Finite Group Databasebeta

← Group #13104317

Character table — Group #13104317

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size111122444444444444444488888888888888882020202020202020252525254040404040404040404040404040404050505050505050505050
order12224455551010101010101010101010105101010202020202020202020202020222244442222101010101010101020202020202020204444444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-111-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1
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
χ51111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ71111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ81111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1
χ911-1-1i−i11111111-1-1-1-1-1-1-1-111-1-1iiii−i−i−i−iii−i−i1-11-1i−ii−i1-11-111-1-111-1-1ii−i−iii−i−ii−i11-1-1ii−i−i
χ1011-1-1i−i11111111-1-1-1-1-1-1-1-111-1-1iiii−i−i−i−iii−i−i1-1-11i−i−ii1-11-111-1-1-1-111ii−i−i−i−iiii−i-1-111−i−iii
χ1111-1-1i−i11111111-1-1-1-1-1-1-1-111-1-1iiii−i−i−i−iii−i−i-111-1−iii−i1-11-1-1-11111-1-1−i−iiiii−i−ii−i-1-111−i−iii
χ1211-1-1i−i11111111-1-1-1-1-1-1-1-111-1-1iiii−i−i−i−iii−i−i-11-11−ii−ii1-11-1-1-111-1-111−i−iii−i−iiii−i11-1-1ii−i−i
χ1311-1-1−ii11111111-1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii−i−iii1-11-1−ii−ii1-11-111-1-111-1-1−i−iii−i−iii−ii11-1-1−i−iii
χ1411-1-1−ii11111111-1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii−i−iii1-1-11−iii−i1-11-111-1-1-1-111−i−iiiii−i−i−ii-1-111ii−i−i
χ1511-1-1−ii11111111-1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii−i−iii-111-1i−i−ii1-11-1-1-11111-1-1ii−i−i−i−iii−ii-1-111ii−i−i
χ1611-1-1−ii11111111-1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii−i−iii-11-11i−ii−i1-11-1-1-111-1-111ii−i−iii−i−i−ii11-1-1−i−iii
χ172222222222222222222222222222222222222200000000-2-2-2-20000000000000000-2-200000000
χ182222-2-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-2-200000000000000002200000000
χ1922-2-22i−2i22222222-2-2-2-2-2-2-2-222-2-22i2i2i2i−2i−2i−2i−2i2i2i−2i−2i00000000-22-220000000000000000−2i2i00000000
χ2022-2-2−2i2i22222222-2-2-2-2-2-2-2-222-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i00000000-22-2200000000000000002i−2i00000000
χ212-22-2002222-2-2-2-2-2-2-2-222222-22-2000000000000000000002-2-2200000000000000000000002-22-2
χ222-22-2002222-2-2-2-2-2-2-2-222222-22-2000000000000000000002-2-220000000000000000000000-22-22
χ232-22-2002222-2-2-2-2-2-2-2-222222-22-200000000000000000000-222-20000000000000000002-22-20000
χ242-22-2002222-2-2-2-2-2-2-2-222222-22-200000000000000000000-222-2000000000000000000-22-220000
χ252-2-22002222-2-2-2-22222-2-2-2-22-2-220000000000000000000022-2-200000000000000000000002i−2i−2i2i
χ262-2-22002222-2-2-2-22222-2-2-2-22-2-220000000000000000000022-2-20000000000000000000000−2i2i2i−2i
χ272-2-22002222-2-2-2-22222-2-2-2-22-2-2200000000000000000000-2-2220000000000000000002-2-220000
χ282-2-22002222-2-2-2-22222-2-2-2-22-2-2200000000000000000000-2-222000000000000000000-222-20000
