Finite Group Databasebeta

← Group #72342067

Character table — Group #72342067

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85
size111122222244446666661212121212121212121212121224242424242424242424242432323232323232324848484848484848646464646464646464646464969696969696969696969696
order1222444444224422222222444444444442222244444443666121212122244888866661212121212121212444444888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111-1-1-1-11111111111111111111-1-1-1-1-111-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ41111111111-1-1-1-11111111111111111111-1-1-1-1-111-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111-1-1-1-11111-1-1111111-1-1-1-1-111-1-1-1111111-1-1-1111-1-1-11111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1111-1-1-1111-1-1-1
χ61111-1-1-1-11111-1-1111111-1-1-1-1-111-1-1-1111111-1-1-1111-1-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1111-1-1-1111
χ71111-1-1-1-111-1-111111111-1-1-1-1-111-1-1-1111-1-1-111-11-1-11111111-1-1-1-111-1-1-1-111-1-1-1-111-1-11111111-1-1-1-1-1-1111
χ81111-1-1-1-111-1-111111111-1-1-1-1-111-1-1-1111-1-1-111-11-1-11111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1111111-1-1-1
χ9222222222222222222222222222222222222222222222-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ102222222222-2-2-2-22222222222222222222-2-2-2-2-222-2-2-2-2-2-1-1-1-1-1-1-1-1000000001111-1-1-1-11111000000000000
χ11222222-2-2-2-20000222222-2-222222-2-2-2-2-2-2000002-2000002222-2-2-2-2000000000000-2-2220000000000000000
χ12222222-2-2-2-20000222222-2-222222-2-2-2-2-2-2000002-200000-1-1-1-1111100000000−i3−i3i3i311-1-1−i3−i3i3i3000000000000
χ13222222-2-2-2-20000222222-2-222222-2-2-2-2-2-2000002-200000-1-1-1-1111100000000i3i3−i3−i311-1-1i3i3−i3−i3000000000000
χ142222-2-222-2-2000022222222-2-2-222222-2-2-200000-2-20000022222222000000000000-2-2-2-20000000000000000
χ152222-2-222-2-2000022222222-2-2-222222-2-2-200000-2-200000-1-1-1-1-1-1-1-100000000−i3−i3i3i31111i3i3−i3−i3000000000000
χ162222-2-222-2-2000022222222-2-2-222222-2-2-200000-2-200000-1-1-1-1-1-1-1-100000000i3i3−i3−i31111−i3−i3i3i3000000000000
χ172222-2-2-2-22222-2-2222222-2-2-2-2-222-2-2-2222222-2-2-2222-2-2-2-1-1-1-1111100000000-1-1-1-1-1-1111111000000000000
χ182222-2-2-2-222-2-222222222-2-2-2-2-222-2-2-2222-2-2-222-22-2-2222-1-1-1-11111000000001111-1-111-1-1-1-1000000000000
χ193333333333333333-1-1-1-1-1-13-1-1-1-13-1-13-1-13-1-1-1-1-1-1-1-13-1-100000000111111110000000000001-1-11-1-11-1-11-1-1
χ203333333333333333-1-1-1-1-1-13-1-1-1-13-1-13-1-13-1-1-1-1-1-1-1-13-1-100000000-1-1-1-1-1-1-1-1000000000000-111-111-111-111
χ2133333333333333-1-133-1-1-1-1-13-1-1-1-13-1-13-1-13-1-1-1-1-1-1-1-13-10000000011111111000000000000-11-1-11-1-11-1-11-1
χ2233333333333333-1-133-1-1-1-1-13-1-1-1-13-1-13-1-13-1-1-1-1-1-1-1-13-100000000-1-1-1-1-1-1-1-10000000000001-111-111-111-11
χ2333333333333333-1-1-1-133-1-1-1-13-1-1-1-13-1-13-1-13-1-1-1-1-1-1-1-130000000011111111000000000000-1-11-1-11-1-11-1-11
χ2433333333333333-1-1-1-133-1-1-1-13-1-1-1-13-1-13-1-13-1-1-1-1-1-1-1-1300000000-1-1-1-1-1-1-1-100000000000011-111-111-111-1
χ253333333333-3-3-3-333-1-1-1-1-1-13-1-1-1-13-1-13-1-1-31111-1-111-311000000001111-1-1-1-10000000000001-1-11-1-1-111-111
χ263333333333-3-3-3-333-1-1-1-1-1-13-1-1-1-13-1-13-1-1-31111-1-111-31100000000-1-1-1-11111000000000000-111-1111-1-11-1-1
