Finite Group Databasebeta

← Group #13104307

Character table — Group #13104307

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size111122444444444444444488888888888888882020202020202020252525254040404040404040404040404040404050505050505050505050
order12224455551010101010101010101010105101010202020202020202020202020444444444444202020202020202020202020202020204488888888
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
χ51111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ61111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111
χ71111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ81111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ91-1-11i−i1111-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−iii−i−ii−ii−i1-11-1ii−i−i11-1-111-1-1ii−i−iii−i−i1-111-1-1ii−i−i
χ101-1-11i−i1111-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−iii−i−ii−i−ii1-1-11ii−i−i11-1-1-1-111ii−i−i−i−iii1-1-1-111−i−iii
χ111-1-11i−i1111-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−iii−i−i−iii−i-111-1ii−i−i-1-11111-1-1−i−iiiii−i−i1-1-1-111−i−iii
χ121-1-11i−i1111-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−iii−i−i−ii−ii-11-11ii−i−i-1-111-1-111−i−iii−i−iii1-111-1-1ii−i−i
χ131-1-11−ii1111-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii−i−iiii−ii−i-11-11−i−iii-1-111-1-111ii−i−iii−i−i1-111-1-1−i−iii
χ141-1-11−ii1111-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii−i−iiii−i−ii-111-1−i−iii-1-11111-1-1ii−i−i−i−iii1-1-1-111ii−i−i
χ151-1-11−ii1111-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii−i−iii−iii−i1-1-11−i−iii11-1-1-1-111−i−iiiii−i−i1-1-1-111ii−i−i
χ161-1-11−ii1111-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii−i−iii−ii−ii1-11-1−i−iii11-1-111-1-1−i−iii−i−iii1-111-1-1−i−iii
χ172222222222222222222222222222222222222200000000-2-2-2-20000000000000000-2-200000000
χ182222-2-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000000000000-2-200000000
χ1922-2-2002222-2-2-2-2-2-2-2-222222-2-22000000000000000000002i−2i2i−2i0000000000000000002−22−2i2−i2i2−i2
χ2022-2-2002222-2-2-2-2-2-2-2-222222-2-22000000000000000000002i−2i2i−2i000000000000000000−22−22−i2i2−i2i2
χ2122-2-2002222-2-2-2-2-2-2-2-222222-2-2200000000000000000000−2i2i−2i2i0000000000000000002−22−2−i2i2−i2i2
χ2222-2-2002222-2-2-2-2-2-2-2-222222-2-2200000000000000000000−2i2i−2i2i000000000000000000−22−22i2−i2i2−i2
χ232-22-20022222222-2-2-2-2-2-2-2-22-22-2000000000000000000002-2-220000000000000000002−2−222−2−22
χ242-22-20022222222-2-2-2-2-2-2-2-22-22-2000000000000000000002-2-22000000000000000000−222−2−222−2
χ252-22-20022222222-2-2-2-2-2-2-2-22-22-200000000000000000000-222-20000000000000000002−2−22−222−2
