Finite Group Databasebeta

← Group #13104225

Character table — Group #13104225

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size111122444444444444444488888888888888882020202020202020252525254040404040404040404040404040404050505050505050505050
order12442455551010101020202020202020205101010101010102020202020202020888888882244404040404040404040404040404040402444444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ51111-1-111111111111111111-1-1-1-1-1-11-1-1-1-111-1-111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ61111-1-111111111111111111-1-1-1-1-1-11-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ71111-1-111111111111111111-1-1-1-1-1-11-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ81111-1-111111111111111111-1-1-1-1-1-11-1-1-1-111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1
χ911-1-11-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1i−ii−ii−ii−i11-1-1ii−i−iii−i−iii−i−iii−i−i1-111-1-111-1-1
χ1011-1-11-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1i−ii−i−ii−ii11-1-1ii−i−iii−i−i−i−iii−i−iii1-1-1-111-1-111
χ1111-1-11-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−ii−iii−ii−i11-1-1−i−iii−i−iiiii−i−iii−i−i1-1-1-111-1-111
χ1211-1-11-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−ii−ii−ii−ii11-1-1−i−iii−i−iii−i−iii−i−iii1-111-1-111-1-1
χ1311-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111111-1-111i−i−iii−i−ii11-1-1ii−i−i−i−iiiii−i−i−i−iii-1111-1-1-1-111
χ1411-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111111-1-111i−i−ii−iii−i11-1-1ii−i−i−i−iii−i−iiiii−i−i-11-1-11111-1-1
χ1511-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111111-1-111−iii−ii−i−ii11-1-1−i−iiiii−i−iii−i−i−i−iii-11-1-11111-1-1
χ1611-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111111-1-111−iii−i−iii−i11-1-1−i−iiiii−i−i−i−iiiii−i−i-1111-1-1-1-111
χ172222222222222222222222222222222222222200000000-2-2-2-20000000000000000-2-200000000
χ182222-2-222222222222222222-2-2-2-2-2-22-2-2-2-222-2-200000000-2-2-2-200000000000000002200000000
χ1922-2-22-222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-200000000-2-2220000000000000000-2200000000
χ2022-2-2-2222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-222222-2-22200000000-2-22200000000000000002-200000000
χ212-22i−2i002222-2-2-2-22i2i2i2i−2i−2i−2i−2i2000000-200002i−2i00000000002-22i−2i00000000000000000000002i−2i2-2
χ222-22i−2i002222-2-2-2-22i2i2i2i−2i−2i−2i−2i2000000-200002i−2i00000000002-22i−2i0000000000000000000000−2i2i-22
χ232-22i−2i002222-2-2-2-22i2i2i2i−2i−2i−2i−2i2000000-200002i−2i0000000000-22−2i2i0000000000000000002-22i−2i0000
χ242-22i−2i002222-2-2-2-22i2i2i2i−2i−2i−2i−2i2000000-200002i−2i0000000000-22−2i2i000000000000000000-22−2i2i0000
χ252-2−2i2i002222-2-2-2-2−2i−2i−2i−2i2i2i2i2i2000000-20000−2i2i00000000002-2−2i2i00000000000000000000002i−2i-22
χ262-2−2i2i002222-2-2-2-2−2i−2i−2i−2i2i2i2i2i2000000-20000−2i2i00000000002-2−2i2i0000000000000000000000−2i2i2-2
χ272-2−2i2i002222-2-2-2-2−2i−2i−2i−2i2i2i2i2i2000000-20000−2i2i0000000000-222i−2i0000000000000000002-2−2i2i0000
