Finite Group Databasebeta

← Group #13104254

Character table — Group #13104254

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size111122444444444444444488888888888888882020202020202020252525254040404040404040404040404040404050505050505050505050
order12224455551010101010101010101010105101010202020202020202020202020224444442222101010102020202020202020202020204444444444
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
χ51111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
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
χ81111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1
χ911-1-1i−i1111-1-111-1-111-1-1-1-111-1-1ii−i−iii−i−iii−i−i1-1i−i1-1i−i1-11-111-1-1ii−i−i11-1-1ii−i−ii−i11-1-1ii−i−i
χ1011-1-1i−i1111-1-111-1-111-1-1-1-111-1-1ii−i−iii−i−iii−i−i1-1i−i-11−ii1-11-111-1-1ii−i−i-1-111−i−iiii−i-1-111−i−iii
χ1111-1-1i−i1111-1-111-1-111-1-1-1-111-1-1ii−i−iii−i−iii−i−i-11−ii1-1i−i1-11-1-1-111−i−iii11-1-1ii−i−ii−i-1-111−i−iii
χ1211-1-1i−i1111-1-111-1-111-1-1-1-111-1-1ii−i−iii−i−iii−i−i-11−ii-11−ii1-11-1-1-111−i−iii-1-111−i−iiii−i11-1-1ii−i−i
χ1311-1-1−ii1111-1-111-1-111-1-1-1-111-1-1−i−iii−i−iii−i−iii1-1−ii1-1−ii1-11-111-1-1−i−iii11-1-1−i−iii−ii11-1-1−i−iii
χ1411-1-1−ii1111-1-111-1-111-1-1-1-111-1-1−i−iii−i−iii−i−iii1-1−ii-11i−i1-11-111-1-1−i−iii-1-111ii−i−i−ii-1-111ii−i−i
χ1511-1-1−ii1111-1-111-1-111-1-1-1-111-1-1−i−iii−i−iii−i−iii-11i−i1-1−ii1-11-1-1-111ii−i−i11-1-1−i−iii−ii-1-111ii−i−i
χ1611-1-1−ii1111-1-111-1-111-1-1-1-111-1-1−i−iii−i−iii−i−iii-11i−i-11i−i1-11-1-1-111ii−i−i-1-111ii−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−2i2222-2-222-2-222-2-2-2-222-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000-22-220000000000000000−2i2i00000000
χ2022-2-2−2i2i2222-2-222-2-222-2-2-2-222-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000-22-2200000000000000002i−2i00000000
χ212-22-200222222-2-2-2-2-2-222-2-22-22-2000000000000000000002-2-220000000000000000002i−2i2i−2i0000
χ222-22-200222222-2-2-2-2-2-222-2-22-22-2000000000000000000002-2-22000000000000000000−2i2i−2i2i0000
χ232-22-200222222-2-2-2-2-2-222-2-22-22-200000000000000000000-222-200000000000000000000002i−2i2i−2i
χ242-22-200222222-2-2-2-2-2-222-2-22-22-200000000000000000000-222-20000000000000000000000−2i2i−2i2i
χ252-2-22002222-2-2-2-222-2-2-2-2222-2-220000000000000000000022-2-20000000000000000002i−2i−2i2i0000
χ262-2-22002222-2-2-2-222-2-2-2-2222-2-220000000000000000000022-2-2000000000000000000−2i2i2i−2i0000
χ272-2-22002222-2-2-2-222-2-2-2-2222-2-2200000000000000000000-2-22200000000000000000000002-2-22
χ282-2-22002222-2-2-2-222-2-2-2-2222-2-2200000000000000000000-2-2220000000000000000000000-222-2
χ29444444−1+5−1−53−523+52−1+5−1−53−523+523−523+52−1+5−1−53−523+52−1+5−1−5-1-1-1-13−523+523−523+52−1+5−1−5−1+5−1−5-1-1-1-1222200000000−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52000000000000000000
χ30444444−1+5−1−53−523+52−1+5−1−53−523+523−523+52−1+5−1−53−523+52−1+5−1−5-1-1-1-13−523+523−523+52−1+5−1−5−1+5−1−5-1-1-1-1-2-2-2-2000000001−521+521−521+521−521+521−521+52000000000000000000
χ314444443−523+52−1−5−1+53−523+52−1−5−1+5−1−5−1+53−523+52−1−5−1+53−523+52-1-1-1-1−1−5−1+5−1−5−1+53−523+523−523+52-1-1-1-100002222000000000000−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−520000000000
