Finite Group Databasebeta

← Group #72341894

Character table — Group #72341894

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size1111222222666612121212121212121212121212121212121216161616242424242424242424242424323232324848484848484848484848484848484848484848484864646464646496969696128128128128
order122244888822442222222244448888882244444444888888366622444444444444448888881212242424248888661212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111-1-1-1-1111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ411111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ5111111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-1
χ6111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-111
χ7111111-1-1-1-11111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ8111111-1-1-1-11111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111
χ91-11-11-1ii−i−i-111-11-1-111-1-1111-1-1iii−i−i−i1-1i−i1-111-1-1i−iii−i−i1-11-11-1i−ii−ii−i1-11-111-1-1i−iii−i−i1-1ii−i−i1-1i−i1-1i−i
χ101-11-11-1ii−i−i-111-11-1-111-1-1111-1-1iii−i−i−i-11−ii1-111-1-1i−iii−i−i1-11-1-11−ii−ii−ii-11-1111-1-1i−iii−i−i1-1ii−i−i-11−ii-11−ii
χ111-11-11-1ii−i−i-111-11-1-1-1-111111-1-1iii−i−i−i1-1i−i-11-1-111i−i−i−iii1-11-1-11−iii−i−ii1-1-11-1-111−ii−i−iii1-1ii−i−i-11−ii1-1i−i
χ121-11-11-1ii−i−i-111-11-1-1-1-111111-1-1iii−i−i−i-11−ii-11-1-111i−i−i−iii1-11-11-1i−i−iii−i-111-1-1-111−ii−i−iii1-1ii−i−i1-1i−i-11−ii
χ131-11-11-1−i−iii-111-11-1-111-1-1111-1-1−i−i−iiii1-1−ii1-111-1-1−ii−i−iii1-11-11-1−ii−ii−ii1-11-111-1-1−ii−i−iii1-1−i−iii1-1−ii1-1−ii
χ141-11-11-1−i−iii-111-11-1-111-1-1111-1-1−i−i−iiii-11i−i1-111-1-1−ii−i−iii1-11-1-11i−ii−ii−i-11-1111-1-1−ii−i−iii1-1−i−iii-11i−i-11i−i
χ151-11-11-1−i−iii-111-11-1-1-1-111111-1-1−i−i−iiii1-1−ii-11-1-111−iiii−i−i1-11-1-11i−i−iii−i1-1-11-1-111i−iii−i−i1-1−i−iii-11i−i1-1−ii
χ161-11-11-1−i−iii-111-11-1-1-1-111111-1-1−i−i−iiii-11i−i-11-1-111−iiii−i−i1-11-11-1−iii−i−ii-111-1-1-111i−iii−i−i1-1−i−iii1-1−ii-11i−i
χ17222222222222222220000222222222222222000000220000-1-1-1-10000220022000000000000-1-1-1-1-1-10000-1-1-1-1
χ1822222222222222222000022222222222-2-2-2-2000000220000-1-1-1-10000-2-200-2-2000000000000-1-1-1-1-1-100001111
χ19222222-2-2-2-22222222000022222-2-2-2-2-2-222-2-2000000-2-20000-1-1-1-10000-2-20022000000000000-1-111110000-1-111
χ20222222-2-2-2-22222222000022222-2-2-2-2-2-2-2-222000000-2-20000-1-1-1-100002200-2-2000000000000-1-11111000011-1-1
χ212222-2-2000022-2-2-22-222222-222-20000000000-2-22-22-200000022220000000000002-22-2000000-2-2000000000000
χ222222-2-2000022-2-2-22-2-2-2-2-22-222-2000000000022-22-220000002222000000000000-22-22000000-2-2000000000000
χ232-22-22-22i2i−2i−2i-222-22-2-20000222-2-22i2i2i−2i−2i−2i2-22i−2i0000002i−2i0000-11-1100002i−2i002-2000000000000-11−i−iii0000-11−ii
χ242-22-22-22i2i−2i−2i-222-22-2-20000222-2-22i2i2i−2i−2i−2i-22−2i2i0000002i−2i0000-11-110000−2i2i00-22000000000000-11−i−iii00001-1i−i