χ282-2−2i2i002222-2-2-2-2−2i−2i−2i−2i2i2i2i2i2000000-20000−2i2i0000000000-222i−2i000000000000000000-222i−2i0000
χ29444444−1+53−523+52−1−5−1+53−523+52−1−5−1+53−523+52−1−5−1+53−523+52−1−5-1−1+53−523+52−1−5-1-1-1−1+53−523+52−1−5-1-1-1-100002222000000000000−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−520000000000
χ30444444−1+53−523+52−1−5−1+53−523+52−1−5−1+53−523+52−1−5−1+53−523+52−1−5-1−1+53−523+52−1−5-1-1-1−1+53−523+52−1−5-1-1-1-10000-2-2-2-20000000000001−521+521−521+521−521+521−521+520000000000
χ314444443−52−1−5−1+53+523−52−1−5−1+53+523−52−1−5−1+53+523−52−1−5−1+53+52-13−52−1−5−1+53+52-1-1-13−52−1−5−1+53+52-1-1-1-1222200000000−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52000000000000000000
χ324444443−52−1−5−1+53+523−52−1−5−1+53+523−52−1−5−1+53+523−52−1−5−1+53+52-13−52−1−5−1+53+52-1-1-13−52−1−5−1+53+52-1-1-1-1-2-2-2-2000000001−521+521−521+521−521+521−521+52000000000000000000
χ334444443+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−52-13+52−1+5−1−53−52-1-1-13+52−1+5−1−53−52-1-1-1-1222200000000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52000000000000000000
χ344444443+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−52-13+52−1+5−1−53−52-1-1-13+52−1+5−1−53−52-1-1-1-1-2-2-2-2000000001+521−521+521−521+521−521+521−52000000000000000000
χ35444444−1−53+523−52−1+5−1−53+523−52−1+5−1−53+523−52−1+5−1−53+523−52−1+5-1−1−53+523−52−1+5-1-1-1−1−53+523−52−1+5-1-1-1-100002222000000000000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+520000000000
χ36444444−1−53+523−52−1+5−1−53+523−52−1+5−1−53+523−52−1+5−1−53+523−52−1+5-1−1−53+523−52−1+5-1-1-1−1−53+523−52−1+5-1-1-1-10000-2-2-2-20000000000001+521−521+521−521+521−521+521−520000000000
χ374444-4-4−1+53−523+52−1−5−1+53−523+52−1−5−1+53−523+52−1−5−1+53−523+52−1−5-11−5−3+52−3−521+511-11−5−3+52−3−521+5-1-111000022-2-2000000000000−1+52−1−52−1+52−1−521−521+521−521+520000000000
χ384444-4-4−1+53−523+52−1−5−1+53−523+52−1−5−1+53−523+52−1−5−1+53−523+52−1−5-11−5−3+52−3−521+511-11−5−3+52−3−521+5-1-1110000-2-2220000000000001−521+521−521+52−1+52−1−52−1+52−1−520000000000
χ394444-4-43−52−1−5−1+53+523−52−1−5−1+53+523−52−1−5−1+53+523−52−1−5−1+53+52-1−3+521+51−5−3−5211-1−3+521+51−5−3−52-1-11122-2-200000000−1+52−1−52−1+52−1−521−521+521−521+52000000000000000000
χ404444-4-43−52−1−5−1+53+523−52−1−5−1+53+523−52−1−5−1+53+523−52−1−5−1+53+52-1−3+521+51−5−3−5211-1−3+521+51−5−3−52-1-111-2-222000000001−521+521−521+52−1+52−1−52−1+52−1−52000000000000000000
χ414444-4-43+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−52-1−3−521−51+5−3+5211-1−3−521−51+5−3+52-1-11122-2-200000000−1−52−1+52−1−52−1+521+521−521+521−52000000000000000000
χ424444-4-43+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−52-1−3−521−51+5−3+5211-1−3−521−51+5−3+52-1-111-2-222000000001+521−521+521−52−1−52−1+52−1−52−1+52000000000000000000
χ434444-4-4−1−53+523−52−1+5−1−53+523−52−1+5−1−53+523−52−1+5−1−53+523−52−1+5-11+5−3−52−3+521−511-11+5−3−52−3+521−5-1-111000022-2-2000000000000−1−52−1+52−1−52−1+521+521−521+521−520000000000