χ262-22-20022222222-2-2-2-2-2-2-2-22-22-200000000000000000000-222-2000000000000000000−222−22−2−22
χ272-2-222i−2i2222-2-2-2-22222-2-2-2-222-2-22i2i2i2i−2i−2i−2i−2i2i2i−2i−2i00000000−2i−2i2i2i0000000000000000-2200000000
χ282-2-22−2i2i2222-2-2-2-22222-2-2-2-222-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i000000002i2i−2i−2i0000000000000000-2200000000
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+51111002200-2-2000000001−521+521−521+520000−1+52−1−52−1+52−1−520000000000
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+5111100-2-2002200000000−1+52−1−52−1+52−1−5200001−521+521−521+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+51−5−3−5211112200-2-20000001−521+521−521+520000−1+52−1−52−1+52−1−5200000000000000
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+51−5−3−521111-2-20022000000−1+52−1−52−1+52−1−5200001−521+521−521+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+5211112200-2-20000001+521−521+521−520000−1−52−1+52−1−52−1+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+521111-2-20022000000−1−52−1+52−1−52−1+5200001+521−521+521−5200000000000000
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+521−51111002200-2-2000000001+521−521+521−520000−1−52−1+52−1−52−1+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+521−5111100-2-2002200000000−1−52−1+52−1−52−1+5200001+521−521+521−520000000000
χ454-4-444i−4i−1+53−523+52−1−51−5−3+52−3−521+5−1+53−523+52−1−51−5−3+52−3−521+5-1-111−2ζ22−2ζ38ζ6+ζ14+2ζ22+2ζ382ζ6+2ζ14+ζ22+ζ38−2ζ6−2ζ142ζ22+2ζ38−ζ6−ζ14−2ζ22−2ζ38−2ζ6−2ζ14−ζ22−ζ382ζ6+2ζ14−i−iii002i−2i002-200000000−1+52−1−521−521+520000−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ140000000000
χ464-4-444i−4i−1+53−523+52−1−51−5−3+52−3−521+5−1+53−523+52−1−51−5−3+52−3−521+5-1-111−2ζ22−2ζ38ζ6+ζ14+2ζ22+2ζ382ζ6+2ζ14+ζ22+ζ38−2ζ6−2ζ142ζ22+2ζ38−ζ6−ζ14−2ζ22−2ζ38−2ζ6−2ζ14−ζ22−ζ382ζ6+2ζ14−i−iii00−2i2i00-22000000001−521+52−1+52−1−520000ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ140000000000
χ474-4-444i−4i3−52−1−5−1+53+52−3+521+51−5−3−523−52−1−5−1+53+52−3+521+51−5−3−52-1-111ζ6+ζ14+2ζ22+2ζ38−2ζ6−2ζ14−2ζ22−2ζ382ζ6+2ζ14+ζ22+ζ38−ζ6−ζ14−2ζ22−2ζ382ζ6+2ζ142ζ22+2ζ38−2ζ6−2ζ14−ζ22−ζ38−i−iii2i−2i002-2000000−1+52−1−521−521+520000−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ1400000000000000
χ484-4-444i−4i3−52−1−5−1+53+52−3+521+51−5−3−523−52−1−5−1+53+52−3+521+51−5−3−52-1-111ζ6+ζ14+2ζ22+2ζ38−2ζ6−2ζ14−2ζ22−2ζ382ζ6+2ζ14+ζ22+ζ38−ζ6−ζ14−2ζ22−2ζ382ζ6+2ζ142ζ22+2ζ38−2ζ6−2ζ14−ζ22−ζ38−i−iii−2i2i00-220000001−521+52−1+52−1−520000ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ1400000000000000
