Finite Group Databasebeta

← Group #72342108

Character table — Group #72342108

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size11112244666688881212121212121212121212121212121212121616242424242424242424242424323232324848484848484848484848484848484848484848484864646464646496969696128128128128
order122244222244888822222244444444444444222244448888366622444444448888888888881212242424244488661212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ3111111111111-1-1-1-1111111111111111111-1-111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1
χ4111111111111-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1
χ5111111-1-111111111111-1-1111-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-1
χ6111111-1-111111111111-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ7111111-1-11111-1-1-1-1111-1-1111-1-1-1-111111111-1-1111111-1-1-1-11111-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-111
χ8111111-1-11111-1-1-1-1111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-111
χ91-1-111-11-11-11-1ii−i−i11-11-1-11-111-1-111-1-1-11i−i1-11-11-11-1ii−i−i1-11-11-1i−ii−i1-1i−ii−ii−i11-1-111-1-11-1ii−i−ii−ii−i1-1i−i
χ101-1-111-11-11-11-1ii−i−i11-11-1-11-111-1-1-1-111-11i−i1-1-11-11-11−i−iii1-11-1-11−iii−i-11−iii−i−ii-1-111-1-1111-1ii−i−i−ii−ii1-1i−i
χ111-1-111-11-11-11-1−i−iii11-11-1-11-111-1-111-1-1-11−ii1-11-11-11-1−i−iii1-11-11-1−ii−ii1-1−ii−ii−ii11-1-111-1-11-1−i−iii−ii−ii1-1−ii
χ121-1-111-11-11-11-1−i−iii11-11-1-11-111-1-1-1-111-11−ii1-1-11-11-11ii−i−i1-11-1-11i−i−ii-11i−i−iii−i-1-111-1-1111-1−i−iiii−ii−i1-1−ii
χ131-1-111-1-111-11-1ii−i−i11-1-11-11-1-1-11111-1-1-11−ii-111-11-11-1ii−i−i1-11-1-11−ii−ii-11−iii−ii−i11-1-1-1-1111-1ii−i−i−iii−i-11−ii
χ141-1-111-1-111-11-1ii−i−i11-1-11-11-1-1-111-1-111-11−ii-11-11-11-11−i−iii1-11-11-1i−i−ii1-1i−ii−i−ii-1-11111-1-11-1ii−i−ii−i−ii-11−ii
χ151-1-111-1-111-11-1−i−iii11-1-11-11-1-1-11111-1-1-11i−i-111-11-11-1−i−iii1-11-1-11i−ii−i-11i−i−ii−ii11-1-1-1-1111-1−i−iiii−i−ii-11i−i
χ161-1-111-1-111-11-1−i−iii11-1-11-11-1-1-111-1-111-11i−i-11-11-11-11ii−i−i1-11-11-1−iii−i1-1−ii−iii−i-1-11111-1-11-1−i−iii−iii−i-11i−i
χ17222222222222222222222222222200002222220000000000-1-1-1-10000220000220000000000-1-1-1-1-1-10000-1-1-1-1
χ18222222222222-2-2-2-2222222222222000022-2-2220000000000-1-1-1-10000-2-20000-2-20000000000-1-111110000-1-111
χ19222222-2-222222222222-2-2222-2-2-2-2000022-2-2-2-20000000000-1-1-1-10000-2-20000220000000000-1-1-1-1-1-100001111
χ20222222-2-22222-2-2-2-2222-2-2222-2-2-2-200002222-2-20000000000-1-1-1-10000220000-2-20000000000-1-11111000011-1-1
χ212222-2-20022-2-200002-2-2002-2200002222-22000022-2-2-2-200002222000000000000002-22-20000-2-2000000000000
χ222222-2-20022-2-200002-2-2002-220000-2-2-2-2-220000-2-222220000222200000000000000-22-220000-2-2000000000000
χ232-2-222-22-22-22-22i2i−2i−2i22-22-2-22-222-2-20000-222i−2i2-20000000000-11-1100002i−2i00002i−2i0000000000-11−i−iii0000-11−ii
χ242-2-222-22-22-22-2−2i−2i2i2i22-22-2-22-222-2-20000-22−2i2i2-20000000000-11-110000−2i2i0000−2i2i0000000000-11ii−i−i0000-11i−i
χ252-2-222-2-222-22-22i2i−2i−2i22-2-22-22-2-2-2220000-22−2i2i-220000000000-11-110000−2i2i00002i−2i0000000000-11−i−iii00001-1i−i
χ262-2-222-2-222-22-2−2i−2i2i2i22-2-22-22-2-2-2220000-222i−2i-220000000000-11-1100002i−2i0000−2i2i0000000000-11ii−i−i00001-1−ii
χ272-2-22-22002-2-2200002-2200-2-2-2000022-2-22200002-2-22-2200002-22-2000000000000002-2-220000-22000000000000
χ282-2-22-22002-2-2200002-2200-2-2-20000-2-222220000-222-22-200002-22-200000000000000-222-20000-22000000000000
