Finite Group Databasebeta

← Group #11923435

Character table — Group #11923435

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222333366666666661212121212121212121216161616161616161818181818181818181832323232323232324848484848484848
order12443612128888222224444466666121212121233661212121288888888883366121212122424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ311111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ411111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ511111111-1-1-1-111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32
χ611111111-1-1-1-111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32
χ711-1-111-1-1ii−i−i111-1-111-1-1-1111-1-111-1-1-11111-1-1-1-1iiiii−i−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ811-1-111-1-1ii−i−i111-1-111-1-1-1111-1-111-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32iiiii−i−i−i−i−i−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14
χ911-1-111-1-1ii−i−i111-1-111-1-1-1111-1-111-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32iiiii−i−i−i−i−i−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22
χ1011-1-111-1-1−i−iii111-1-111-1-1-1111-1-111-1-1-11111-1-1-1-1−i−i−i−i−iiiiii1111-1-1-1-1−i−iii−i−iii
χ1111-1-111-1-1−i−iii111-1-111-1-1-1111-1-111-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−i−i−i−i−iiiiii−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14
χ1211-1-111-1-1−i−iii111-1-111-1-1-1111-1-111-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−i−i−i−i−iiiiii−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22
χ132222-1-1-1-100002222222222-1-1-1-1-1-1-1-1-1-1222222220000000000-1-1-1-1-1-1-1-100000000
χ142222-1-1-1-100002222222222-1-1-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i300000000001+i321−i321+i321−i321+i321+i321−i321−i3200000000
χ152222-1-1-1-100002222222222-1-1-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i300000000001−i321+i321−i321+i321−i321−i321+i321+i3200000000
χ1622-2-2-1-1110000222-2-222-2-2-2-1-1-111-1-11112222-2-2-2-20000000000-1-1-1-1111100000000
χ1722-2-2-1-1110000222-2-222-2-2-2-1-1-111-1-1111−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i300000000001+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i3200000000
χ1822-2-2-1-1110000222-2-222-2-2-2-1-1-111-1-1111−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i300000000001−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i3200000000
χ193333333333333-1-1-1-1-1-13-1-13-1-1-1-1-1-13-1-1000000003-1-1-1-13-1-1-1-10000000000000000
χ20333333333333-13-1-1-1-1-1-13-1-13-1-1-1-1-1-13-100000000-13-1-1-1-13-1-1-10000000000000000
χ21333333333333-1-13-1-1-1-1-1-13-1-13-1-1-1-1-1-1300000000-1-13-1-1-1-13-1-10000000000000000
χ22333333333333-1-1-13-13-1-1-1-1-1-1-13-13-1-1-1-100000000-1-1-13-1-1-1-13-10000000000000000
χ23333333333333-1-1-1-13-13-1-1-1-1-1-1-13-13-1-1-100000000-1-1-1-13-1-1-1-130000000000000000
χ2433333333-3-3-3-33-1-1-1-1-1-13-1-13-1-1-1-1-1-13-1-100000000-31111-311110000000000000000
χ2533333333-3-3-3-3-13-1-1-1-1-1-13-1-13-1-1-1-1-1-13-1000000001-31111-31110000000000000000
χ2633333333-3-3-3-3-1-13-1-1-1-1-1-13-1-13-1-1-1-1-1-130000000011-31111-3110000000000000000
χ2733333333-3-3-3-3-1-1-13-13-1-1-1-1-1-1-13-13-1-1-1-100000000111-31111-310000000000000000
χ2833333333-3-3-3-3-1-1-1-13-13-1-1-1-1-1-1-13-13-1-1-1000000001111-31111-30000000000000000
χ2933-3-333-3-33i3i−3i−3i3-1-111-1-1-3113-1-111-1-1-311000000003i−i−i−i−i−3iiiii0000000000000000
χ3033-3-333-3-33i3i−3i−3i-13-111-1-11-31-13-111-1-11-3100000000−i3i−i−i−ii−3iiii0000000000000000
χ3133-3-333-3-33i3i−3i−3i-1-1311-1-111-3-1-1311-1-111-300000000−i−i3i−i−iii−3iii0000000000000000
χ3233-3-333-3-33i3i−3i−3i-1-1-11-3-13111-1-1-11-3-1311100000000−i−i−i−i3iiiii−3i0000000000000000
χ3333-3-333-3-33i3i−3i−3i-1-1-1-313-1111-1-1-1-313-111100000000−i−i−i3i−iiii−3ii0000000000000000
χ3433-3-333-3-3−3i−3i3i3i3-1-111-1-1-3113-1-111-1-1-31100000000−3iiiii3i−i−i−i−i0000000000000000
χ3533-3-333-3-3−3i−3i3i3i-13-111-1-11-31-13-111-1-11-3100000000i−3iiii−i3i−i−i−i0000000000000000
χ3633-3-333-3-3−3i−3i3i3i-1-1311-1-111-3-1-1311-1-111-300000000ii−3iii−i−i3i−i−i0000000000000000
