Finite Group Databasebeta

← Group #11722358

Character table — Group #11722358

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size1111222233333333666666121212121212181818181818181818181818242424242424242424242424363636363636
order1244361212336612121212246612126661212128888242424242424242433366612121212121224661212
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ311111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ411111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321−i321+i321−i32
χ511111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ611111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321+i321−i321+i32
χ711-1-111-1-11111-1-1-1-1-11-1-111-1-1-111111-1-111-1-111-1-1111111-1-1-1-1-1-11-111-1-1
χ811-1-111-1-11111-1-1-1-1-11-1-111-1-1-1111-1-111-1-111-1-111111111-1-1-1-1-1-1-11-1-111
χ911-1-111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-111+i321−i32−1−i32−1+i32-11+i321−i321−1−i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i321-1−1−i32−1+i321+i321−i32
χ1011-1-111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-111+i321−i32−1−i32−1+i32-11+i321−i321−1−i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i32-111+i321−i32−1−i32−1+i32
χ1111-1-111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-111−i321+i32−1+i32−1−i32-11−i321+i321−1+i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i321-1−1+i32−1−i321−i321+i32
χ1211-1-111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-111−i321+i32−1+i32−1−i32-11−i321+i321−1+i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i32-111−i321+i32−1+i32−1−i32
χ132222222222222222222222222222000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000
χ1422222222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i322−1−i3−1+i3−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3000000000000-11+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32000000
χ1522222222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i322−1+i3−1−i3−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3000000000000-11−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32000000
χ1622-2-222-2-22222-2-2-2-2-22-2-222-2-2-2222000000000000-1-1-1-1-1-1111111000000
χ1722-2-222-2-2−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i3-221+i31−i3−1−i3−1+i3-21+i31−i32−1−i3−1+i3000000000000-11+i321−i32-11+i321−i3211−1−i32−1−i32−1+i32−1+i32000000
χ1822-2-222-2-2−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i3-221−i31+i3−1+i3−1−i3-21−i31+i32−1+i3−1−i3000000000000-11−i321+i32-11−i321+i3211−1+i32−1+i32−1−i32−1−i32000000
χ192-22i−2i2-22i−2i22-2-22i−2i2i−2i000000000000−i2i22−2−i2i22−2−i2i22−2-1-1-1111i−ii−ii−i000000
χ202-22i−2i2-22i−2i22-2-22i−2i2i−2i000000000000i2−i2−22i2−i2−22i2−i2−22-1-1-1111i−ii−ii−i000000
χ212-22i−2i2-22i−2i−1−i3−1+i31+i31−i32ζ22−2ζ222ζ14−2ζ14000000000000−i2i22−2ζ7+ζ13−ζ7−ζ13−ζ7+ζ13ζ7−ζ13ζ5+ζ23−ζ5−ζ23ζ5−ζ23−ζ5+ζ23-11+i321−i321−1−i32−1+i32i−iζ22−ζ22ζ14−ζ14000000
χ222-22i−2i2-22i−2i−1−i3−1+i31+i31−i32ζ22−2ζ222ζ14−2ζ14000000000000i2−i2−22−ζ7−ζ13ζ7+ζ13ζ7−ζ13−ζ7+ζ13−ζ5−ζ23ζ5+ζ23−ζ5+ζ23ζ5−ζ23-11+i321−i321−1−i32−1+i32i−iζ22−ζ22ζ14−ζ14000000
χ232-22i−2i2-22i−2i−1+i3−1−i31−i31+i32ζ14−2ζ142ζ22−2ζ22000000000000−i2i22−2ζ5+ζ23−ζ5−ζ23ζ5−ζ23−ζ5+ζ23ζ7+ζ13−ζ7−ζ13−ζ7+ζ13ζ7−ζ13-11−i321+i321−1+i32−1−i32i−iζ14−ζ14ζ22−ζ22000000
χ242-22i−2i2-22i−2i−1+i3−1−i31−i31+i32ζ14−2ζ142ζ22−2ζ22000000000000i2−i2−22−ζ5−ζ23ζ5+ζ23−ζ5+ζ23ζ5−ζ23−ζ7−ζ13ζ7+ζ13ζ7−ζ13−ζ7+ζ13-11−i321+i321−1+i32−1−i32i−iζ14−ζ14ζ22−ζ22000000
χ252-2−2i2i2-2−2i2i22-2-2−2i2i−2i2i000000000000−i2i2−22−i2i2−22−i2i2−22-1-1-1111−ii−ii−ii000000
χ262-2−2i2i2-2−2i2i22-2-2−2i2i−2i2i000000000000i2−i22−2i2−i22−2i2−i22−2-1-1-1111−ii−ii−ii000000
χ272-2−2i2i2-2−2i2i−1−i3−1+i31+i31−i3−2ζ222ζ22−2ζ142ζ14000000000000−i2i2−22ζ7+ζ13−ζ7−ζ13ζ7−ζ13−ζ7+ζ13ζ5+ζ23−ζ5−ζ23−ζ5+ζ23ζ5−ζ23-11+i321−i321−1−i32−1+i32−ii−ζ22ζ22−ζ14ζ14000000
χ282-2−2i2i2-2−2i2i−1−i3−1+i31+i31−i3−2ζ222ζ22−2ζ142ζ14000000000000i2−i22−2−ζ7−ζ13ζ7+ζ13−ζ7+ζ13ζ7−ζ13−ζ5−ζ23ζ5+ζ23ζ5−ζ23−ζ5+ζ23-11+i321−i321−1−i32−1+i32−ii−ζ22ζ22−ζ14ζ14000000