χ273333333333-3-3-3-3-1-133-1-1-1-1-13-1-1-1-13-1-13-11-3111-1-1111-31000000001111-1-1-1-1000000000000-11-1-11-11-111-11
χ283333333333-3-3-3-3-1-133-1-1-1-1-13-1-1-1-13-1-13-11-3111-1-1111-3100000000-1-1-1-111110000000000001-111-11-11-1-11-1
χ293333333333-3-3-3-3-1-1-1-133-1-1-1-13-1-1-1-13-1-1311-311-1-11111-3000000001111-1-1-1-1000000000000-1-11-1-1111-111-1
χ303333333333-3-3-3-3-1-1-1-133-1-1-1-13-1-1-1-13-1-1311-311-1-11111-300000000-1-1-1-1111100000000000011-111-1-1-11-1-11
χ313333-3-3-3-33333-3-333-1-1-1-111-311-1-1-3113-1-13-1-1111-1-1-1-3110000000011-1-111-1-10000000000001-1-1-1111-1-1-111
χ323333-3-3-3-33333-3-333-1-1-1-111-311-1-1-3113-1-13-1-1111-1-1-1-31100000000-1-111-1-111000000000000-1111-1-1-1111-1-1
χ333333-3-3-3-33333-3-3-1-133-1-1111-31-1-11-31-13-1-13-1111-1-1-11-310000000011-1-111-1-1000000000000-11-11-11-11-11-11
χ343333-3-3-3-33333-3-3-1-133-1-1111-31-1-11-31-13-1-13-1111-1-1-11-3100000000-1-111-1-1110000000000001-11-11-11-11-11-1
χ353333-3-3-3-33333-3-3-1-1-1-1331111-3-1-111-3-1-13-1-13111-1-1-111-30000000011-1-111-1-1000000000000-1-1111-1-1-1111-1
χ363333-3-3-3-33333-3-3-1-1-1-1331111-3-1-111-3-1-13-1-13111-1-1-111-300000000-1-111-1-11100000000000011-1-1-1111-1-1-11
χ373333-3-3-3-333-3-33333-1-1-1-111-311-1-1-3113-1-1-311-1-11-1113-1-10000000011-1-1-1-1110000000000001-1-1-111-1111-1-1
χ383333-3-3-3-333-3-33333-1-1-1-111-311-1-1-3113-1-1-311-1-11-1113-1-100000000-1-11111-1-1000000000000-1111-1-11-1-1-111
χ393333-3-3-3-333-3-333-1-133-1-1111-31-1-11-31-13-11-31-1-11-111-13-10000000011-1-1-1-111000000000000-11-11-111-11-11-1
χ403333-3-3-3-333-3-333-1-133-1-1111-31-1-11-31-13-11-31-1-11-111-13-100000000-1-11111-1-10000000000001-11-11-1-11-11-11
χ413333-3-3-3-333-3-333-1-1-1-1331111-3-1-111-3-1-1311-3-1-11-111-1-130000000011-1-1-1-111000000000000-1-1111-111-1-1-11
χ423333-3-3-3-333-3-333-1-1-1-1331111-3-1-111-3-1-1311-3-1-11-111-1-1300000000-1-11111-1-100000000000011-1-1-11-1-1111-1
χ4344-4-44i−4i4i−4i4-44-44i−4i000000000000000000000000000000011-1-1ii−i−i2-22i−2i2-22i−2i1-11-11-1i−ii−ii−i000000000000
χ4444-4-44i−4i4i−4i4-44-44i−4i000000000000000000000000000000011-1-1ii−i−i-22−2i2i-22−2i2i1-11-11-1i−ii−ii−i000000000000
χ4544-4-44i−4i4i−4i4-4-44−4i4i000000000000000000000000000000011-1-1ii−i−i2-22i−2i-22−2i2i-11-111-1i−i−ii−ii000000000000
χ4644-4-44i−4i4i−4i4-4-44−4i4i000000000000000000000000000000011-1-1ii−i−i-22−2i2i2-22i−2i-11-111-1i−i−ii−ii000000000000
χ4744-4-4−4i4i−4i4i4-44-4−4i4i000000000000000000000000000000011-1-1−i−iii2-2−2i2i2-2−2i2i1-11-11-1−ii−ii−ii000000000000
χ4844-4-4−4i4i−4i4i4-44-4−4i4i000000000000000000000000000000011-1-1−i−iii-222i−2i-222i−2i1-11-11-1−ii−ii−ii000000000000
χ4944-4-4−4i4i−4i4i4-4-444i−4i000000000000000000000000000000011-1-1−i−iii2-2−2i2i-222i−2i-11-111-1−iii−ii−i000000000000
χ5044-4-4−4i4i−4i4i4-4-444i−4i000000000000000000000000000000011-1-1−i−iii-222i−2i2-2−2i2i-11-111-1−iii−ii−i000000000000
χ514-4-4400000000004-44-44-4000004-40000000000000000004-4-44000000000000000000000000000000000000
χ524-4-4400000000004-44-44-4000004-4000000000000000000-222-2−2i32i3−2i32i300000000000000000000000000000000
χ534-4-4400000000004-44-44-4000004-4000000000000000000-222-22i3−2i32i3−2i300000000000000000000000000000000
χ5466666666666666-2-2-2-2-2-222-2-2-222-2-2-2-2-2-2-2-2-2222222-2-2-20000000000000000000000000000000000000000