χ324444443−523+52−1−5−1+53−523+52−1−5−1+5−1−5−1+53−523+52−1−5−1+53−523+52-1-1-1-1−1−5−1+5−1−5−1+53−523+523−523+52-1-1-1-10000-2-2-2-20000000000001−521+521−521+521−521+521−521+520000000000
χ334444443+523−52−1+5−1−53+523−52−1+5−1−5−1+5−1−53+523−52−1+5−1−53+523−52-1-1-1-1−1+5−1−5−1+5−1−53+523−523+523−52-1-1-1-100002222000000000000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+520000000000
χ344444443+523−52−1+5−1−53+523−52−1+5−1−5−1+5−1−53+523−52−1+5−1−53+523−52-1-1-1-1−1+5−1−5−1+5−1−53+523−523+523−52-1-1-1-10000-2-2-2-20000000000001+521−521+521−521+521−521+521−520000000000
χ35444444−1−5−1+53+523−52−1−5−1+53+523−523+523−52−1−5−1+53+523−52−1−5−1+5-1-1-1-13+523−523+523−52−1−5−1+5−1−5−1+5-1-1-1-1222200000000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52000000000000000000
χ36444444−1−5−1+53+523−52−1−5−1+53+523−523+523−52−1−5−1+53+523−52−1−5−1+5-1-1-1-13+523−523+523−52−1−5−1+5−1−5−1+5-1-1-1-1-2-2-2-2000000001+521−521+521−521+521−521+521−52000000000000000000
χ374444-4-4−1+5−1−53−523+52−1+5−1−53−523+523−523+52−1+5−1−53−523+52−1+5−1−5-1-1-1-1−3+52−3−52−3+52−3−521−51+51−51+5111122-2-200000000−1+52−1−52−1+52−1−521−521+521−521+52000000000000000000
χ384444-4-4−1+5−1−53−523+52−1+5−1−53−523+523−523+52−1+5−1−53−523+52−1+5−1−5-1-1-1-1−3+52−3−52−3+52−3−521−51+51−51+51111-2-222000000001−521+521−521+52−1+52−1−52−1+52−1−52000000000000000000
χ394444-4-43−523+52−1−5−1+53−523+52−1−5−1+5−1−5−1+53−523+52−1−5−1+53−523+52-1-1-1-11+51−51+51−5−3+52−3−52−3+52−3−521111000022-2-2000000000000−1+52−1−52−1+52−1−521−521+521−521+520000000000
χ404444-4-43−523+52−1−5−1+53−523+52−1−5−1+5−1−5−1+53−523+52−1−5−1+53−523+52-1-1-1-11+51−51+51−5−3+52−3−52−3+52−3−5211110000-2-2220000000000001−521+521−521+52−1+52−1−52−1+52−1−520000000000
χ414444-4-43+523−52−1+5−1−53+523−52−1+5−1−5−1+5−1−53+523−52−1+5−1−53+523−52-1-1-1-11−51+51−51+5−3−52−3+52−3−52−3+521111000022-2-2000000000000−1−52−1+52−1−52−1+521+521−521+521−520000000000
χ424444-4-43+523−52−1+5−1−53+523−52−1+5−1−5−1+5−1−53+523−52−1+5−1−53+523−52-1-1-1-11−51+51−51+5−3−52−3+52−3−52−3+5211110000-2-2220000000000001+521−521+521−52−1−52−1+52−1−52−1+520000000000
χ434444-4-4−1−5−1+53+523−52−1−5−1+53+523−523+523−52−1−5−1+53+523−52−1−5−1+5-1-1-1-1−3−52−3+52−3−52−3+521+51−51+51−5111122-2-200000000−1−52−1+52−1−52−1+521+521−521+521−52000000000000000000
χ444444-4-4−1−5−1+53+523−52−1−5−1+53+523−523+523−52−1−5−1+53+523−52−1−5−1+5-1-1-1-1−3−52−3+52−3−52−3+521+51−51+51−51111-2-222000000001+521−521+521−52−1−52−1+52−1−52−1+52000000000000000000
χ4544-4-44i−4i−1+5−1−53−523+521−51+53−523+52−3+52−3−52−1+5−1−5−3+52−3−521−51+5-1-111ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ19−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ19−2ζ11−2ζ19−2ζ3−2ζ72ζ11+2ζ192ζ3+2ζ7−i−iii2-22i−2i00000000−1+52−1−521−521+52−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7000000000000000000
χ4644-4-44i−4i−1+5−1−53−523+521−51+53−523+52−3+52−3−52−1+5−1−5−3+52−3−521−51+5-1-111ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ19−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ19−2ζ11−2ζ19−2ζ3−2ζ72ζ11+2ζ192ζ3+2ζ7−i−iii-22−2i2i000000001−521+52−1+52−1−52ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7000000000000000000
