Finite Group Databasebeta

← Group #72340584

Character table — Group #72340584

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1111111133333333121212121212121212121212121212121212121212121212242424242424242464646464646464646464646464646464
order1244888822448888222244444444888888888888444488883366121212122424242424242424
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111−1−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
χ3111111111111111111111111111111111111111111111111−1+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
χ41111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ51111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32
χ61111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32
χ711-1-1ii−i−i11-1-1ii−i−i1111-1-1-1-111-1-1iiii−i−i−i−iii−i−i11-1-1ii−i−i1111-1-1-1-1ii−i−iii−i−i
χ811-1-1ii−i−i11-1-1ii−i−i1111-1-1-1-111-1-1iiii−i−i−i−iii−i−i11-1-1ii−i−i−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14
χ911-1-1ii−i−i11-1-1ii−i−i1111-1-1-1-111-1-1iiii−i−i−i−iii−i−i11-1-1ii−i−i−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22
χ1011-1-1−i−iii11-1-1−i−iii1111-1-1-1-111-1-1−i−i−i−iiiii−i−iii11-1-1−i−iii1111-1-1-1-1−i−iii−i−iii
χ1111-1-1−i−iii11-1-1−i−iii1111-1-1-1-111-1-1−i−i−i−iiiii−i−iii11-1-1−i−iii−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14
χ1211-1-1−i−iii11-1-1−i−iii1111-1-1-1-111-1-1−i−i−i−iiiii−i−iii11-1-1−i−iii−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22
χ13333333333333333333-1-133-1-1-1-1-1-133-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ143333333333333333-1-133-1-133-1-1-1-1-1-133-1-133-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ153333333333333333-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-10000000000000000
χ163333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13-13-13-13-10000000000000000
χ173333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13-13-13-130000000000000000
χ183333-3-3-3-33333-3-3-3-333-1-133-1-1-1-1-1-1-3-311-3-3111111-1-1-1-111110000000000000000
χ193333-3-3-3-33333-3-3-3-3-1-133-1-133-1-1-1-111-3-311-3-31111-1-1-1-111110000000000000000
χ203333-3-3-3-33333-3-3-3-3-1-1-1-1-1-1-1-1333311111111-3-3-3-3-1-1-1-111110000000000000000
χ213333-3-3-3-33333-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-11111111111113-13-1-31-310000000000000000
χ223333-3-3-3-33333-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-1111111111111-13-131-31-30000000000000000
χ2333-3-33i3i−3i−3i33-3-33i3i−3i−3i33-1-1-3-311-1-1113i3i−i−i−3i−3iii−i−iii-1-111−i−iii0000000000000000
χ2433-3-33i3i−3i−3i33-3-33i3i−3i−3i-1-13311-3-3-1-111−i−i3i3iii−3i−3i−i−iii-1-111−i−iii0000000000000000
χ2533-3-33i3i−3i−3i33-3-33i3i−3i−3i-1-1-1-1111133-3-3−i−i−i−iiiii3i3i−3i−3i-1-111−i−iii0000000000000000
χ2633-3-33i3i−3i−3i33-3-33i3i−3i−3i-1-1-1-11111-1-111−i−i−i−iiiii−i−iii3-1-313i−i−3ii0000000000000000
χ2733-3-33i3i−3i−3i33-3-33i3i−3i−3i-1-1-1-11111-1-111−i−i−i−iiiii−i−iii-131-3−i3ii−3i0000000000000000
χ2833-3-3−3i−3i3i3i33-3-3−3i−3i3i3i33-1-1-3-311-1-111−3i−3iii3i3i−i−iii−i−i-1-111ii−i−i0000000000000000
χ2933-3-3−3i−3i3i3i33-3-3−3i−3i3i3i-1-13311-3-3-1-111ii−3i−3i−i−i3i3iii−i−i-1-111ii−i−i0000000000000000
χ3033-3-3−3i−3i3i3i33-3-3−3i−3i3i3i-1-1-1-1111133-3-3iiii−i−i−i−i−3i−3i3i3i-1-111ii−i−i0000000000000000
χ3133-3-3−3i−3i3i3i33-3-3−3i−3i3i3i-1-1-1-11111-1-111iiii−i−i−i−iii−i−i3-1-31−3ii3i−i0000000000000000
χ3233-3-3−3i−3i3i3i33-3-3−3i−3i3i3i-1-1-1-11111-1-111iiii−i−i−i−iii−i−i-131-3i−3i−i3i0000000000000000
χ334-44i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ134-44i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ130000000000000000000000000000000011-1-1i−ii−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ344-44i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ134-44i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ1300000000000000000000000000000000−1−i32−1+i321+i321−i32ζ22−ζ22ζ14−ζ14−ζ7ζ7ζ13−ζ13−ζ23ζ23ζ5−ζ5
χ354-44i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ134-44i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ1300000000000000000000000000000000−1+i32−1−i321−i321+i32ζ14−ζ14ζ22−ζ22−ζ23ζ23ζ5−ζ5−ζ7ζ7ζ13−ζ13
χ364-44i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ134-44i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ130000000000000000000000000000000011-1-1i−ii−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ374-44i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ134-44i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ1300000000000000000000000000000000−1−i32−1+i321+i321−i32ζ22−ζ22ζ14−ζ14ζ7−ζ7−ζ13ζ13ζ23−ζ23−ζ5ζ5