χ444444-4-4−1−53+523−52−1+5−1−53+523−52−1+5−1−53+523−52−1+5−1−53+523−52−1+5-11+5−3−52−3+521−511-11+5−3−52−3+521−5-1-1110000-2-2220000000000001+521−521+521−52−1−52−1+52−1−52−1+520000000000
χ4544-4-44-4−1+53−523+52−1−5−1+53−523+52−1−51−5−3+52−3−521+51−5−3+52−3−521+5-1−1+53−523+52−1−5-1-1-11−5−3+52−3−521+5111100002i−2i2i−2i000000000000−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ70000000000
χ4644-4-44-4−1+53−523+52−1−5−1+53−523+52−1−51−5−3+52−3−521+51−5−3+52−3−521+5-1−1+53−523+52−1−5-1-1-11−5−3+52−3−521+511110000−2i2i−2i2i000000000000ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ70000000000
χ4744-4-44-43−52−1−5−1+53+523−52−1−5−1+53+52−3+521+51−5−3−52−3+521+51−5−3−52-13−52−1−5−1+53+52-1-1-1−3+521+51−5−3−5211112i−2i2i−2i00000000−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7000000000000000000
χ4844-4-44-43−52−1−5−1+53+523−52−1−5−1+53+52−3+521+51−5−3−52−3+521+51−5−3−52-13−52−1−5−1+53+52-1-1-1−3+521+51−5−3−521111−2i2i−2i2i00000000ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7000000000000000000
χ4944-4-44-43+52−1+5−1−53−523+52−1+5−1−53−52−3−521−51+5−3+52−3−521−51+5−3+52-13+52−1+5−1−53−52-1-1-1−3−521−51+5−3+5211112i−2i2i−2i00000000−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19000000000000000000
χ5044-4-44-43+52−1+5−1−53−523+52−1+5−1−53−52−3−521−51+5−3+52−3−521−51+5−3+52-13+52−1+5−1−53−52-1-1-1−3−521−51+5−3+521111−2i2i−2i2i00000000ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19000000000000000000
χ5144-4-44-4−1−53+523−52−1+5−1−53+523−52−1+51+5−3−52−3+521−51+5−3−52−3+521−5-1−1−53+523−52−1+5-1-1-11+5−3−52−3+521−5111100002i−2i2i−2i000000000000−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ190000000000
χ5244-4-44-4−1−53+523−52−1+5−1−53+523−52−1+51+5−3−52−3+521−51+5−3−52−3+521−5-1−1−53+523−52−1+5-1-1-11+5−3−52−3+521−511110000−2i2i−2i2i000000000000ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ190000000000
χ5344-4-4-44−1+53−523+52−1−5−1+53−523+52−1−51−5−3+52−3−521+51−5−3+52−3−521+5-11−5−3+52−3−521+511-1−1+53−523+52−1−511-1-100002i−2i−2i2i000000000000−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ70000000000
χ5444-4-4-44−1+53−523+52−1−5−1+53−523+52−1−51−5−3+52−3−521+51−5−3+52−3−521+5-11−5−3+52−3−521+511-1−1+53−523+52−1−511-1-10000−2i2i2i−2i000000000000ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ70000000000
χ5544-4-4-443−52−1−5−1+53+523−52−1−5−1+53+52−3+521+51−5−3−52−3+521+51−5−3−52-1−3+521+51−5−3−5211-13−52−1−5−1+53+5211-1-12i−2i−2i2i00000000−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7000000000000000000
χ5644-4-4-443−52−1−5−1+53+523−52−1−5−1+53+52−3+521+51−5−3−52−3+521+51−5−3−52-1−3+521+51−5−3−5211-13−52−1−5−1+53+5211-1-1−2i2i2i−2i00000000ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7000000000000000000
χ5744-4-4-443+52−1+5−1−53−523+52−1+5−1−53−52−3−521−51+5−3+52−3−521−51+5−3+52-1−3−521−51+5−3+5211-13+52−1+5−1−53−5211-1-12i−2i−2i2i00000000−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19000000000000000000
χ5844-4-4-443+52−1+5−1−53−523+52−1+5−1−53−52−3−521−51+5−3+52−3−521−51+5−3+52-1−3−521−51+5−3+5211-13+52−1+5−1−53−5211-1-1−2i2i2i−2i00000000ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19000000000000000000