χ4744-4-44i−4i3−523+52−1−5−1+5−3+52−3−52−1−5−1+51+51−53−523+521+51−5−3+52−3−52-1-111−2ζ3−2ζ7−2ζ11−2ζ192ζ3+2ζ72ζ11+2ζ19ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ19−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ19−i−iii00002-22i−2i000000000000−1+52−1−521−521+52−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ70000000000
χ4844-4-44i−4i3−523+52−1−5−1+5−3+52−3−52−1−5−1+51+51−53−523+521+51−5−3+52−3−52-1-111−2ζ3−2ζ7−2ζ11−2ζ192ζ3+2ζ72ζ11+2ζ19ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ19−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ19−i−iii0000-22−2i2i0000000000001−521+52−1+52−1−52ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ70000000000
χ4944-4-44i−4i3+523−52−1+5−1−5−3−52−3+52−1+5−1−51−51+53+523−521−51+5−3−52−3+52-1-111−2ζ11−2ζ19−2ζ3−2ζ72ζ11+2ζ192ζ3+2ζ72ζ3+2ζ7+ζ11+ζ19ζ3+ζ7+2ζ11+2ζ19−2ζ3−2ζ7−ζ11−ζ19−ζ3−ζ7−2ζ11−2ζ19−i−iii00002-22i−2i000000000000−1−52−1+521+521−52−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ190000000000
χ5044-4-44i−4i3+523−52−1+5−1−5−3−52−3+52−1+5−1−51−51+53+523−521−51+5−3−52−3+52-1-111−2ζ11−2ζ19−2ζ3−2ζ72ζ11+2ζ192ζ3+2ζ72ζ3+2ζ7+ζ11+ζ19ζ3+ζ7+2ζ11+2ζ19−2ζ3−2ζ7−ζ11−ζ19−ζ3−ζ7−2ζ11−2ζ19−i−iii0000-22−2i2i0000000000001+521−52−1−52−1+52ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ190000000000
χ5144-4-44i−4i−1−5−1+53+523−521+51−53+523−52−3−52−3+52−1−5−1+5−3−52−3+521+51−5-1-1112ζ3+2ζ7+ζ11+ζ19ζ3+ζ7+2ζ11+2ζ19−2ζ3−2ζ7−ζ11−ζ19−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−2ζ11−2ζ192ζ3+2ζ72ζ11+2ζ19−i−iii2-22i−2i00000000−1−52−1+521+521−52−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19000000000000000000
χ5244-4-44i−4i−1−5−1+53+523−521+51−53+523−52−3−52−3+52−1−5−1+5−3−52−3+521+51−5-1-1112ζ3+2ζ7+ζ11+ζ19ζ3+ζ7+2ζ11+2ζ19−2ζ3−2ζ7−ζ11−ζ19−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−2ζ11−2ζ192ζ3+2ζ72ζ11+2ζ19−i−iii-22−2i2i000000001+521−52−1−52−1+52ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19000000000000000000
χ5344-4-4−4i4i−1+5−1−53−523+521−51+53−523+52−3+52−3−52−1+5−1−5−3+52−3−521−51+5-1-111−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ19ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ192ζ11+2ζ192ζ3+2ζ7−2ζ11−2ζ19−2ζ3−2ζ7ii−i−i2-2−2i2i00000000−1+52−1−521−521+52ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7000000000000000000
χ5444-4-4−4i4i−1+5−1−53−523+521−51+53−523+52−3+52−3−52−1+5−1−5−3+52−3−521−51+5-1-111−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ19ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ192ζ11+2ζ192ζ3+2ζ7−2ζ11−2ζ19−2ζ3−2ζ7ii−i−i-222i−2i000000001−521+52−1+52−1−52−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7000000000000000000
χ5544-4-4−4i4i3−523+52−1−5−1+5−3+52−3−52−1−5−1+51+51−53−523+521+51−5−3+52−3−52-1-1112ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ19−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ19ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ19ii−i−i00002-2−2i2i000000000000−1+52−1−521−521+52ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ70000000000