χ556666666666-6-6-6-6-2-2-2-2-2-222-2-2-222-2-2-2-2-2-2222-2-222-2-22220000000000000000000000000000000000000000
χ56666666-6-6-6-6000066-2-2-2-2226-2-2-2-2-622-62200000-22000000000000000000000000000000000000000000000
χ57666666-6-6-6-60000-2-266-2-222-26-2-2-22-622-6200000-22000000000000000000000000000000000000000000000
χ58666666-6-6-6-60000-2-2-2-26622-2-26-2-222-622-600000-22000000000000000000000000000000000000000000000
χ59666666-6-6-6-60000-2-2-2-2-2-2-2-2-2-2-2222222220004-42-24-40000000000000000000000000000000000000000000
χ60666666-6-6-6-60000-2-2-2-2-2-2-2-2-2-2-222222222000-442-2-440000000000000000000000000000000000000000000
χ616666-6-666-6-6000066-2-2-2-2-2-2-622-2-26-2-2-6220000022000000000000000000000000000000000000000000000
χ626666-6-666-6-60000-2-266-2-2-2-22-62-2-2-26-22-620000022000000000000000000000000000000000000000000000
χ636666-6-666-6-60000-2-2-2-266-2-222-6-2-2-2-2622-60000022000000000000000000000000000000000000000000000
χ646666-6-666-6-60000-2-2-2-2-2-22222222-2-2-22220004-4-2-2-440000000000000000000000000000000000000000000
χ656666-6-666-6-60000-2-2-2-2-2-22222222-2-2-2222000-44-2-24-40000000000000000000000000000000000000000000
χ666666-6-6-6-66666-6-6-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-22222220000000000000000000000000000000000000000
χ676666-6-6-6-666-6-666-2-2-2-2-2-2-2-222222222-2-2-222222-22-2-2-2-2-20000000000000000000000000000000000000000
χ6888-8-88i−8i8i−8i8-88-88i−8i0000000000000000000000000000000-1-111−i−iii00000000-11-11-11−ii−ii−ii000000000000
χ6988-8-88i−8i8i−8i8-8-88−8i8i0000000000000000000000000000000-1-111−i−iii000000001-11-1-11−iii−ii−i000000000000
χ7088-8-88i−8i−8i8i-880000000000000000000000000000000000022-2-2−2i−2i2i2i000000000000-222i−2i0000000000000000
χ7188-8-88i−8i−8i8i-8800000000000000000000000000000000000-1-111ii−i−i00000000−i3i3i3−i31-1−ii3−3−33000000000000
χ7288-8-88i−8i−8i8i-8800000000000000000000000000000000000-1-111ii−i−i00000000i3−i3−i3i31-1−ii−333−3000000000000
χ7388-8-8−8i8i8i−8i-880000000000000000000000000000000000022-2-22i2i−2i−2i000000000000-22−2i2i0000000000000000
χ7488-8-8−8i8i8i−8i-8800000000000000000000000000000000000-1-111−i−iii00000000−i3i3i3−i31-1i−i−333−3000000000000
χ7588-8-8−8i8i8i−8i-8800000000000000000000000000000000000-1-111−i−iii00000000i3−i3−i3i31-1i−i3−3−33000000000000
χ7688-8-8−8i8i−8i8i8-88-8−8i8i0000000000000000000000000000000-1-111ii−i−i00000000-11-11-11i−ii−ii−i000000000000
χ7788-8-8−8i8i−8i8i8-8-888i−8i0000000000000000000000000000000-1-111ii−i−i000000001-11-1-11i−i−ii−ii000000000000
χ7812-12-1212000000000012-12-44-4400000-440000000000000000000000000000000000000000000000000000000000
χ7912-12-12120000000000-4412-12-4400000-440000000000000000000000000000000000000000000000000000000000
χ8012-12-12120000000000-44-4412-1200000-440000000000000000000000000000000000000000000000000000000000
χ8112-12-12120000000000-44-44-448-80004-40000000000000000000000000000000000000000000000000000000000
χ8212-12-12120000000000-44-44-44-880004-40000000000000000000000000000000000000000000000000000000000
χ8316-1616-16000000000000000000000000000000000000000004-44-4000000000000000000000000000000000000
χ8416-1616-1600000000000000000000000000000000000000000-22-2223−23−232300000000000000000000000000000000
χ8516-1616-1600000000000000000000000000000000000000000-22-22−232323−2300000000000000000000000000000000

Here i is the imaginary unit (i² = −1).