Finite Group Databasebeta

← Group #13167650

Character table — Group #13167650

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size11222224448888888888888888888888889918181818183636365454545454545454727272727272216216
order1234688122424333666121212121212242424242424242424242424224668812242444448888441212121244
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ511111-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-11111-1-1-1-11-111-1-11-1
χ611111-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-11111-1-1-1-1-11-1-111-11
χ711111-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-111111-111-1-1-11
χ811111-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-11111-11-1-1111-1
χ92222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-20000000000000000
χ1022222-2-22-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2220000000000000000
χ11222-2200-200222222-2-2-2-2-2-200000000000022-22200-20022-2-2000000000000
χ12222-2200-200222222-2-2-2-2-2-200000000000022-22200-200-2-222000000000000
χ13222-2200-200222222-2-2-2-2-2-2000000000000-2-22-2-200200000022-2-200000000
χ14222-2200-200222222-2-2-2-2-2-2000000000000-2-22-2-2002000000-2-22200000000
χ1522-12-122-1-1-12-1-12-1-122-1-1-1-12222-1-1-1-1-1-1-1-1222-1-122-1-1-10000000022-1-1-1-100
χ1622-12-122-1-1-12-1-12-1-122-1-1-1-12222-1-1-1-1-1-1-1-1222-1-122-1-1-100000000-2-2111100
χ1722-12-122-1-1-12-1-12-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-211-2-211100000000003−33−300
χ1822-12-122-1-1-12-1-12-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-211-2-21110000000000−33−3300
χ1922-12-1-2-2-1112-1-12-1-122-1-1-1-1-2-2-2-211111111222-1-1-2-2-111000000002-2-1-11100
χ2022-12-1-2-2-1112-1-12-1-122-1-1-1-1-2-2-2-211111111222-1-1-2-2-11100000000-2211-1-100
χ2122-12-1-2-2-1112-1-12-1-122-1-1-1-1-2-2-2-211111111-2-2-211221-1-100000000003−3−3300
χ2222-12-1-2-2-1112-1-12-1-122-1-1-1-1-2-2-2-211111111-2-2-211221-1-10000000000−333−300
χ232-220-2−i2i20−i2i2222-2-2-2000000−i2−i2i2i2−i2−i2−i2−i2i2i2i2i22-202-2−i2i20−i2i2002i−2i2−22−200000000
χ242-220-2−i2i20−i2i2222-2-2-2000000−i2−i2i2i2−i2−i2−i2−i2i2i2i2i22-202-2−i2i20−i2i200−2i2i−22−2200000000
χ252-220-2−i2i20−i2i2222-2-2-2000000−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2-220-22i2−i20i2−i22i−2i002−2−2200000000
χ262-220-2−i2i20−i2i2222-2-2-2000000−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2-220-22i2−i20i2−i2−2i2i00−222−200000000
χ272-220-2i2−i20i2−i2222-2-2-2000000i2i2−i2−i2i2i2i2i2−i2−i2−i2−i22-202-2i2−i20i2−i2002i−2i−22−2200000000
χ282-220-2i2−i20i2−i2222-2-2-2000000i2i2−i2−i2i2i2i2i2−i2−i2−i2−i22-202-2i2−i20i2−i200−2i2i2−22−200000000