χ384-44i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ134-44i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ1300000000000000000000000000000000−1+i32−1−i321−i321+i32ζ14−ζ14ζ22−ζ22ζ23−ζ23−ζ5ζ5ζ7−ζ7−ζ13ζ13
χ394-4−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ234-4−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ230000000000000000000000000000000011-1-1−ii−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ404-4−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ234-4−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ2300000000000000000000000000000000−1−i32−1+i321+i321−i32−ζ22ζ22−ζ14ζ14ζ13−ζ13−ζ7ζ7ζ5−ζ5−ζ23ζ23
χ414-4−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ234-4−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ2300000000000000000000000000000000−1+i32−1−i321−i321+i32−ζ14ζ14−ζ22ζ22ζ5−ζ5−ζ23ζ23ζ13−ζ13−ζ7ζ7
χ424-4−4i4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ234-4−4i4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ230000000000000000000000000000000011-1-1−ii−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ434-4−4i4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ234-4−4i4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ2300000000000000000000000000000000−1−i32−1+i321+i321−i32−ζ22ζ22−ζ14ζ14−ζ13ζ13ζ7−ζ7−ζ5ζ5ζ23−ζ23
χ444-4−4i4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ234-4−4i4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ2300000000000000000000000000000000−1+i32−1−i321−i321+i32−ζ14ζ14−ζ22ζ22−ζ5ζ5ζ23−ζ23−ζ13ζ13ζ7−ζ7
χ456-66i−6i6ζ7+6ζ23−6ζ7−6ζ23−6ζ5−6ζ136ζ5+6ζ13-22−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-22-22i−2i2i−2i2-22i−2i2ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ466-66i−6i6ζ7+6ζ23−6ζ7−6ζ23−6ζ5−6ζ136ζ5+6ζ13-22−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-2-222i−2i−2i2i-22−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ476-66i−6i6ζ7+6ζ23−6ζ7−6ζ23−6ζ5−6ζ136ζ5+6ζ13-22−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-222-2−2i2i2i−2i-22−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ486-66i−6i6ζ7+6ζ23−6ζ7−6ζ23−6ζ5−6ζ136ζ5+6ζ13-22−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-22-22−2i2i−2i2i2-22i−2i−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ496-66i−6i−6ζ7−6ζ236ζ7+6ζ236ζ5+6ζ13−6ζ5−6ζ13-22−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-22-22i−2i2i−2i2-22i−2i−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ506-66i−6i−6ζ7−6ζ236ζ7+6ζ236ζ5+6ζ13−6ζ5−6ζ13-22−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-2-222i−2i−2i2i-22−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ516-66i−6i−6ζ7−6ζ236ζ7+6ζ236ζ5+6ζ13−6ζ5−6ζ13-22−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-222-2−2i2i2i−2i-22−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ526-66i−6i−6ζ7−6ζ236ζ7+6ζ236ζ5+6ζ13−6ζ5−6ζ13-22−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-22-22−2i2i−2i2i2-22i−2i2ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ536-6−6i6i−6ζ5−6ζ136ζ5+6ζ136ζ7+6ζ23−6ζ7−6ζ23-222i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232-22-2−2i2i−2i2i2-2−2i2i−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ546-6−6i6i−6ζ5−6ζ136ζ5+6ζ136ζ7+6ζ23−6ζ7−6ζ23-222i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232-2-22−2i2i2i−2i-222i−2i−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ556-6−6i6i−6ζ5−6ζ136ζ5+6ζ136ζ7+6ζ23−6ζ7−6ζ23-222i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23-222-22i−2i−2i2i-222i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ566-6−6i6i−6ζ5−6ζ136ζ5+6ζ136ζ7+6ζ23−6ζ7−6ζ23-222i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23-22-222i−2i2i−2i2-2−2i2i2ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ576-6−6i6i6ζ5+6ζ13−6ζ5−6ζ13−6ζ7−6ζ236ζ7+6ζ23-222i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-22-2−2i2i−2i2i2-2−2i2i2ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ586-6−6i6i6ζ5+6ζ13−6ζ5−6ζ13−6ζ7−6ζ236ζ7+6ζ23-222i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-2-22−2i2i2i−2i-222i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ596-6−6i6i6ζ5+6ζ13−6ζ5−6ζ13−6ζ7−6ζ236ζ7+6ζ23-222i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23-222-22i−2i−2i2i-222i−2i−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ606-6−6i6i6ζ5+6ζ13−6ζ5−6ζ13−6ζ7−6ζ236ζ7+6ζ23-222i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23-22-222i−2i2i−2i2-2−2i2i−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ611212121212121212-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ6212121212-12-12-12-12-4-4-4-44444000000000000000000000000000000000000000000000000
χ631212-12-1212i12i−12i−12i-4-444−4i−4i4i4i000000000000000000000000000000000000000000000000
χ641212-12-12−12i−12i12i12i-4-4444i4i−4i−4i000000000000000000000000000000000000000000000000

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