χ5644-4-4−4i4i3−523+52−1−5−1+5−3+52−3−52−1−5−1+51+51−53−523+521+51−5−3+52−3−52-1-1112ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ19−ζ3−ζ7−2ζ11−2ζ19−2ζ3−2ζ7−ζ11−ζ19ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ7+ζ11+ζ19ii−i−i0000-222i−2i0000000000001−521+52−1+52−1−52−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ70000000000
χ5744-4-4−4i4i3+523−52−1+5−1−5−3−52−3+52−1+5−1−51−51+53+523−521−51+5−3−52−3+52-1-1112ζ11+2ζ192ζ3+2ζ7−2ζ11−2ζ19−2ζ3−2ζ7−2ζ3−2ζ7−ζ11−ζ19−ζ3−ζ7−2ζ11−2ζ192ζ3+2ζ7+ζ11+ζ19ζ3+ζ7+2ζ11+2ζ19ii−i−i00002-2−2i2i000000000000−1−52−1+521+521−52ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ190000000000
χ5844-4-4−4i4i3+523−52−1+5−1−5−3−52−3+52−1+5−1−51−51+53+523−521−51+5−3−52−3+52-1-1112ζ11+2ζ192ζ3+2ζ7−2ζ11−2ζ19−2ζ3−2ζ7−2ζ3−2ζ7−ζ11−ζ19−ζ3−ζ7−2ζ11−2ζ192ζ3+2ζ7+ζ11+ζ19ζ3+ζ7+2ζ11+2ζ19ii−i−i0000-222i−2i0000000000001+521−52−1−52−1+52−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ190000000000
χ5944-4-4−4i4i−1−5−1+53+523−521+51−53+523−52−3−52−3+52−1−5−1+5−3−52−3+521+51−5-1-111−2ζ3−2ζ7−ζ11−ζ19−ζ3−ζ7−2ζ11−2ζ192ζ3+2ζ7+ζ11+ζ19ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ19ii−i−i2-2−2i2i00000000−1−52−1+521+521−52ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19000000000000000000
χ6044-4-4−4i4i−1−5−1+53+523−521+51−53+523−52−3−52−3+52−1−5−1+5−3−52−3+521+51−5-1-111−2ζ3−2ζ7−ζ11−ζ19−ζ3−ζ7−2ζ11−2ζ192ζ3+2ζ7+ζ11+ζ19ζ3+ζ7+2ζ11+2ζ192ζ3+2ζ72ζ11+2ζ19−2ζ3−2ζ7−2ζ11−2ζ19ii−i−i-222i−2i000000001+521−52−1−52−1+52−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19000000000000000000
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-2-2-2-222-2-222-2-2222233-3-3−2i−2i2i2i−2i−2i2i2i3i3i−3i−3i00000000000000000000000000000000000000
χ6488-8-8−8i8i-2-2-2-222-2-222-2-2222233-3-32i2i−2i−2i2i2i−2i−2i−3i−3i3i3i00000000000000000000000000000000000000
χ658-88-800-2-2-2-2-2-2222222-2-2223-33-3000000005i−5i5i−5i00000000000000000000000000000000000000
χ668-88-800-2-2-2-2-2-2222222-2-2223-33-300000000−5i5i−5i5i00000000000000000000000000000000000000
χ678-88-800−2+25−2−253−53+5−2+25−2−25−3+5−3−5−3+5−3−52−252+253−53+52−252+25-22-2200000000000000000000000000000000000000000000000000
χ688-88-8003−53+5−2−25−2+253−53+52+252−252+252−25−3+5−3−5−2−25−2+25−3+5−3−5-22-2200000000000000000000000000000000000000000000000000
χ698-88-8003+53−5−2+25−2−253+53−52−252+252−252+25−3−5−3+5−2+25−2−25−3−5−3+5-22-2200000000000000000000000000000000000000000000000000
χ708-88-800−2−25−2+253+53−5−2−25−2+25−3−5−3+5−3−5−3+52+252−253+53−52+252−25-22-2200000000000000000000000000000000000000000000000000
χ718-8-8800-2-2-2-22222-2-22222-2-23-3-33000000005-5-5500000000000000000000000000000000000000
χ728-8-8800-2-2-2-22222-2-22222-2-23-3-3300000000-555-500000000000000000000000000000000000000
χ738-8-8800−2+25−2−253−53+52−252+25−3+5−3−53−53+52−252+25−3+5−3−5−2+25−2−25-222-200000000000000000000000000000000000000000000000000
χ748-8-88003−53+5−2−25−2+25−3+5−3−52+252−25−2−25−2+25−3+5−3−52+252−253−53+5-222-200000000000000000000000000000000000000000000000000
χ758-8-88003+53−5−2+25−2−25−3−5−3+52−252+25−2+25−2−25−3−5−3+52−252+253+53−5-222-200000000000000000000000000000000000000000000000000
χ768-8-8800−2−25−2+253+53−52+252−25−3−5−3+53+53−52+252−25−3−5−3+5−2−25−2+25-222-200000000000000000000000000000000000000000000000000

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