χ252-22-22-2−2i−2i2i2i-222-22-2-20000222-2-2−2i−2i−2i2i2i2i2-2−2i2i000000−2i2i0000-11-110000−2i2i002-2000000000000-11ii−i−i0000-11i−i
χ262-22-22-2−2i−2i2i2i-222-22-2-20000222-2-2−2i−2i−2i2i2i2i-222i−2i000000−2i2i0000-11-1100002i−2i00-22000000000000-11ii−i−i00001-1−ii
χ272-22-2-220000-22-22-2-2222-2-22-22-220000000000-222-2-220000002-22-20000000000002-2-22000000-22000000000000
χ282-22-2-220000-22-22-2-22-2-2222-22-2200000000002-2-222-20000002-22-2000000000000-222-2000000-22000000000000
χ2933333333333333-1-1-11111-1-1-1-1-13-1-13-1-13333111111-1-1111100001111-1-111-1-111-1-1-1-111-1-1-1-1000000-1-1-1-10000
χ3033333333333333-1-1-11111-1-1-1-1-13-1-13-1-1-3-3-3-3111111-1-111110000-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-100000011110000
χ3133333333333333-1-1-1-1-1-1-1-1-1-1-1-13-1-13-1-13333-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111100000011110000
χ3233333333333333-1-1-1-1-1-1-1-1-1-1-1-13-1-13-1-1-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-100001111111111111111-1-11111000000-1-1-1-10000
χ33333333-3-3-3-33333-1-1-11111-1-1-1-1-1-311-31133-3-311111111-1-1-1-1000011-1-111-1-1-1-111-1-1-1-1-1-11111000000-1-1110000
χ34333333-3-3-3-33333-1-1-11111-1-1-1-1-1-311-311-3-33311111111-1-1-1-10000-1-111-1-11111-1-1-1-1-1-1-1-1111100000011-1-10000
χ35333333-3-3-3-33333-1-1-1-1-1-1-1-1-1-1-1-1-311-31133-3-3-1-1-1-1-1-11111110000-1-1111111-1-1-1-1111111-1-1-1-100000011-1-10000
χ36333333-3-3-3-33333-1-1-1-1-1-1-1-1-1-1-1-1-311-311-3-333-1-1-1-1-1-1111111000011-1-1-1-1-1-11111111111-1-1-1-1000000-1-1110000
χ373-33-33-33i3i−3i−3i-333-3-11111-1-1-1-1-1113i−i−i−3iii3-33i−3i1-111-1-1−iiii−i−i00001-1i−i−iii−i-111-1-1-111i−i−i−iii000000-11−ii0000
χ383-33-33-33i3i−3i−3i-333-3-11111-1-1-1-1-1113i−i−i−3iii-33−3i3i1-111-1-1−iiii−i−i0000-11−iii−i−ii1-1-11-1-111i−i−i−iii0000001-1i−i0000
χ393-33-33-33i3i−3i−3i-333-3-111-1-111-1-1-1113i−i−i−3iii3-33i−3i-11-1-111−ii−i−iii0000-11−ii−ii−ii-11-1111-1-1−iiii−i−i0000001-1i−i0000
χ403-33-33-33i3i−3i−3i-333-3-111-1-111-1-1-1113i−i−i−3iii-33−3i3i-11-1-111−ii−i−iii00001-1i−ii−ii−i1-11-111-1-1−iiii−i−i000000-11−ii0000
χ413-33-33-3−3i−3i3i3i-333-3-11111-1-1-1-1-111−3iii3i−i−i3-3−3i3i1-111-1-1i−i−i−iii00001-1−iii−i−ii-111-1-1-111−iiii−i−i000000-11i−i0000
χ423-33-33-3−3i−3i3i3i-333-3-11111-1-1-1-1-111−3iii3i−i−i-333i−3i1-111-1-1i−i−i−iii0000-11i−i−iii−i1-1-11-1-111−iiii−i−i0000001-1−ii0000
χ433-33-33-3−3i−3i3i3i-333-3-111-1-111-1-1-111−3iii3i−i−i3-3−3i3i-11-1-111i−iii−i−i0000-11i−ii−ii−i-11-1111-1-1i−i−i−iii0000001-1−ii0000
χ443-33-33-3−3i−3i3i3i-333-3-111-1-111-1-1-111−3iii3i−i−i-333i−3i-11-1-111i−iii−i−i00001-1−ii−ii−ii1-11-111-1-1i−i−i−iii000000-11i−i0000
χ454444-4-4000044-4-4-44-400004-444-40000000000000000000000-2-2-2-2000000000000000000000022000000000000
χ464-44-4-440000-44-44-4-4400004-44-440000000000000000000000-22-2200000000000000000000002-2000000000000
