Finite Group Databasebeta

← Group #11920361

Character table — Group #11920361

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size112222233444446666688888888121212121216161616161616161618181818242432323232323236363636363672727272
order12346882224122424466886999121818182412242436363672727272727244446121818183636362488882444
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111-1-111111111-1111-1111-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111-1-111111111-1111-1111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111-1-1111-11-1-1111-1-11111-11111-11-1-1111-1-1-1-1-1-111111-1111-1-1-111-1-1-1-1-111-1
χ611111-1-1111-11-1-1111-1-11111-11111-11-1-1111-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-111111-1-11
χ711111-1-111-111-1-1111-1-1-11111111-111-1-1111-1-1-1-1-1-11111-11-1-1-111111-1-1-1-11-1-11
χ811111-1-111-111-1-1111-1-1-11111111-111-1-1111-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-11111-111-1
χ922222222222222222222-1-1-12-1-1-122222-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-10000000000
χ10222222222-2-222222222-2-1-1-1-2-1-1-1-2-2222-1-1-1-1-1-1-1-1-10000-2-21111110000000000
χ1122222-2-2222-22-2-2222-2-22-1-1-1-2-1-1-12-22-2-2-1-1-111111100002-2-1-1-11110000000000
χ1222222-2-222-222-2-2222-2-2-2-1-1-12-1-1-1-222-2-2-1-1-11111110000-22111-1-1-10000000000
χ13222-22002200-200-222000222022200-200-2-2-2000000222200000000-2-200000000
χ14222-22002200-200-222000222022200-200-2-2-2000000-2-2-2-2000000002200000000
χ1522-12-1222222-1-1-12-1-122-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-1ζ44−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
χ1622-12-1222222-1-1-12-1-122-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68-1ζ4−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−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52-1−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
χ1822-12-12222-2-2-1-1-12-1-1221ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ681ζ44−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
χ1922-12-12222-2-2-1-1-12-1-1221ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ681ζ4−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
χ2022-12-12222-2-2-1-1-12-1-1221−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ521−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
χ2122-12-1-2-2222-2-1112-1-1-2-2-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ681ζ44−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
χ2222-12-1-2-2222-2-1112-1-1-2-2-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ681ζ4−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
χ2322-12-1-2-2222-2-1112-1-1-2-2-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ521−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
χ2422-12-1-2-222-22-1112-1-1-2-21ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-1ζ44−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
χ2522-12-1-2-222-22-1112-1-1-2-21ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68-1ζ4−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−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52-1−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
χ272-220-2−i2i22-2000−i2i202-2−i2i202220-2-2-2000−i2i2000−i2i2−i2i2−i2i22i−2i2i−2i00000000002−22−20000
χ282-220-2−i2i22-2000−i2i202-2−i2i202220-2-2-2000−i2i2000−i2i2−i2i2−i2i2−2i2i−2i2i0000000000−22−220000
χ292-220-2i2−i22-2000i2−i202-2i2−i202220-2-2-2000i2−i2000i2−i2i2−i2i2−i22i−2i2i−2i0000000000−22−220000
χ302-220-2i2−i22-2000i2−i202-2i2−i202220-2-2-2000i2−i2000i2−i2i2−i2i2−i2−2i2i−2i2i00000000002−22−20000
χ313333333-1-133333-1-1-1-1-130003000-1-1-1-1-100000000011-1-1-1-10000001-111-1-111-1-1
χ323333333-1-133333-1-1-1-1-130003000-1-1-1-1-1000000000-1-111-1-1000000-11-1-111-1-111
χ333333333-1-1-3-3333-1-1-1-1-1-3000-300011-1-1-100000000011-1-1110000001-111-1-1-1-111
χ343333333-1-1-3-3333-1-1-1-1-1-3000-300011-1-1-1000000000-1-11111000000-11-1-11111-1-1