χ293333333333333333-1-1-133-1-1-1-1-1-1-11111-1-133-1-1111111111100001111-1-11111-1-111-1-1-1-1-1-1-1-1000000-1-1-1-10000
χ303333333333333333-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111100000011110000
χ31333333333333-3-3-3-3-1-1-133-1-1-1-1-1-1-11111-1-1-3-3-1-1111111-1-1-1-1000011-1-11111-1-111-1-1-1-1-1-1-1-1-1-100000011110000
χ32333333333333-3-3-3-3-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-1-1-1-1-1-1-1-111110000-1-11111-1-111111111111111000000-1-1-1-10000
χ33333333-3-333333333-1-1-1-3-3-1-1-111111111-1-1-3-31111111111110000-1-1-1-111-1-1-1-1-1-111-1-1-1-1111100000011-1-10000
χ34333333-3-333333333-1-1-1-3-3-1-1-11111-1-1-1-1-1-1-3-311-1-1-1-1-1-1-1-1-1-100001111111111-1-1-1-11111-1-1-1-1000000-1-1110000
χ35333333-3-33333-3-3-3-3-1-1-1-3-3-1-1-111111111-1-13311111111-1-1-1-10000-1-111-1-1-1-11111-1-1-1-1-1-11111000000-1-1110000
χ36333333-3-33333-3-3-3-3-1-1-1-3-3-1-1-11111-1-1-1-1-1-13311-1-1-1-1-1-11111000011-1-1-1-111-1-111111111-1-1-1-100000011-1-10000
χ373-3-333-33-33-33-33i3i−3i−3i-1-113-31-11-1-11111-1-11-13i−3i-111-11-11-1ii−i−i00001-1i−i−ii1-1i−i−iii−i-1-111-1-111000000−ii−ii0000
χ383-3-333-33-33-33-33i3i−3i−3i-1-113-31-11-1-111-1-1111-13i−3i-11-11-11-11−i−iii0000-11−ii−ii-11−ii−ii−ii11-1-111-1-1000000i−ii−i0000
χ393-3-333-33-33-33-3−3i−3i3i3i-1-113-31-11-1-11111-1-11-1−3i3i-111-11-11-1−i−iii00001-1−iii−i1-1−iii−i−ii-1-111-1-111000000i−ii−i0000
χ403-3-333-33-33-33-3−3i−3i3i3i-1-113-31-11-1-111-1-1111-1−3i3i-11-11-11-11ii−i−i0000-11i−ii−i-11i−ii−ii−i11-1-111-1-1000000−ii−ii0000
χ413-3-333-3-333-33-33i3i−3i−3i-1-11-331-1111-1-111-1-11-1−3i3i1-11-11-11-1ii−i−i0000-11−iii−i-11−ii−iii−i-1-11111-1-1000000i−i−ii0000
χ423-3-333-3-333-33-33i3i−3i−3i-1-11-331-1111-1-1-1-1111-1−3i3i1-1-11-11-11−i−iii00001-1i−ii−i1-1i−i−ii−ii11-1-1-1-111000000−iii−i0000
χ433-3-333-3-333-33-3−3i−3i3i3i-1-11-331-1111-1-111-1-11-13i−3i1-11-11-11-1−i−iii0000-11i−i−ii-11i−ii−i−ii-1-11111-1-1000000−iii−i0000
χ443-3-333-3-333-33-3−3i−3i3i3i-1-11-331-1111-1-1-1-1111-13i−3i1-1-11-11-11ii−i−i00001-1−ii−ii1-1−iii−ii−i11-1-1-1-111000000i−i−ii0000
χ454444-4-40044-4-400004-4-4004-4400000000-4400000000000000-2-2-2-2000000000000000000000022000000000000
χ464-4-44-44004-4-4400004-4400-4-4-4000000004400000000000000-22-2200000000000000000000002-2000000000000
χ4766666666-2-2-2-200002-2-2-2-222-2-2-2-2-200002-200220000002222000000220000-2-200-2-20000000000000000000000
χ4866666666-2-2-2-200002-2-2-2-222-2-2-2-2-200002-20022000000-2-2-2-2000000-2-200002200220000000000000000000000
χ4966666666-2-2-2-20000-222-2-2-2-2222222222-2200-2-2-2-2-2-22200000000-2-20000220000000000000000000000000000
χ5066666666-2-2-2-20000-222-2-2-2-222222-2-2-2-2-2200-2-22222-2-200000000220000-2-20000000000000000000000000000
χ51666666-6-6-2-2-2-200002-2-22222-2222200002-200-2-20000002222000000-2-200002200-2-20000000000000000000000
χ52666666-6-6-2-2-2-200002-2-22222-2222200002-200-2-2000000-2-2-2-2000000220000-2-200220000000000000000000000
χ53666666-6-6-2-2-2-20000-22222-2-22-2-2-2-22222-220022-2-2-2-22200000000220000-2-20000000000000000000000000000
χ54666666-6-6-2-2-2-20000-22222-2-22-2-2-2-2-2-2-2-2-2200222222-2-200000000-2-20000220000000000000000000000000000
χ556666-6-60066-6-60000-22200-22-2000022222-2000022-2-2-2-20000000000000000000000-22-22000000000000000000
χ566666-6-60066-6-60000-22200-22-20000-2-2-2-22-20000-2-2222200000000000000000000002-22-2000000000000000000
χ576666-6-600-2-2220000-2-2-200-2224-44-42222220000-2-222-2-2000000000000000000000000002-22-200000000000000
χ586666-6-600-2-2220000-2-2-200-2224-44-4-2-2-2-222000022-2-22200000000000000000000000000-22-2200000000000000
