Finite Group Databasebeta

← Group #11920357

Character table — Group #11920357

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size112222233444446666688888888121212121216161616161616161618181818242432323232323236363636363672727272
order123468822221224244668866999181818221224243636367272727272724444661818181818182488884444
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111-1-111111111-1-1111111-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111-1-111111111-1-1111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111-1-1111-11-1-1111-1-11-11111111-11-1-1111-1-1-1-1-1-111111-1111-1-1-111-1-1-1-11-11-1
χ611111-1-1111-11-1-1111-1-11-11111111-11-1-1111-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-11111-11-11
χ711111-1-111-111-1-1111-1-1-11111111-111-1-1111-1-1-1-1-1-11111-11-1-1-111111-1-1-1-1-11-11
χ811111-1-111-111-1-1111-1-1-11111111-111-1-1111-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-111111-11-1
χ9222222222222222222222-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-10000000000
χ10222222222-2-222222222-2-2-1-1-1-1-1-1-2-2222-1-1-1-1-1-1-1-1-10000-2-21111110000000000
χ1122222-2-2222-22-2-2222-2-22-2-1-1-1-1-1-12-22-2-2-1-1-111111100002-2-1-1-11110000000000
χ1222222-2-222-222-2-2222-2-2-22-1-1-1-1-1-1-222-2-2-1-1-11111110000-22111-1-1-10000000000
χ13222-22002200-200-222000022222200-200-2-2-2000000222200000000-2-200000000
χ14222-22002200-200-222000022222200-200-2-2-2000000-2-2-2-2000000002200000000
χ1522-12-1222222-1-1-12-1-122-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ6822-1-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ680000-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ680000000000
χ1622-12-1222222-1-1-12-1-122-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ6822-1-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ680000-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ680000000000
χ1722-12-1222222-1-1-12-1-122-1-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ5222-1-1-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ520000-1-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ520000000000
χ1822-12-12222-2-2-1-1-12-1-12211ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-2-2-1-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68000011−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ680000000000
χ1922-12-12222-2-2-1-1-12-1-12211ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68-2-2-1-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68000011−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ680000000000
χ2022-12-12222-2-2-1-1-12-1-12211−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52-2-2-1-1-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ4−ζ68ζ44−ζ52+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4−ζ44+ζ52000011ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ520000000000
χ2122-12-1-2-2222-2-1112-1-1-2-2-11ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ682-2-111ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ680000-11ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ680000000000
χ2222-12-1-2-2222-2-1112-1-1-2-2-11ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ682-2-111ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ680000-11ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ680000000000
χ2322-12-1-2-2222-2-1112-1-1-2-2-11−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ522-2-111−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ520000-11−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ520000000000
χ2422-12-1-2-222-22-1112-1-1-2-21-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-22-111ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ6800001-1−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ680000000000
χ2522-12-1-2-222-22-1112-1-1-2-21-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68-22-111ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ52ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ6800001-1−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ680000000000
χ2622-12-1-2-222-22-1112-1-1-2-21-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52-22-111−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4+ζ68ζ4+ζ68−ζ44+ζ52−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4+ζ44−ζ5200001-1ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ520000000000
χ272-220-22−22-20002−202-22−200222-2-2-20002−20002−22−22−22i−2i2i−2i0000000000−i2i2−i2i20000
χ282-220-22−22-20002−202-22−200222-2-2-20002−20002−22−22−2−2i2i−2i2i0000000000i2−i2i2−i20000