χ29444444−1+53−523+52−1−5−1+53−523+52−1−5−1+53−523+52−1−5−1+53−523+52−1−5-1-1-1-1−1+53−523+52−1−5−1+53−523+52−1−5-1-1-1-10022002200000000−1+52−1−52−1+52−1−520000−1+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+52−1−5-1-1-1-1−1+53−523+52−1−5−1+53−523+52−1−5-1-1-1-100-2-200-2-2000000001−521+521−521+5200001−521+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+52-1-1-1-13−52−1−5−1+53+523−52−1−5−1+53+52-1-1-1-1220022000000−1+52−1−52−1+52−1−520000−1+52−1−52−1+52−1−5200000000000000
χ324444443−52−1−5−1+53+523−52−1−5−1+53+523−52−1−5−1+53+523−52−1−5−1+53+52-1-1-1-13−52−1−5−1+53+523−52−1−5−1+53+52-1-1-1-1-2-200-2-20000001−521+521−521+5200001−521+521−521+5200000000000000
χ334444443+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−52-1-1-1-13+52−1+5−1−53−523+52−1+5−1−53−52-1-1-1-1220022000000−1−52−1+52−1−52−1+520000−1−52−1+52−1−52−1+5200000000000000
χ344444443+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−52-1-1-1-13+52−1+5−1−53−523+52−1+5−1−53−52-1-1-1-1-2-200-2-20000001+521−521+521−5200001+521−521+521−5200000000000000
χ35444444−1−53+523−52−1+5−1−53+523−52−1+5−1−53+523−52−1+5−1−53+523−52−1+5-1-1-1-1−1−53+523−52−1+5−1−53+523−52−1+5-1-1-1-10022002200000000−1−52−1+52−1−52−1+520000−1−52−1+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+5-1-1-1-1−1−53+523−52−1+5−1−53+523−52−1+5-1-1-1-100-2-200-2-2000000001+521−521+521−5200001+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+52−1−5-1-1-1-11−5−3+52−3−521+51−5−3+52−3−521+51111002200-2-200000000−1+52−1−52−1+52−1−5200001−521+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+52−1−5-1-1-1-11−5−3+52−3−521+51−5−3+52−3−521+5111100-2-20022000000001−521+521−521+520000−1+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+52-1-1-1-1−3+521+51−5−3−52−3+521+51−5−3−5211112200-2-2000000−1+52−1−52−1+52−1−5200001−521+521−521+5200000000000000
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+52-1-1-1-1−3+521+51−5−3−52−3+521+51−5−3−521111-2-200220000001−521+521−521+520000−1+52−1−52−1+52−1−5200000000000000
χ414444-4-43+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−52-1-1-1-1−3−521−51+5−3+52−3−521−51+5−3+5211112200-2-2000000−1−52−1+52−1−52−1+5200001+521−521+521−5200000000000000
χ424444-4-43+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−523+52−1+5−1−53−52-1-1-1-1−3−521−51+5−3+52−3−521−51+5−3+521111-2-200220000001+521−521+521−520000−1−52−1+52−1−52−1+5200000000000000
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+5-1-1-1-11+5−3−52−3+521−51+5−3−52−3+521−51111002200-2-200000000−1−52−1+52−1−52−1+5200001+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+5-1-1-1-11+5−3−52−3+521−51+5−3−52−3+521−5111100-2-20022000000001+521−521+521−520000−1−52−1+52−1−52−1+520000000000
χ4544-4-44i−4i−1+53−523+52−1−5−1+53−523+52−1−51−5−3+52−3−521+51−5−3+52−3−521+5-1-111−2ζ11−2ζ19ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ19−2ζ3−2ζ72ζ11+2ζ19−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ192ζ3+2ζ7−i−iii002-2002i−2i00000000−1+52−1−521−521+520000−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ70000000000
χ4644-4-44i−4i−1+53−523+52−1−5−1+53−523+52−1−51−5−3+52−3−521+51−5−3+52−3−521+5-1-111−2ζ11−2ζ19ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ19−2ζ3−2ζ72ζ11+2ζ19−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ192ζ3+2ζ7−i−iii00-2200−2i2i000000001−521+52−1+52−1−520000ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ70000000000