χ292-220-2i2−i20i2−i2222-2-2-2000000i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2-220-22−i2i20−i2i22i−2i00−222−200000000
χ302-220-2i2−i20i2−i2222-2-2-2000000i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2-220-22−i2i20−i2i2−2i2i002−2−2200000000
χ3144-2-4-2002004-2-24-2-2-4-4222200000000000044-4-2-2002000000000000000000
χ3244-2-4-2002004-2-24-2-2-4-42222000000000000-4-442200-2000000000000000000
χ334-4-202−2i22i20i2−i24-2-2-422000000−2i2−2i22i22i2i2i2i2i2−i2−i2−i2−i24-40-22−2i22i20i2−i20000000000000000
χ344-4-202−2i22i20i2−i24-2-2-422000000−2i2−2i22i22i2i2i2i2i2−i2−i2−i2−i2-4402-22i2−2i20−i2i20000000000000000
χ354-4-2022i2−2i20−i2i24-2-2-4220000002i22i2−2i2−2i2−i2−i2−i2−i2i2i2i2i24-40-222i2−2i20−i2i20000000000000000
χ364-4-2022i2−2i20−i2i24-2-2-4220000002i22i2−2i2−2i2−i2−i2−i2−i2i2i2i2i2-4402-2−2i22i20i2−i20000000000000000
χ378888888888-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ3888888-8-88-8-8-1-1-1-1-1-1-1-1-1-1-1-111111111111100000000000000000000000000
χ39888-8800-800-1-1-1-1-1-11111113i−3i3i−3i3i3i−3i−3i3i3i−3i−3i00000000000000000000000000
χ40888-8800-800-1-1-1-1-1-1111111−3i3i−3i3i−3i−3i3i3i−3i−3i3i3i00000000000000000000000000
χ4188-48-488-4-4-4-11−3i321+3i32-11−3i321+3i32-1-11−3i321−3i321+3i321+3i32-1-1-1-11−3i321+3i321−3i321+3i321−3i321+3i321−3i321+3i3200000000000000000000000000
χ4288-48-488-4-4-4-11+3i321−3i32-11+3i321−3i32-1-11+3i321+3i321−3i321−3i32-1-1-1-11+3i321−3i321+3i321−3i321+3i321−3i321+3i321−3i3200000000000000000000000000
χ4388-48-4-8-8-444-11−3i321+3i32-11−3i321+3i32-1-11−3i321−3i321+3i321+3i321111−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i3200000000000000000000000000
χ4488-48-4-8-8-444-11+3i321−3i32-11+3i321−3i32-1-11+3i321+3i321−3i321−3i321111−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i3200000000000000000000000000
χ4588-4-8-400400-11−3i321+3i32-11−3i321+3i3211−1+3i32−1+3i32−1−3i32−1−3i323i−3i3i−3i3ζ223ζ14−3ζ22−3ζ143ζ223ζ14−3ζ22−3ζ1400000000000000000000000000
χ4688-4-8-400400-11−3i321+3i32-11−3i321+3i3211−1+3i32−1+3i32−1−3i32−1−3i32−3i3i−3i3i−3ζ22−3ζ143ζ223ζ14−3ζ22−3ζ143ζ223ζ1400000000000000000000000000
χ4788-4-8-400400-11+3i321−3i32-11+3i321−3i3211−1−3i32−1−3i32−1+3i32−1+3i323i−3i3i−3i3ζ143ζ22−3ζ14−3ζ223ζ143ζ22−3ζ14−3ζ2200000000000000000000000000
χ4888-4-8-400400-11+3i321−3i32-11+3i321−3i3211−1−3i32−1−3i32−1+3i32−1+3i32−3i3i−3i3i−3ζ14−3ζ223ζ143ζ22−3ζ14−3ζ223ζ143ζ2200000000000000000000000000
χ498-880-8−4i24i20−4i24i2-1-1-11113i−3i3i−3i3i−3i−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−2ζ5+ζ7−2ζ13+ζ2300000000000000000000000000