χ5944-4-4-44−1−53+523−52−1+5−1−53+523−52−1+51+5−3−52−3+521−51+5−3−52−3+521−5-11+5−3−52−3+521−511-1−1−53+523−52−1+511-1-100002i−2i−2i2i000000000000−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ190000000000
χ6044-4-4-44−1−53+523−52−1+5−1−53+523−52−1+51+5−3−52−3+521−51+5−3−52−3+521−5-11+5−3−52−3+521−511-1−1−53+523−52−1+511-1-10000−2i2i2i−2i000000000000ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ190000000000
χ61888888-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-23-2-2-2-2333-2-2-2-2333300000000000000000000000000000000000000
χ628888-8-8-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-232222-3-33222233-3-300000000000000000000000000000000000000
χ6388-8-88-8-2-2-2-2-2-2-2-2222222223-2-2-2-23332222-3-3-3-300000000000000000000000000000000000000
χ6488-8-8-88-2-2-2-2-2-2-2-22222222232222-3-33-2-2-2-2-3-33300000000000000000000000000000000000000
χ658-88i−8i00-2-2-2-22222−2i−2i−2i−2i2i2i2i2i300005-5-300003i−3i5i−5i00000000000000000000000000000000000000
χ668-88i−8i00-2-2-2-22222−2i−2i−2i−2i2i2i2i2i30000-55-300003i−3i−5i5i00000000000000000000000000000000000000
χ678-88i−8i00−2+253−53+5−2−252−25−3+5−3−52+25−4ζ11−4ζ192ζ3+2ζ7+4ζ11+4ζ194ζ3+4ζ7+2ζ11+2ζ19−4ζ3−4ζ74ζ11+4ζ19−2ζ3−2ζ7−4ζ11−4ζ19−4ζ3−4ζ7−2ζ11−2ζ194ζ3+4ζ7-200000020000−2i2i0000000000000000000000000000000000000000
χ688-88i−8i003−5−2−25−2+253+5−3+52+252−25−3−52ζ3+2ζ7+4ζ11+4ζ19−4ζ3−4ζ7−4ζ11−4ζ194ζ3+4ζ7+2ζ11+2ζ19−2ζ3−2ζ7−4ζ11−4ζ194ζ3+4ζ74ζ11+4ζ19−4ζ3−4ζ7−2ζ11−2ζ19-200000020000−2i2i0000000000000000000000000000000000000000
χ698-88i−8i003+5−2+25−2−253−5−3−52−252+25−3+54ζ3+4ζ7+2ζ11+2ζ19−4ζ11−4ζ19−4ζ3−4ζ72ζ3+2ζ7+4ζ11+4ζ19−4ζ3−4ζ7−2ζ11−2ζ194ζ11+4ζ194ζ3+4ζ7−2ζ3−2ζ7−4ζ11−4ζ19-200000020000−2i2i0000000000000000000000000000000000000000
χ708-88i−8i00−2−253+53−5−2+252+25−3−5−3+52−25−4ζ3−4ζ74ζ3+4ζ7+2ζ11+2ζ192ζ3+2ζ7+4ζ11+4ζ19−4ζ11−4ζ194ζ3+4ζ7−4ζ3−4ζ7−2ζ11−2ζ19−2ζ3−2ζ7−4ζ11−4ζ194ζ11+4ζ19-200000020000−2i2i0000000000000000000000000000000000000000
χ718-8−8i8i00-2-2-2-222222i2i2i2i−2i−2i−2i−2i300005-5-30000−3i3i−5i5i00000000000000000000000000000000000000
χ728-8−8i8i00-2-2-2-222222i2i2i2i−2i−2i−2i−2i30000-55-30000−3i3i5i−5i00000000000000000000000000000000000000
χ738-8−8i8i00−2+253−53+5−2−252−25−3+5−3−52+254ζ11+4ζ19−2ζ3−2ζ7−4ζ11−4ζ19−4ζ3−4ζ7−2ζ11−2ζ194ζ3+4ζ7−4ζ11−4ζ192ζ3+2ζ7+4ζ11+4ζ194ζ3+4ζ7+2ζ11+2ζ19−4ζ3−4ζ7-2000000200002i−2i0000000000000000000000000000000000000000
χ748-8−8i8i003−5−2−25−2+253+5−3+52+252−25−3−5−2ζ3−2ζ7−4ζ11−4ζ194ζ3+4ζ74ζ11+4ζ19−4ζ3−4ζ7−2ζ11−2ζ192ζ3+2ζ7+4ζ11+4ζ19−4ζ3−4ζ7−4ζ11−4ζ194ζ3+4ζ7+2ζ11+2ζ19-2000000200002i−2i0000000000000000000000000000000000000000
χ758-8−8i8i003+5−2+25−2−253−5−3−52−252+25−3+5−4ζ3−4ζ7−2ζ11−2ζ194ζ11+4ζ194ζ3+4ζ7−2ζ3−2ζ7−4ζ11−4ζ194ζ3+4ζ7+2ζ11+2ζ19−4ζ11−4ζ19−4ζ3−4ζ72ζ3+2ζ7+4ζ11+4ζ19-2000000200002i−2i0000000000000000000000000000000000000000
χ768-8−8i8i00−2−253+53−5−2+252+25−3−5−3+52−254ζ3+4ζ7−4ζ3−4ζ7−2ζ11−2ζ19−2ζ3−2ζ7−4ζ11−4ζ194ζ11+4ζ19−4ζ3−4ζ74ζ3+4ζ7+2ζ11+2ζ192ζ3+2ζ7+4ζ11+4ζ19−4ζ11−4ζ19-2000000200002i−2i0000000000000000000000000000000000000000

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