χ4744-4-44i−4i3−52−1−5−1+53+523−52−1−5−1+53+52−3+521+51−5−3−52−3+521+51−5−3−52-1-111ζ3+ζ7+2ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ192ζ3+2ζ7+ζ11+ζ19−ζ3−ζ7−2ζ11−2ζ192ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−ζ11−ζ19−i−iii2-2002i−2i000000−1+52−1−521−521+520000−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ700000000000000
χ4844-4-44i−4i3−52−1−5−1+53+523−52−1−5−1+53+52−3+521+51−5−3−52−3+521+51−5−3−52-1-111ζ3+ζ7+2ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ192ζ3+2ζ7+ζ11+ζ19−ζ3−ζ7−2ζ11−2ζ192ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−ζ11−ζ19−i−iii-2200−2i2i0000001−521+52−1+52−1−520000ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ700000000000000
χ4944-4-44i−4i3+52−1+5−1−53−523+52−1+5−1−53−52−3−521−51+5−3+52−3−521−51+5−3+52-1-1112ζ3+2ζ7+ζ11+ζ19−2ζ11−2ζ19−2ζ3−2ζ7ζ3+ζ7+2ζ11+2ζ19−2ζ3−2ζ7−ζ11−ζ192ζ11+2ζ192ζ3+2ζ7−ζ3−ζ7−2ζ11−2ζ19−i−iii2-2002i−2i000000−1−52−1+521+521−520000−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ1900000000000000
χ5044-4-44i−4i3+52−1+5−1−53−523+52−1+5−1−53−52−3−521−51+5−3+52−3−521−51+5−3+52-1-1112ζ3+2ζ7+ζ11+ζ19−2ζ11−2ζ19−2ζ3−2ζ7ζ3+ζ7+2ζ11+2ζ19−2ζ3−2ζ7−ζ11−ζ192ζ11+2ζ192ζ3+2ζ7−ζ3−ζ7−2ζ11−2ζ19−i−iii-2200−2i2i0000001+521−52−1−52−1+520000ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ1900000000000000
χ5144-4-44i−4i−1−53+523−52−1+5−1−53+523−52−1+51+5−3−52−3+521−51+5−3−52−3+521−5-1-111−2ζ3−2ζ72ζ3+2ζ7+ζ11+ζ19ζ3+ζ7+2ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7−ζ11−ζ19−ζ3−ζ7−2ζ11−2ζ192ζ11+2ζ19−i−iii002-2002i−2i00000000−1−52−1+521+521−520000−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ190000000000
χ5244-4-44i−4i−1−53+523−52−1+5−1−53+523−52−1+51+5−3−52−3+521−51+5−3−52−3+521−5-1-111−2ζ3−2ζ72ζ3+2ζ7+ζ11+ζ19ζ3+ζ7+2ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7−ζ11−ζ19−ζ3−ζ7−2ζ11−2ζ192ζ11+2ζ19−i−iii00-2200−2i2i000000001+521−52−1−52−1+520000ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ190000000000
χ5344-4-4−4i4i−1+53−523+52−1−5−1+53−523+52−1−51−5−3+52−3−521+51−5−3+52−3−521+5-1-1112ζ11+2ζ19−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ192ζ3+2ζ7−2ζ11−2ζ19ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ19−2ζ3−2ζ7ii−i−i002-200−2i2i00000000−1+52−1−521−521+520000ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ70000000000
χ5444-4-4−4i4i−1+53−523+52−1−5−1+53−523+52−1−51−5−3+52−3−521+51−5−3+52−3−521+5-1-1112ζ11+2ζ19−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ192ζ3+2ζ7−2ζ11−2ζ19ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ19−2ζ3−2ζ7ii−i−i00-22002i−2i000000001−521+52−1+52−1−520000−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ70000000000
χ5544-4-4−4i4i3−52−1−5−1+53+523−52−1−5−1+53+52−3+521+51−5−3−52−3+521+51−5−3−52-1-111−ζ3−ζ7−2ζ11−2ζ192ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−ζ11−ζ19ζ3+ζ7+2ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ192ζ3+2ζ7+ζ11+ζ19ii−i−i2-200−2i2i000000−1+52−1−521−521+520000ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ700000000000000
χ5644-4-4−4i4i3−52−1−5−1+53+523−52−1−5−1+53+52−3+521+51−5−3−52−3+521+51−5−3−52-1-111−ζ3−ζ7−2ζ11−2ζ192ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−ζ11−ζ19ζ3+ζ7+2ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ192ζ3+2ζ7+ζ11+ζ19ii−i−i-22002i−2i0000001−521+52−1+52−1−520000−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ700000000000000