χ292-2−2i2i2-2−2i2i−1+i3−1−i31−i31+i3−2ζ142ζ14−2ζ222ζ22000000000000−i2i2−22ζ5+ζ23−ζ5−ζ23−ζ5+ζ23ζ5−ζ23ζ7+ζ13−ζ7−ζ13ζ7−ζ13−ζ7+ζ13-11−i321+i321−1+i32−1−i32−ii−ζ14ζ14−ζ22ζ22000000
χ302-2−2i2i2-2−2i2i−1+i3−1−i31−i31+i3−2ζ142ζ14−2ζ222ζ22000000000000i2−i22−2−ζ5−ζ23ζ5+ζ23ζ5−ζ23−ζ5+ζ23−ζ7−ζ13ζ7+ζ13−ζ7+ζ13ζ7−ζ13-11−i321+i321−1+i32−1−i32−ii−ζ14ζ14−ζ22ζ22000000
χ313333333333333333-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000-1-1-1-1-1-1
χ323333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000111111
χ3333333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-1-11+i321−i321+i321−i32-11+i321−i32-11+i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32000000000000-1-11+i321−i321+i321−i32
χ3433333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-1-11+i321−i321+i321−i32-11+i321−i32-11+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3200000000000011−1−i32−1+i32−1−i32−1+i32
χ3533333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32-1-11−i321+i321−i321+i32-11−i321+i32-11−i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32000000000000-1-11−i321+i321−i321+i32
χ3633333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32-1-11−i321+i321−i321+i32-11−i321+i32-11−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3200000000000011−1+i32−1−i32−1+i32−1−i32
χ3733-3-333-3-33333-3-3-3-31-111-1-1111-1-1-111-1-111-1-111-1-1000000000000-11-1-111
χ3833-3-333-3-33333-3-3-3-31-111-1-1111-1-1-1-1-111-1-111-1-1110000000000001-111-1-1
χ3933-3-333-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323+3i323−3i323−3i321-1−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32000000000000-111+i321−i32−1−i32−1+i32
χ4033-3-333-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323+3i323−3i323−3i321-1−1−i32−1+i321+i321−i321−1−i32−1+i32-11+i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i320000000000001-1−1−i32−1+i321+i321−i32
χ4133-3-333-3-3−3+3i32−3−3i32−3+3i32−3−3i323−3i323−3i323+3i323+3i321-1−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32000000000000-111−i321+i32−1+i32−1−i32
χ4233-3-333-3-3−3+3i32−3−3i32−3+3i32−3−3i323−3i323−3i323+3i323+3i321-1−1+i32−1−i321−i321+i321−1+i32−1−i32-11−i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i320000000000001-1−1+i32−1−i321−i321+i32
χ434-44i−4i4-44i−4i44-4-44i−4i4i−4i000000000000000000000000111-1-1-1−ii−ii−ii000000
χ444-44i−4i4-44i−4i−2−2i3−2+2i32+2i32−2i34ζ22−4ζ224ζ14−4ζ140000000000000000000000001−1−i32−1+i32-11+i321−i32−ii−ζ22ζ22−ζ14ζ14000000
χ454-44i−4i4-44i−4i−2+2i3−2−2i32−2i32+2i34ζ14−4ζ144ζ22−4ζ220000000000000000000000001−1+i32−1−i32-11−i321+i32−ii−ζ14ζ14−ζ22ζ22000000
χ464-4−4i4i4-4−4i4i44-4-4−4i4i−4i4i000000000000000000000000111-1-1-1i−ii−ii−i000000
χ474-4−4i4i4-4−4i4i−2−2i3−2+2i32+2i32−2i3−4ζ224ζ22−4ζ144ζ140000000000000000000000001−1−i32−1+i32-11+i321−i32i−iζ22−ζ22ζ14−ζ14000000
χ484-4−4i4i4-4−4i4i−2+2i3−2−2i32−2i32+2i3−4ζ144ζ14−4ζ224ζ220000000000000000000000001−1+i32−1−i32-11−i321+i32i−iζ14−ζ14ζ22−ζ22000000
χ496666-3-3-3-300000000660000-300-300000000000000000000000000000000
χ506666-3-3-3-300000000-2-244441-2-21-2-2000000000000000000000000000000
χ516666-3-3-3-300000000-2-2−2−2i3−2+2i3−2−2i3−2+2i311+i31−i311+i31−i3000000000000000000000000000000
χ526666-3-3-3-300000000-2-2−2+2i3−2−2i3−2+2i3−2−2i311−i31+i311−i31+i3000000000000000000000000000000
χ5366-6-6-3-333000000002-2-4-444-1221-2-2000000000000000000000000000000
χ5466-6-6-3-333000000002-22+2i32−2i3−2−2i3−2+2i3-1−1−i3−1+i311+i31−i3000000000000000000000000000000
χ5566-6-6-3-333000000002-22−2i32+2i3−2+2i3−2−2i3-1−1+i3−1−i311−i31+i3000000000000000000000000000000
χ5666-6-6-3-33300000000-660000300-300000000000000000000000000000000
χ5712-1212i−12i-66−6i6i00000000000000000000000000000000000000000000000000
χ5812-12−12i12i-666i−6i00000000000000000000000000000000000000000000000000

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