χ494-4-444i−4i3+52−1+5−1−53−52−3−521−51+5−3+523+52−1+5−1−53−52−3−521−51+5−3+52-1-1112ζ6+2ζ14+ζ22+ζ38−2ζ22−2ζ38−2ζ6−2ζ14ζ6+ζ14+2ζ22+2ζ38−2ζ6−2ζ14−ζ22−ζ382ζ22+2ζ382ζ6+2ζ14−ζ6−ζ14−2ζ22−2ζ38−i−iii2i−2i002-2000000−1−52−1+521+521−520000−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ3800000000000000
χ504-4-444i−4i3+52−1+5−1−53−52−3−521−51+5−3+523+52−1+5−1−53−52−3−521−51+5−3+52-1-1112ζ6+2ζ14+ζ22+ζ38−2ζ22−2ζ38−2ζ6−2ζ14ζ6+ζ14+2ζ22+2ζ38−2ζ6−2ζ14−ζ22−ζ382ζ22+2ζ382ζ6+2ζ14−ζ6−ζ14−2ζ22−2ζ38−i−iii−2i2i00-220000001+521−52−1−52−1+520000ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ3800000000000000
χ514-4-444i−4i−1−53+523−52−1+51+5−3−52−3+521−5−1−53+523−52−1+51+5−3−52−3+521−5-1-111−2ζ6−2ζ142ζ6+2ζ14+ζ22+ζ38ζ6+ζ14+2ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ14−ζ22−ζ38−ζ6−ζ14−2ζ22−2ζ382ζ22+2ζ38−i−iii002i−2i002-200000000−1−52−1+521+521−520000−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ380000000000
χ524-4-444i−4i−1−53+523−52−1+51+5−3−52−3+521−5−1−53+523−52−1+51+5−3−52−3+521−5-1-111−2ζ6−2ζ142ζ6+2ζ14+ζ22+ζ38ζ6+ζ14+2ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ14−ζ22−ζ38−ζ6−ζ14−2ζ22−2ζ382ζ22+2ζ38−i−iii00−2i2i00-22000000001+521−52−1−52−1+520000ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ380000000000
χ534-4-44−4i4i−1+53−523+52−1−51−5−3+52−3−521+5−1+53−523+52−1−51−5−3+52−3−521+5-1-1112ζ22+2ζ38−ζ6−ζ14−2ζ22−2ζ38−2ζ6−2ζ14−ζ22−ζ382ζ6+2ζ14−2ζ22−2ζ38ζ6+ζ14+2ζ22+2ζ382ζ6+2ζ14+ζ22+ζ38−2ζ6−2ζ14ii−i−i002i−2i00-22000000001−521+52−1+52−1−520000−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ140000000000
χ544-4-44−4i4i−1+53−523+52−1−51−5−3+52−3−521+5−1+53−523+52−1−51−5−3+52−3−521+5-1-1112ζ22+2ζ38−ζ6−ζ14−2ζ22−2ζ38−2ζ6−2ζ14−ζ22−ζ382ζ6+2ζ14−2ζ22−2ζ38ζ6+ζ14+2ζ22+2ζ382ζ6+2ζ14+ζ22+ζ38−2ζ6−2ζ14ii−i−i00−2i2i002-200000000−1+52−1−521−521+520000ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ140000000000
χ554-4-44−4i4i3−52−1−5−1+53+52−3+521+51−5−3−523−52−1−5−1+53+52−3+521+51−5−3−52-1-111−ζ6−ζ14−2ζ22−2ζ382ζ6+2ζ142ζ22+2ζ38−2ζ6−2ζ14−ζ22−ζ38ζ6+ζ14+2ζ22+2ζ38−2ζ6−2ζ14−2ζ22−2ζ382ζ6+2ζ14+ζ22+ζ38ii−i−i2i−2i00-220000001−521+52−1+52−1−520000−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ1400000000000000
χ564-4-44−4i4i3−52−1−5−1+53+52−3+521+51−5−3−523−52−1−5−1+53+52−3+521+51−5−3−52-1-111−ζ6−ζ14−2ζ22−2ζ382ζ6+2ζ142ζ22+2ζ38−2ζ6−2ζ14−ζ22−ζ38ζ6+ζ14+2ζ22+2ζ38−2ζ6−2ζ14−2ζ22−2ζ382ζ6+2ζ14+ζ22+ζ38ii−i−i−2i2i002-2000000−1+52−1−521−521+520000ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ1400000000000000
χ574-4-44−4i4i3+52−1+5−1−53−52−3−521−51+5−3+523+52−1+5−1−53−52−3−521−51+5−3+52-1-111−2ζ6−2ζ14−ζ22−ζ382ζ22+2ζ382ζ6+2ζ14−ζ6−ζ14−2ζ22−2ζ382ζ6+2ζ14+ζ22+ζ38−2ζ22−2ζ38−2ζ6−2ζ14ζ6+ζ14+2ζ22+2ζ38ii−i−i2i−2i00-220000001+521−52−1−52−1+520000−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ3800000000000000
