Finite Group Databasebeta

← Group #63691

Character table — Group #63691

Order 288.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30
size11112222668888888888881212181818183636
order124436121224999181818363636363636612888824
χ1111111111111111111111111111111
χ2111111111111111111111111-1-1-1-1-1-1
χ311-1-111-1-1-11111111-1-1-1-1-1-1-1111-1-11-1
χ411-1-111-1-1-11111111-1-1-1-1-1-1-11-1-111-11
χ52222222222-1-1-1-1-1-1-1-1-1-1-1-122000000
χ62222-1-1-1-122ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68-1-1000000
χ72222-1-1-1-122ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68-1-1000000
χ82222-1-1-1-122−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52-1-1000000
χ922-2-222-2-2-22-1-1-1-1-1-1111111-22000000
χ1022-2-2-1-111-22ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ681-1000000
χ1122-2-2-1-111-22ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ681-1000000
χ1222-2-2-1-111-22−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ521-1000000
χ132-22i−2i2-22i−2i00-1-1-1111i−ii−ii−i00−i2i22−200
χ142-22i−2i2-22i−2i00-1-1-1111i−ii−ii−i00i2−i2−2200
χ152-2−2i2i2-2−2i2i00-1-1-1111−ii−ii−ii00−i2i2−2200
χ162-2−2i2i2-2−2i2i00-1-1-1111−ii−ii−ii00i2−i22−200
χ1733333333-1-1000000000000-1-11111-1-1
χ1833333333-1-1000000000000-1-1-1-1-1-111
χ1933-3-333-3-31-10000000000001-111-1-1-11
χ2033-3-333-3-31-10000000000001-1-1-1111-1
χ214-44i−4i4-44i−4i00111-1-1-1−ii−ii−ii00000000
χ224-44i−4i-22−2i2i00−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ14+ζ62−ζ70−ζ14−ζ62+ζ70ζ22−ζ62+ζ70−ζ22+ζ62−ζ70−ζ14−ζ22ζ14+ζ2200000000
χ234-44i−4i-22−2i2i00ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ14−ζ22ζ14+ζ22ζ14+ζ62−ζ70−ζ14−ζ62+ζ70ζ22−ζ62+ζ70−ζ22+ζ62−ζ7000000000
χ244-44i−4i-22−2i2i00−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ22−ζ62+ζ70−ζ22+ζ62−ζ70−ζ14−ζ22ζ14+ζ22ζ14+ζ62−ζ70−ζ14−ζ62+ζ7000000000
χ254-4−4i4i4-4−4i4i00111-1-1-1i−ii−ii−i00000000
χ264-4−4i4i-222i−2i00−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ14−ζ62+ζ70ζ14+ζ62−ζ70−ζ22+ζ62−ζ70ζ22−ζ62+ζ70ζ14+ζ22−ζ14−ζ2200000000
χ274-4−4i4i-222i−2i00ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ14+ζ22−ζ14−ζ22−ζ14−ζ62+ζ70ζ14+ζ62−ζ70−ζ22+ζ62−ζ70ζ22−ζ62+ζ7000000000
χ284-4−4i4i-222i−2i00−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68−ζ22+ζ62−ζ70ζ22−ζ62+ζ70ζ14+ζ22−ζ14−ζ22−ζ14−ζ62+ζ70ζ14+ζ62−ζ7000000000
χ296666-3-3-3-3-2-200000000000011000000
χ3066-6-6-3-3332-2000000000000-11000000

Here ζ is a primitive root of unity of order 72 (ζ72 = 1); i = ζ18.