χ596666-6-600-2-2220000-2-2-200-222-44-442222220000-2-222-2-200000000000000000000000000-22-2200000000000000
χ606666-6-600-2-2220000-2-2-200-222-44-44-2-2-2-222000022-2-222000000000000000000000000002-22-200000000000000
χ616-6-666-66-6-22-2200002-22-22-222-2-2220000-2-2002-20000002i2i−2i−2i0000002i−2i0000−2i2i00−2i2i0000000000000000000000
χ626-6-666-66-6-22-2200002-22-22-222-2-2220000-2-2002-2000000−2i−2i2i2i000000−2i2i00002i−2i002i−2i0000000000000000000000
χ636-6-666-66-6-22-220000-22-2-222-2-222-2-222-2-22200-22-22-222-200000000-2200002-20000000000000000000000000000
χ646-6-666-66-6-22-220000-22-2-222-2-222-2-2-2-2222200-222-22-2-22000000002-20000-220000000000000000000000000000
χ656-6-666-6-66-22-2200002-222-2-22222-2-20000-2-200-220000002i2i−2i−2i000000−2i2i00002i−2i00−2i2i0000000000000000000000
χ666-6-666-6-66-22-2200002-222-2-22222-2-20000-2-200-22000000−2i−2i2i2i0000002i−2i0000−2i2i002i−2i0000000000000000000000
χ676-6-666-6-66-22-220000-22-22-22-2-2-2-22222-2-222002-2-22-222-2000000002-20000-220000000000000000000000000000
χ686-6-666-6-66-22-220000-22-22-22-2-2-2-222-2-22222002-22-22-2-2200000000-2200002-20000000000000000000000000000
χ696-6-66-66006-6-660000-22-200222000022-2-2-2-200002-2-22-220000000000000000000000-222-2000000000000000000
χ706-6-66-66006-6-660000-22-2002220000-2-222-2-20000-222-22-200000000000000000000002-2-22000000000000000000
χ716-6-66-6600-222-20000-2-220022-24-4-4422-2-2-220000-222-2-22000000000000000000000000002-2-2200000000000000
χ726-6-66-6600-222-20000-2-220022-24-4-44-2-222-2200002-2-222-200000000000000000000000000-222-200000000000000
χ736-6-66-6600-222-20000-2-220022-2-444-422-2-2-220000-222-2-2200000000000000000000000000-222-200000000000000
χ746-6-66-6600-222-20000-2-220022-2-444-4-2-222-2200002-2-222-2000000000000000000000000002-2-2200000000000000
χ7588-8-8000000002i2−2i22i2−2i20000000000004-44-40000000000002i2−2i22i2−2i222-2-2000000000000000000000000i2−i2i2−i200000000
χ7688-8-8000000002i2−2i22i2−2i2000000000000-44-44000000000000−2i22i2−2i22i222-2-2000000000000000000000000i2−i2i2−i200000000
χ7788-8-800000000−2i22i2−2i22i20000000000004-44-4000000000000−2i22i2−2i22i222-2-2000000000000000000000000−i2i2−i2i200000000
χ7888-8-800000000−2i22i2−2i22i2000000000000-44-440000000000002i2−2i22i2−2i222-2-2000000000000000000000000−i2i2−i2i200000000
χ798-88-80000000022−22−22220000000000004-4-4400000000000022−22−22222-2-220000000000000000000000002−2−2200000000
χ808-88-80000000022−22−2222000000000000-444-4000000000000−222222−222-2-220000000000000000000000002−2−2200000000
χ818-88-800000000−222222−220000000000004-4-44000000000000−222222−222-2-22000000000000000000000000−222−200000000
χ828-88-800000000−222222−22000000000000-444-400000000000022−22−22222-2-22000000000000000000000000−222−200000000
χ8312121212-12-1200-4-4440000444004-4-400000000-4-4000000000000000000000000000000000000000000000000000000
χ8412-12-1212-121200-444-4000044-400-4-44000000004-4000000000000000000000000000000000000000000000000000000
χ851616-16-16000000004i2−4i24i2−4i200000000000000000000000000000000-2-222000000000000000000000000−i2i2−i2i200000000
χ861616-16-1600000000−4i24i2−4i24i200000000000000000000000000000000-2-222000000000000000000000000i2−i2i2−i200000000
χ8716-1616-160000000042−42−424200000000000000000000000000000000-222-2000000000000000000000000−222−200000000
χ8816-1616-1600000000−424242−4200000000000000000000000000000000-222-20000000000000000000000002−2−2200000000

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