χ3533333-3-3-1-13-33-3-3-1-1-1113000-3000-11-11100000000011-1-1-110000001-1-1-111-11-11
χ3633333-3-3-1-13-33-3-3-1-1-1113000-3000-11-111000000000-1-111-11000000-1111-1-11-11-1
χ3733333-3-3-1-1-333-3-3-1-1-111-300030001-1-11100000000011-1-11-10000001-1-1-1111-11-1
χ3833333-3-3-1-1-333-3-3-1-1-111-300030001-1-111000000000-1-1111-1000000-1111-1-1-11-11
χ39444-44004400-400-444000-2-2-20-2-2-200-4002220000000000000000000000000000
χ4044-2-4-2004400200-4-2-20002ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52−2ζ4−2ζ6802ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52−2ζ4−2ζ6800200−2ζ44+2ζ52−2ζ68−2ζ4+2ζ44−2ζ522ζ4+2ζ680000000000000000000000000000
χ4144-2-4-2004400200-4-2-20002ζ4−2ζ44+2ζ52−2ζ4−2ζ682ζ44−2ζ52+2ζ6802ζ4−2ζ44+2ζ52−2ζ4−2ζ682ζ44−2ζ52+2ζ6800200−2ζ4+2ζ44−2ζ522ζ4+2ζ68−2ζ44+2ζ52−2ζ680000000000000000000000000000
χ4244-2-4-2004400200-4-2-2000−2ζ4−2ζ682ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ520−2ζ4−2ζ682ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52002002ζ4+2ζ68−2ζ44+2ζ52−2ζ68−2ζ4+2ζ44−2ζ520000000000000000000000000000
χ434-440-4−2i22i24-4000−2i22i204-4−2i22i20-2-2-20222000−2i22i2000i2−i2i2−i2i2−i20000000000000000000000
χ444-440-42i2−2i24-40002i2−2i204-42i2−2i20-2-2-202220002i2−2i2000−i2i2−i2i2−i2i20000000000000000000000
χ454-4-202−2i22i24-4000i2−i20-22−2i22i202ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52−2ζ4−2ζ680−2ζ44+2ζ52−2ζ68−2ζ4+2ζ44−2ζ522ζ4+2ζ68000i2−i2000−ζ5+ζ7−ζ23−ζ53+ζ61−ζ71ζ5−ζ7+ζ23+ζ53−ζ61+ζ71−ζ7−ζ13−ζ31+ζ53−ζ61+ζ71ζ7+ζ13+ζ31−ζ53+ζ61−ζ71ζ5+ζ13+ζ23+ζ31−ζ5−ζ13−ζ23−ζ310000000000000000000000
χ464-4-202−2i22i24-4000i2−i20-22−2i22i202ζ4−2ζ44+2ζ52−2ζ4−2ζ682ζ44−2ζ52+2ζ680−2ζ4+2ζ44−2ζ522ζ4+2ζ68−2ζ44+2ζ52−2ζ68000i2−i2000−ζ7−ζ13−ζ31+ζ53−ζ61+ζ71ζ7+ζ13+ζ31−ζ53+ζ61−ζ71ζ5+ζ13+ζ23+ζ31−ζ5−ζ13−ζ23−ζ31−ζ5+ζ7−ζ23−ζ53+ζ61−ζ71ζ5−ζ7+ζ23+ζ53−ζ61+ζ710000000000000000000000
χ474-4-202−2i22i24-4000i2−i20-22−2i22i20−2ζ4−2ζ682ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ5202ζ4+2ζ68−2ζ44+2ζ52−2ζ68−2ζ4+2ζ44−2ζ52000i2−i2000ζ5+ζ13+ζ23+ζ31−ζ5−ζ13−ζ23−ζ31−ζ5+ζ7−ζ23−ζ53+ζ61−ζ71ζ5−ζ7+ζ23+ζ53−ζ61+ζ71−ζ7−ζ13−ζ31+ζ53−ζ61+ζ71ζ7+ζ13+ζ31−ζ53+ζ61−ζ710000000000000000000000
χ484-4-2022i2−2i24-4000−i2i20-222i2−2i202ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ52−2ζ4−2ζ680−2ζ44+2ζ52−2ζ68−2ζ4+2ζ44−2ζ522ζ4+2ζ68000−i2i2000ζ5−ζ7+ζ23+ζ53−ζ61+ζ71−ζ5+ζ7−ζ23−ζ53+ζ61−ζ71ζ7+ζ13+ζ31−ζ53+ζ61−ζ71−ζ7−ζ13−ζ31+ζ53−ζ61+ζ71−ζ5−ζ13−ζ23−ζ31ζ5+ζ13+ζ23+ζ310000000000000000000000
χ494-4-2022i2−2i24-4000−i2i20-222i2−2i202ζ4−2ζ44+2ζ52−2ζ4−2ζ682ζ44−2ζ52+2ζ680−2ζ4+2ζ44−2ζ522ζ4+2ζ68−2ζ44+2ζ52−2ζ68000−i2i2000ζ7+ζ13+ζ31−ζ53+ζ61−ζ71−ζ7−ζ13−ζ31+ζ53−ζ61+ζ71−ζ5−ζ13−ζ23−ζ31ζ5+ζ13+ζ23+ζ31ζ5−ζ7+ζ23+ζ53−ζ61+ζ71−ζ5+ζ7−ζ23−ζ53+ζ61−ζ710000000000000000000000
χ504-4-2022i2−2i24-4000−i2i20-222i2−2i20−2ζ4−2ζ682ζ44−2ζ52+2ζ682ζ4−2ζ44+2ζ5202ζ4+2ζ68−2ζ44+2ζ52−2ζ68−2ζ4+2ζ44−2ζ52000−i2i2000−ζ5−ζ13−ζ23−ζ31ζ5+ζ13+ζ23+ζ31ζ5−ζ7+ζ23+ζ53−ζ61+ζ71−ζ5+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
χ5366-36-366-2-266-3-3-3-211-2-2-3000-3000-2-21110000000000000110000000000000000
χ5466-36-366-2-2-6-6-3-3-3-211-2-230003000221110000000000000-1-10000000000000000
χ5566-36-3-6-6-2-26-6-333-21122-30003000-221-1-100000000000001-10000000000000000
χ5666-36-3-6-6-2-2-66-333-211223000-30002-21-1-10000000000000-110000000000000000
χ576-660-6−3i23i2-22000−3i23i20-22i2−i200000000000i2−i20000000002i−2i−2i2i00000000002−2−220000
χ586-660-6−3i23i2-22000−3i23i20-22i2−i200000000000i2−i2000000000−2i2i2i−2i0000000000−222−20000
χ596-660-63i2−3i2-220003i2−3i20-22−i2i200000000000−i2i20000000002i−2i−2i2i0000000000−222−20000
χ606-660-63i2−3i2-220003i2−3i20-22−i2i200000000000−i2i2000000000−2i2i2i−2i00000000002−2−220000
χ611212-6-12-600-4-400600422000000000000-2000000000000000000000000000000000
χ6212-12-606−6i26i2-440003i2−3i202-22i2−2i200000000000−i2i20000000000000000000000000000000
χ6312-12-6066i2−6i2-44000−3i23i202-2−2i22i200000000000i2−i20000000000000000000000000000000

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