χ5744-4-4−4i4i3+52−1+5−1−53−523+52−1+5−1−53−52−3−521−51+5−3+52−3−521−51+5−3+52-1-111−2ζ3−2ζ7−ζ11−ζ192ζ11+2ζ192ζ3+2ζ7−ζ3−ζ7−2ζ11−2ζ192ζ3+2ζ7+ζ11+ζ19−2ζ11−2ζ19−2ζ3−2ζ7ζ3+ζ7+2ζ11+2ζ19ii−i−i2-200−2i2i000000−1−52−1+521+521−520000ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ1900000000000000
χ5844-4-4−4i4i3+52−1+5−1−53−523+52−1+5−1−53−52−3−521−51+5−3+52−3−521−51+5−3+52-1-111−2ζ3−2ζ7−ζ11−ζ192ζ11+2ζ192ζ3+2ζ7−ζ3−ζ7−2ζ11−2ζ192ζ3+2ζ7+ζ11+ζ19−2ζ11−2ζ19−2ζ3−2ζ7ζ3+ζ7+2ζ11+2ζ19ii−i−i-22002i−2i0000001+521−52−1−52−1+520000−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ1900000000000000
χ5944-4-4−4i4i−1−53+523−52−1+5−1−53+523−52−1+51+5−3−52−3+521−51+5−3−52−3+521−5-1-1112ζ3+2ζ7−2ζ3−2ζ7−ζ11−ζ19−ζ3−ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7+ζ11+ζ19ζ3+ζ7+2ζ11+2ζ19−2ζ11−2ζ19ii−i−i002-200−2i2i00000000−1−52−1+521+521−520000ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ190000000000
χ6044-4-4−4i4i−1−53+523−52−1+5−1−53+523−52−1+51+5−3−52−3+521−51+5−3−52−3+521−5-1-1112ζ3+2ζ7−2ζ3−2ζ7−ζ11−ζ19−ζ3−ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7+ζ11+ζ19ζ3+ζ7+2ζ11+2ζ19−2ζ11−2ζ19ii−i−i00-22002i−2i000000001+521−52−1−52−1+520000−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ190000000000
χ61888888-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-23333-2-2-2-2-2-2-2-2333300000000000000000000000000000000000000
χ628888-8-8-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2333322222222-3-3-3-300000000000000000000000000000000000000
χ6388-8-88i−8i-2-2-2-2-2-2-2-22222222233-3-3−2i−2i−2i−2i2i2i2i2i3i3i−3i−3i00000000000000000000000000000000000000
χ6488-8-8−8i8i-2-2-2-2-2-2-2-22222222233-3-32i2i2i2i−2i−2i−2i−2i−3i−3i3i3i00000000000000000000000000000000000000
χ658-88-800-2-2-2-222222222-2-2-2-23-33-3000000005i−5i5i−5i00000000000000000000000000000000000000
χ668-88-800-2-2-2-222222222-2-2-2-23-33-300000000−5i5i−5i5i00000000000000000000000000000000000000
χ678-88-800−2+253−53+5−2−252−25−3+5−3−52+252−25−3+5−3−52+25−2+253−53+5−2−25-22-2200000000000000000000000000000000000000000000000000
χ688-88-8003−5−2−25−2+253+5−3+52+252−25−3−5−3+52+252−25−3−53−5−2−25−2+253+5-22-2200000000000000000000000000000000000000000000000000
χ698-88-8003+5−2+25−2−253−5−3−52−252+25−3+5−3−52−252+25−3+53+5−2+25−2−253−5-22-2200000000000000000000000000000000000000000000000000
χ708-88-800−2−253+53−5−2+252+25−3−5−3+52−252+25−3−5−3+52−25−2−253+53−5−2+25-22-2200000000000000000000000000000000000000000000000000
χ718-8-8800-2-2-2-22222-2-2-2-222223-3-33000000005-5-5500000000000000000000000000000000000000
χ728-8-8800-2-2-2-22222-2-2-2-222223-3-3300000000-555-500000000000000000000000000000000000000
χ738-8-8800−2+253−53+5−2−252−25−3+5−3−52+25−2+253−53+5−2−252−25−3+5−3−52+25-222-200000000000000000000000000000000000000000000000000
χ748-8-88003−5−2−25−2+253+5−3+52+252−25−3−53−5−2−25−2+253+5−3+52+252−25−3−5-222-200000000000000000000000000000000000000000000000000
χ758-8-88003+5−2+25−2−253−5−3−52−252+25−3+53+5−2+25−2−253−5−3−52−252+25−3+5-222-200000000000000000000000000000000000000000000000000
χ768-8-8800−2−253+53−5−2+252+25−3−5−3+52−25−2−253+53−5−2+252+25−3−5−3+52−25-222-200000000000000000000000000000000000000000000000000

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