χ508-880-8−4i24i20−4i24i2-1-1-1111−3i3i−3i3i−3i3i2ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23ζ5−2ζ7+ζ13−2ζ2300000000000000000000000000
χ518-880-84i2−4i204i2−4i2-1-1-11113i−3i3i−3i3i−3iζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ232ζ5−ζ7+2ζ13−ζ2300000000000000000000000000
χ528-880-84i2−4i204i2−4i2-1-1-1111−3i3i−3i3i−3i3i−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−ζ5+2ζ7−ζ13+2ζ2300000000000000000000000000
χ538-8-404−4i24i202i2−2i2-11−3i321+3i321−1+3i32−1−3i323i−3i3ζ22−3ζ223ζ14−3ζ14−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5−ζ7+2ζ13−ζ232ζ5−ζ7−ζ13−ζ23−ζ5+2ζ7−ζ13−ζ23−ζ5−ζ7−ζ13+2ζ23ζ5+ζ7−2ζ13+ζ23−2ζ5+ζ7+ζ13+ζ23ζ5−2ζ7+ζ13+ζ23ζ5+ζ7+ζ13−2ζ2300000000000000000000000000
χ548-8-404−4i24i202i2−2i2-11−3i321+3i321−1+3i32−1−3i32−3i3i−3ζ223ζ22−3ζ143ζ142ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13−ζ23−ζ5−ζ7−ζ13+2ζ23−ζ5−ζ7+2ζ13−ζ232ζ5−ζ7−ζ13−ζ23ζ5−2ζ7+ζ13+ζ23ζ5+ζ7+ζ13−2ζ23ζ5+ζ7−2ζ13+ζ23−2ζ5+ζ7+ζ13+ζ2300000000000000000000000000
χ558-8-404−4i24i202i2−2i2-11+3i321−3i321−1−3i32−1+3i323i−3i3ζ14−3ζ143ζ22−3ζ22−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7−ζ13−ζ23−ζ5−ζ7+2ζ13−ζ23−ζ5−ζ7−ζ13+2ζ23−ζ5+2ζ7−ζ13−ζ23−2ζ5+ζ7+ζ13+ζ23ζ5+ζ7−2ζ13+ζ23ζ5+ζ7+ζ13−2ζ23ζ5−2ζ7+ζ13+ζ2300000000000000000000000000
χ568-8-404−4i24i202i2−2i2-11+3i321−3i321−1−3i32−1+3i32−3i3i−3ζ143ζ14−3ζ223ζ222ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5−ζ7−ζ13+2ζ23−ζ5+2ζ7−ζ13−ζ232ζ5−ζ7−ζ13−ζ23−ζ5−ζ7+2ζ13−ζ23ζ5+ζ7+ζ13−2ζ23ζ5−2ζ7+ζ13+ζ23−2ζ5+ζ7+ζ13+ζ23ζ5+ζ7−2ζ13+ζ2300000000000000000000000000
χ578-8-4044i2−4i20−2i22i2-11−3i321+3i321−1+3i32−1−3i323i−3i3ζ22−3ζ223ζ14−3ζ14ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5+ζ7−2ζ13+ζ23−2ζ5+ζ7+ζ13+ζ23ζ5−2ζ7+ζ13+ζ23ζ5+ζ7+ζ13−2ζ23−ζ5−ζ7+2ζ13−ζ232ζ5−ζ7−ζ13−ζ23−ζ5+2ζ7−ζ13−ζ23−ζ5−ζ7−ζ13+2ζ2300000000000000000000000000
χ588-8-4044i2−4i20−2i22i2-11−3i321+3i321−1+3i32−1−3i32−3i3i−3ζ223ζ22−3ζ143ζ14−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13+ζ23ζ5+ζ7+ζ13−2ζ23ζ5+ζ7−2ζ13+ζ23−2ζ5+ζ7+ζ13+ζ23−ζ5+2ζ7−ζ13−ζ23−ζ5−ζ7−ζ13+2ζ23−ζ5−ζ7+2ζ13−ζ232ζ5−ζ7−ζ13−ζ2300000000000000000000000000
χ598-8-4044i2−4i20−2i22i2-11+3i321−3i321−1−3i32−1+3i323i−3i3ζ14−3ζ143ζ22−3ζ22ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7+ζ13+ζ23ζ5+ζ7−2ζ13+ζ23ζ5+ζ7+ζ13−2ζ23ζ5−2ζ7+ζ13+ζ232ζ5−ζ7−ζ13−ζ23−ζ5−ζ7+2ζ13−ζ23−ζ5−ζ7−ζ13+2ζ23−ζ5+2ζ7−ζ13−ζ2300000000000000000000000000
χ608-8-4044i2−4i20−2i22i2-11+3i321−3i321−1−3i32−1+3i32−3i3i−3ζ143ζ14−3ζ223ζ22−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5+ζ7+ζ13−2ζ23ζ5−2ζ7+ζ13+ζ23−2ζ5+ζ7+ζ13+ζ23ζ5+ζ7−2ζ13+ζ23−ζ5−ζ7−ζ13+2ζ23−ζ5+2ζ7−ζ13−ζ232ζ5−ζ7−ζ13−ζ23−ζ5−ζ7+2ζ13−ζ2300000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.