χ3733-3-333-3-3−3i−3i3i3i-1-1-11-3-13111-1-1-11-3-1311100000000iiii−3i−i−i−i−i3i0000000000000000
χ3833-3-333-3-3−3i−3i3i3i-1-1-1-313-1111-1-1-1-313-111100000000iii−3ii−i−i−i3i−i0000000000000000
χ394-44i−4i4-44i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ130000000000000000000011-1-1i−ii−i000000000011-1-1i−ii−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ404-44i−4i4-44i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ1300000000000000000000−1−i32−1+i321+i321−i32ζ22−ζ22ζ14−ζ140000000000−1−i32−1+i321+i321−i32ζ22−ζ22ζ14−ζ14−ζ7ζ7ζ13−ζ13−ζ23ζ23ζ5−ζ5
χ414-44i−4i4-44i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ1300000000000000000000−1+i32−1−i321−i321+i32ζ14−ζ14ζ22−ζ220000000000−1+i32−1−i321−i321+i32ζ14−ζ14ζ22−ζ22−ζ23ζ23ζ5−ζ5−ζ7ζ7ζ13−ζ13
χ424-44i−4i4-44i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ130000000000000000000011-1-1i−ii−i000000000011-1-1i−ii−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ434-44i−4i4-44i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ1300000000000000000000−1−i32−1+i321+i321−i32ζ22−ζ22ζ14−ζ140000000000−1−i32−1+i321+i321−i32ζ22−ζ22ζ14−ζ14ζ7−ζ7−ζ13ζ13ζ23−ζ23−ζ5ζ5
χ444-44i−4i4-44i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ1300000000000000000000−1+i32−1−i321−i321+i32ζ14−ζ14ζ22−ζ220000000000−1+i32−1−i321−i321+i32ζ14−ζ14ζ22−ζ22ζ23−ζ23−ζ5ζ5ζ7−ζ7−ζ13ζ13
χ454-4−4i4i4-4−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ230000000000000000000011-1-1−ii−ii000000000011-1-1−ii−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ464-4−4i4i4-4−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ2300000000000000000000−1−i32−1+i321+i321−i32−ζ22ζ22−ζ14ζ140000000000−1−i32−1+i321+i321−i32−ζ22ζ22−ζ14ζ14ζ13−ζ13−ζ7ζ7ζ5−ζ5−ζ23ζ23
χ474-4−4i4i4-4−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ2300000000000000000000−1+i32−1−i321−i321+i32−ζ14ζ14−ζ22ζ220000000000−1+i32−1−i321−i321+i32−ζ14ζ14−ζ22ζ22ζ5−ζ5−ζ23ζ23ζ13−ζ13−ζ7ζ7
χ484-4−4i4i4-4−4i4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ230000000000000000000011-1-1−ii−ii000000000011-1-1−ii−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ494-4−4i4i4-4−4i4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ2300000000000000000000−1−i32−1+i321+i321−i32−ζ22ζ22−ζ14ζ140000000000−1−i32−1+i321+i321−i32−ζ22ζ22−ζ14ζ14−ζ13ζ13ζ7−ζ7−ζ5ζ5ζ23−ζ23
χ504-4−4i4i4-4−4i4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ2300000000000000000000−1+i32−1−i321−i321+i32−ζ14ζ14−ζ22ζ220000000000−1+i32−1−i321−i321+i32−ζ14ζ14−ζ22ζ22−ζ5ζ5ζ23−ζ23−ζ13ζ13ζ7−ζ7
χ516666-3-3-3-300006-2-2-2-2-2-26-2-2-3111111-3110000000000000000000000000000000000
χ526666-3-3-3-30000-26-2-2-2-2-2-26-21-3111111-310000000000000000000000000000000000
χ536666-3-3-3-30000-2-26-2-2-2-2-2-2611-3111111-30000000000000000000000000000000000
χ546666-3-3-3-30000-2-2-26-26-2-2-2-2111-31-311110000000000000000000000000000000000
χ556666-3-3-3-30000-2-2-2-26-26-2-2-21111-31-31110000000000000000000000000000000000
χ5666-6-6-3-33300006-2-222-2-2-622-311-1-1113-1-10000000000000000000000000000000000
χ5766-6-6-3-3330000-26-222-2-22-621-31-1-111-13-10000000000000000000000000000000000
χ5866-6-6-3-3330000-2-2622-2-222-611-3-1-111-1-130000000000000000000000000000000000
χ5966-6-6-3-3330000-2-2-22-6-26222111-131-3-1-1-10000000000000000000000000000000000
χ6066-6-6-3-3330000-2-2-2-626-22221113-1-31-1-1-10000000000000000000000000000000000
χ618-88i−8i-44−4i4i00000000000000000000000022-2-22i−2i2i−2i0000000000-1-111−ii−ii00000000
χ628-88i−8i-44−4i4i000000000000000000000000−1−i3−1+i31+i31−i32ζ22−2ζ222ζ14−2ζ1400000000001+i321−i32−1−i32−1+i32−ζ22ζ22−ζ14ζ1400000000
χ638-88i−8i-44−4i4i000000000000000000000000−1+i3−1−i31−i31+i32ζ14−2ζ142ζ22−2ζ2200000000001−i321+i32−1+i32−1−i32−ζ14ζ14−ζ22ζ2200000000
χ648-8−8i8i-444i−4i00000000000000000000000022-2-2−2i2i−2i2i0000000000-1-111i−ii−i00000000
χ658-8−8i8i-444i−4i000000000000000000000000−1−i3−1+i31+i31−i3−2ζ222ζ22−2ζ142ζ1400000000001+i321−i32−1−i32−1+i32ζ22−ζ22ζ14−ζ1400000000
χ668-8−8i8i-444i−4i000000000000000000000000−1+i3−1−i31−i31+i3−2ζ142ζ14−2ζ222ζ2200000000001−i321+i32−1+i32−1−i32ζ14−ζ14ζ22−ζ2200000000

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