χ292-220-2−222-2000−2202-2−2200222-2-2-2000−22000−22−22−222i−2i2i−2i0000000000i2−i2i2−i20000
χ302-220-2−222-2000−2202-2−2200222-2-2-2000−22000−22−22−22−2i2i−2i2i0000000000−i2i2−i2i20000
χ313333333-1-133333-1-1-1-1-133000000-1-1-1-1-100000000011-1-1-1-10000001-111-1-111-1-1
χ323333333-1-133333-1-1-1-1-133000000-1-1-1-1-1000000000-1-111-1-1000000-11-1-111-1-111
χ333333333-1-1-3-3333-1-1-1-1-1-3-300000011-1-1-100000000011-1-1110000001-111-1-1-1-111
χ343333333-1-1-3-3333-1-1-1-1-1-3-300000011-1-1-1000000000-1-11111000000-11-1-11111-1-1
χ3533333-3-3-1-13-33-3-3-1-1-1113-3000000-11-11100000000011-1-1-110000001-1-1-1111-1-11
χ3633333-3-3-1-13-33-3-3-1-1-1113-3000000-11-111000000000-1-111-11000000-1111-1-1-111-1
χ3733333-3-3-1-1-333-3-3-1-1-111-330000001-1-11100000000011-1-11-10000001-1-1-111-111-1
χ3833333-3-3-1-1-333-3-3-1-1-111-330000001-1-111000000000-1-1111-1000000-1111-1-11-1-11
χ39444-44004400-400-4440000-2-2-2-2-2-200-4002220000000000000000000000000000
χ4044-2-4-2004400200-4-2-200002ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52−2ζ4−2ζ682ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52−2ζ4−2ζ6800200−2ζ44+2ζ52−2ζ68−2ζ4+2ζ44−2ζ522ζ4+2ζ680000000000000000000000000000
χ4144-2-4-2004400200-4-2-200002ζ4−2ζ44+2ζ52−2ζ4−2ζ682ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52−2ζ4−2ζ682ζ44−2ζ52+2ζ6800200−2ζ4+2ζ44−2ζ522ζ4+2ζ68−2ζ44+2ζ52−2ζ680000000000000000000000000000
χ4244-2-4-2004400200-4-2-20000−2ζ4−2ζ682ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52−2ζ4−2ζ682ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52002002ζ4+2ζ68−2ζ44+2ζ52−2ζ68−2ζ4+2ζ44−2ζ520000000000000000000000000000
χ434-440-422−224-400022−2204-422−2200-2-2-222200022−22000−22−22−220000000000000000000000
χ444-440-4−22224-4000−222204-4−222200-2-2-2222000−22220002−22−22−20000000000000000000000
χ454-4-20222−224-4000−220-2222−22002ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52−2ζ4−2ζ68−2ζ44+2ζ52−2ζ68−2ζ4+2ζ44−2ζ522ζ4+2ζ68000−22000ζ5+ζ7−ζ23+ζ53−ζ61−ζ71−ζ5−ζ7+ζ23−ζ53+ζ61+ζ71−ζ7+ζ13−ζ31−ζ53+ζ61+ζ71ζ7−ζ13+ζ31+ζ53−ζ61−ζ71−ζ5−ζ13+ζ23+ζ31ζ5+ζ13−ζ23−ζ310000000000000000000000
χ464-4-20222−224-4000−220-2222−22002ζ4−2ζ44+2ζ52−2ζ4−2ζ682ζ44−2ζ52+2ζ68−2ζ4+2ζ44−2ζ522ζ4+2ζ68−2ζ44+2ζ52−2ζ68000−22000−ζ7+ζ13−ζ31−ζ53+ζ61+ζ71ζ7−ζ13+ζ31+ζ53−ζ61−ζ71−ζ5−ζ13+ζ23+ζ31ζ5+ζ13−ζ23−ζ31ζ5+ζ7−ζ23+ζ53−ζ61−ζ71−ζ5−ζ7+ζ23−ζ53+ζ61+ζ710000000000000000000000
χ474-4-20222−224-4000−220-2222−2200−2ζ4−2ζ682ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ522ζ4+2ζ68−2ζ44+2ζ52−2ζ68−2ζ4+2ζ44−2ζ52000−22000−ζ5−ζ13+ζ23+ζ31ζ5+ζ13−ζ23−ζ31ζ5+ζ7−ζ23+ζ53−ζ61−ζ71−ζ5−ζ7+ζ23−ζ53+ζ61+ζ71−ζ7+ζ13−ζ31−ζ53+ζ61+ζ71ζ7−ζ13+ζ31+ζ53−ζ61−ζ710000000000000000000000
χ484-4-202−22224-40002−20-22−2222002ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52−2ζ4−2ζ68−2ζ44+2ζ52−2ζ68−2ζ4+2ζ44−2ζ522ζ4+2ζ680002−2000−ζ5−ζ7+ζ23−ζ53+ζ61+ζ71ζ5+ζ7−ζ23+ζ53−ζ61−ζ71ζ7−ζ13+ζ31+ζ53−ζ61−ζ71−ζ7+ζ13−ζ31−ζ53+ζ61+ζ71ζ5+ζ13−ζ23−ζ31−ζ5−ζ13+ζ23+ζ310000000000000000000000
χ494-4-202−22224-40002−20-22−2222002ζ4−2ζ44+2ζ52−2ζ4−2ζ682ζ44−2ζ52+2ζ68−2ζ4+2ζ44−2ζ522ζ4+2ζ68−2ζ44+2ζ52−2ζ680002−2000ζ7−ζ13+ζ31+ζ53−ζ61−ζ71−ζ7+ζ13−ζ31−ζ53+ζ61+ζ71ζ5+ζ13−ζ23−ζ31−ζ5−ζ13+ζ23+ζ31−ζ5−ζ7+ζ23−ζ53+ζ61+ζ71ζ5+ζ7−ζ23+ζ53−ζ61−ζ710000000000000000000000
χ504-4-202−22224-40002−20-22−222200−2ζ4−2ζ682ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ522ζ4+2ζ68−2ζ44+2ζ52−2ζ68−2ζ4+2ζ44−2ζ520002−2000ζ5+ζ13−ζ23−ζ31−ζ5−ζ13+ζ23+ζ31−ζ5−ζ7+ζ23−ζ53+ζ61+ζ71ζ5+ζ7−ζ23+ζ53−ζ61−ζ71ζ7−ζ13+ζ31+ζ53−ζ61−ζ71−ζ7+ζ13−ζ31−ζ53+ζ61+ζ710000000000000000000000
χ51666-6600-2-200-6002-2-200000000000020000000000022-2-200000000-2200000000
χ52666-6600-2-200-6002-2-2000000000000200000000000-2-222000000002-200000000
χ5366-36-366-2-266-3-3-3-211-2-2-3-3000000-2-21110000000000000110000000000000000
χ5466-36-366-2-2-6-6-3-3-3-211-2-233000000221110000000000000-1-10000000000000000
χ5566-36-3-6-6-2-26-6-333-21122-33000000-221-1-100000000000001-10000000000000000
χ5666-36-3-6-6-2-2-66-333-211223-30000002-21-1-10000000000000-110000000000000000
χ576-660-632−32-2200032−320-22−2200000000000−220000000002i−2i−2i2i0000000000−i2i2i2−i20000
χ586-660-632−32-2200032−320-22−2200000000000−22000000000−2i2i2i−2i0000000000i2−i2−i2i20000
χ596-660-6−3232-22000−32320-222−2000000000002−20000000002i−2i−2i2i0000000000i2−i2−i2i20000
χ606-660-6−3232-22000−32320-222−2000000000002−2000000000−2i2i2i−2i0000000000−i2i2i2−i20000
χ611212-6-12-600-4-400600422000000000000-2000000000000000000000000000000000
χ6212-12-60662−62-44000−323202-2−2222000000000002−20000000000000000000000000000000
χ6312-12-606−6262-4400032−3202-222−2200000000000−220000000000000000000000000000000

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