−52−3−52−1+5−1+5−1−5−1−5-11−51+5−3+52−3−5211-11−51+53−523+5211-1-1-2-2220000001−521+521−521+52−1+52−1−52−1+52−1−52000000000000000
χ4744-4-443−523+52−1−5−1+53−523+52−1−5−1+51+51+51−51−53−523−523+523+52-1−3+52−3−521+51−511-1−3+52−3−52−1−5−1+511-1-100002-2-220000000000−1+52−1−521−521+521−521+52−1+52−1−520000000
χ4844-4-443−523+52−1−5−1+53−523+52−1−5−1+51+51+51−51−53−523−523+523+52-1−3+52−3−521+51−511-1−3+52−3−52−1−5−1+511-1-10000-222-200000000001−521+52−1+52−1−52−1+52−1−521−521+520000000
χ4944-4-443+523−52−1+5−1−53+523−52−1+5−1−51−51−51+51+53+523+523−523−52-1−3−52−3+521−51+511-1−3−52−3+52−1+5−1−511-1-100002-2-220000000000−1−52−1+521+521−521+521−52−1−52−1+520000000
χ5044-4-443+523−52−1+5−1−53+523−52−1+5−1−51−51−51+51+53+523+523−523−52-1−3−52−3+521−51+511-1−3−52−3+52−1+5−1−511-1-10000-222-200000000001+521−52−1−52−1+52−1−52−1+521+521−520000000
χ5144-4-44−1−5−1+53+523−52−1−5−1+53+523−52−3−52−3−52−3+52−3+52−1−5−1−5−1+5−1+5-11+51−5−3−52−3+5211-11+51−53+523−5211-1-122-2-2000000−1−52−1+52−1−52−1+521+521−521+521−52000000000000000
χ5244-4-44−1−5−1+53+523−52−1−5−1+53+523−52−3−52−3−52−3+52−3+52−1−5−1−5−1+5−1+5-11+51−5−3−52−3+5211-11+51−53+523−5211-1-1-2-2220000001+521−521+521−52−1−52−1+52−1−52−1+52000000000000000
χ534-40004444-4-4-4-4000000004000000-400000000000000004-400000000000000000000000
χ544-40004444-4-4-4-4000000004000000-40000000000000000-4400000000000000000000000
χ5588888-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-23-2-2-2-2333-2-2-2-23333000000000000000000000000000000000
χ56888-8-8-2-2-2-2-2-2-2-2222222223-2-2-2-23332222-3-3-3-3000000000000000000000000000000000
χ5788-88-8-2-2-2-2-2-2-2-2-2-2-2-2222232222-3-33-2-22233-3-3000000000000000000000000000000000
χ5888-8-88-2-2-2-2-2-2-2-22222-2-2-2-232222-3-3322-2-2-3-333000000000000000000000000000000000
χ598-8000-2-2-2-222222i5−2i52i5−2i52i5−2i52i5−2i5300005-5-30000i5−i5i5−i5000000000000000000000000000000000
χ608-8000-2-2-2-222222i5−2i52i5−2i5−2i52i5−2i52i530000-55-30000i5−i5−i5i5000000000000000000000000000000000
χ618-8000-2-2-2-22222−2i52i5−2i52i52i5−2i52i5−2i530000-55-30000−i5i5i5−i5000000000000000000000000000000000
χ628-8000-2-2-2-22222−2i52i5−2i52i5−2i52i5−2i52i5300005-5-30000−i5i5−i5i5000000000000000000000000000000000
χ638-8000−2+25−2−253−53+52−252+25−3+5−3−56ζ3+6ζ7+4ζ11+4ζ19−6ζ3−6ζ7−4ζ11−4ζ19−4ζ3−4ζ7−6ζ11−6ζ194ζ3+4ζ7+6ζ11+6ζ190000-200000020000−2i52i500000000000000000000000000000000000
χ648-8000−2+25−2−253−53+52−252+25−3+5−3−5−6ζ3−6ζ7−4ζ11−4ζ196ζ3+6ζ7+4ζ11+4ζ194ζ3+4ζ7+6ζ11+6ζ19−4ζ3−4ζ7−6ζ11−6ζ190000-2000000200002i5−2i500000000000000000000000000000000000
χ658-80003−53+5−2−25−2+25−3+5−3−52+252−2500006ζ3+6ζ7+4ζ11+4ζ19−6ζ3−6ζ7−4ζ11−4ζ19−4ζ3−4ζ7−6ζ11−6ζ194ζ3+4ζ7+6ζ11+6ζ19-20000002000000−2i52i5000000000000000000000000000000000
χ668-80003−53+5−2−25−2+25−3+5−3−52+252−250000−6ζ3−6ζ7−4ζ11−4ζ196ζ3+6ζ7+4ζ11+4ζ194ζ3+4ζ7+6ζ11+6ζ19−4ζ3−4ζ7−6ζ11−6ζ19-200000020000002i5−2i5000000000000000000000000000000000
χ678-80003+53−5−2+25−2−25−3−5−3+52−252+250000−4ζ3−4ζ7−6ζ11−6ζ194ζ3+4ζ7+6ζ11+6ζ196ζ3+6ζ7+4ζ11+4ζ19−6ζ3−6ζ7−4ζ11−4ζ19-20000002000000−2i52i5000000000000000000000000000000000
χ688-80003+53−5−2+25−2−25−3−5−3+52−252+2500004ζ3+4ζ7+6ζ11+6ζ19−4ζ3−4ζ7−6ζ11−6ζ19−6ζ3−6ζ7−4ζ11−4ζ196ζ3+6ζ7+4ζ11+4ζ19-200000020000002i5−2i5000000000000000000000000000000000
χ698-8000−2−25−2+253+53−52+252−25−3−5−3+5−4ζ3−4ζ7−6ζ11−6ζ194ζ3+4ζ7+6ζ11+6ζ196ζ3+6ζ7+4ζ11+4ζ19−6ζ3−6ζ7−4ζ11−4ζ190000-200000020000−2i52i500000000000000000000000000000000000
χ708-8000−2−25−2+253+53−52+252−25−3−5−3+54ζ3+4ζ7+6ζ11+6ζ19−4ζ3−4ζ7−6ζ11−6ζ19−6ζ3−6ζ7−4ζ11−4ζ196ζ3+6ζ7+4ζ11+4ζ190000-2000000200002i5−2i500000000000000000000000000000000000

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