χ584-4-44−4i4i3+52−1+5−1−53−52−3−521−51+5−3+523+52−1+5−1−53−52−3−521−51+5−3+52-1-111−2ζ6−2ζ14−ζ22−ζ382ζ22+2ζ382ζ6+2ζ14−ζ6−ζ14−2ζ22−2ζ382ζ6+2ζ14+ζ22+ζ38−2ζ22−2ζ38−2ζ6−2ζ14ζ6+ζ14+2ζ22+2ζ38ii−i−i−2i2i002-2000000−1−52−1+521+521−520000ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ3800000000000000
χ594-4-44−4i4i−1−53+523−52−1+51+5−3−52−3+521−5−1−53+523−52−1+51+5−3−52−3+521−5-1-1112ζ6+2ζ14−2ζ6−2ζ14−ζ22−ζ38−ζ6−ζ14−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14+ζ22+ζ38ζ6+ζ14+2ζ22+2ζ38−2ζ22−2ζ38ii−i−i002i−2i00-22000000001+521−52−1−52−1+520000−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ380000000000
χ604-4-44−4i4i−1−53+523−52−1+51+5−3−52−3+521−5−1−53+523−52−1+51+5−3−52−3+521−5-1-1112ζ6+2ζ14−2ζ6−2ζ14−ζ22−ζ38−ζ6−ζ14−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14+ζ22+ζ38ζ6+ζ14+2ζ22+2ζ38−2ζ22−2ζ38ii−i−i00−2i2i002-200000000−1−52−1+521+521−520000ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ380000000000
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
χ6388-8-800-2-2-2-222222222-2-2-2-23-3-33000000005-55-500000000000000000000000000000000000000
χ6488-8-800-2-2-2-222222222-2-2-2-23-3-3300000000-55-5500000000000000000000000000000000000000
χ6588-8-800−2+253−53+5−2−252−25−3+5−3−52+252−25−3+5−3−52+25−2+253−53+5−2−25-222-200000000000000000000000000000000000000000000000000
χ6688-8-8003−5−2−25−2+253+5−3+52+252−25−3−5−3+52+252−25−3−53−5−2−25−2+253+5-222-200000000000000000000000000000000000000000000000000
χ6788-8-8003+5−2+25−2−253−5−3−52−252+25−3+5−3−52−252+25−3+53+5−2+25−2−253−5-222-200000000000000000000000000000000000000000000000000
χ6888-8-800−2−253+53−5−2+252+25−3−5−3+52−252+25−3−5−3+52−25−2−253+53−5−2+25-222-200000000000000000000000000000000000000000000000000
χ698-88-800-2-2-2-2-2-2-2-2222222223-33-3000000005i−5i−5i5i00000000000000000000000000000000000000
χ708-88-800-2-2-2-2-2-2-2-2222222223-33-300000000−5i5i5i−5i00000000000000000000000000000000000000
χ718-88-800−2+253−53+5−2−25−2+253−53+5−2−252−25−3+5−3−52+252−25−3+5−3−52+25-22-2200000000000000000000000000000000000000000000000000
χ728-88-8003−5−2−25−2+253+53−5−2−25−2+253+5−3+52+252−25−3−5−3+52+252−25−3−5-22-2200000000000000000000000000000000000000000000000000
χ738-88-8003+5−2+25−2−253−53+5−2+25−2−253−5−3−52−252+25−3+5−3−52−252+25−3+5-22-2200000000000000000000000000000000000000000000000000
χ748-88-800−2−253+53−5−2+25−2−253+53−5−2+252+25−3−5−3+52−252+25−3−5−3+52−25-22-2200000000000000000000000000000000000000000000000000
χ758-8-888i−8i-2-2-2-22222-2-2-2-2222233-3-3−2i−2i−2i−2i2i2i2i2i3i3i−3i−3i00000000000000000000000000000000000000
χ768-8-88−8i8i-2-2-2-22222-2-2-2-2222233-3-32i2i2i2i−2i−2i−2i−2i−3i−3i3i3i00000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.