χ476666666666-2-2-2-22-220000-2-222-2-2-2-2-2-2-200000000002200000000222200-2-200-2-2000000000000000000000000
χ486666666666-2-2-2-22-220000-2-222-2-2-2-2-2-2-200000000002200000000-2-2-2-200220022000000000000000000000000
χ496666666666-2-2-2-2-22-2222222-2-22-222-222000022-2-2-2-2-2-2222200000000000000000000-2-2000000000000000000
χ506666666666-2-2-2-2-22-2-2-2-2-222-2-22-222-2220000-2-22222-2-2-2-2-2-20000000000000000000022000000000000000000
χ51666666-6-6-6-6-2-2-2-22-220000-2-222-22222220000000000-2-20000000022-2-2002200-2-2000000000000000000000000
χ52666666-6-6-6-6-2-2-2-22-220000-2-222-22222220000000000-2-200000000-2-22200-2-20022000000000000000000000000
χ53666666-6-6-6-6-2-2-2-2-22-2222222-2-222-2-22-2-2000022-2-2-2-222-2-2-2-20000000000000000000022000000000000000000
χ54666666-6-6-6-6-2-2-2-2-22-2-2-2-2-222-2-222-2-22-2-20000-2-2222222222200000000000000000000-2-2000000000000000000
χ556666-6-6000066-6-62-222222-22-2-220000000000-2-22-22-20000000000000000000000-22-2200000000000000000000
χ566666-6-6000066-6-62-22-2-2-2-2-22-2-22000000000022-22-2200000000000000000000002-22-200000000000000000000
χ576666-6-60000-2-22222222222-2-2-2-204i−4i04i−4i0000-2-2-22-2200000000000000000000000000002i−2i2i−2i00000000000000
χ586666-6-60000-2-22222222222-2-2-2-20−4i4i0−4i4i0000-2-2-22-220000000000000000000000000000−2i2i−2i2i00000000000000
χ596666-6-60000-2-222222-2-2-2-22-2-2-2-204i−4i04i−4i0000222-22-20000000000000000000000000000−2i2i−2i2i00000000000000
χ606666-6-60000-2-222222-2-2-2-22-2-2-2-20−4i4i0−4i4i0000222-22-200000000000000000000000000002i−2i2i−2i00000000000000
χ616-66-66-66i6i−6i−6i2-2-2222-20000-2-22-22−2i−2i−2i2i2i2i00000000002i−2i000000002-22i−2i00−2i2i00-22000000000000000000000000
χ626-66-66-66i6i−6i−6i2-2-2222-20000-2-22-22−2i−2i−2i2i2i2i00000000002i−2i00000000-22−2i2i002i−2i002-2000000000000000000000000
χ636-66-66-66i6i−6i−6i2-2-22-2-2222-2-222-22-2−2i2i2i2i−2i−2i00002-2-2-222−2i2i2i2i−2i−2i00000000000000000000−2i2i000000000000000000
χ646-66-66-66i6i−6i−6i2-2-22-2-22-2-22222-22-2−2i2i2i2i−2i−2i0000-2222-2-2−2i2i−2i−2i2i2i000000000000000000002i−2i000000000000000000
χ656-66-66-6−6i−6i6i6i2-2-2222-20000-2-22-222i2i2i−2i−2i−2i0000000000−2i2i000000002-2−2i2i002i−2i00-22000000000000000000000000
χ666-66-66-6−6i−6i6i6i2-2-2222-20000-2-22-222i2i2i−2i−2i−2i0000000000−2i2i00000000-222i−2i00−2i2i002-2000000000000000000000000
χ676-66-66-6−6i−6i6i6i2-2-22-2-2222-2-222-22-22i−2i−2i−2i2i2i00002-2-2-2222i−2i−2i−2i2i2i000000000000000000002i−2i000000000000000000
χ686-66-66-6−6i−6i6i6i2-2-22-2-22-2-22222-22-22i−2i−2i−2i2i2i0000-2222-2-22i−2i2i2i−2i−2i00000000000000000000−2i2i000000000000000000
χ696-66-6-6600002-22-22-2-222-2-22-2-22204-40-440000-22-222-200000000000000000000000000002-2-2200000000000000
χ706-66-6-6600002-22-22-2-222-2-22-2-2220-4404-40000-22-222-20000000000000000000000000000-222-200000000000000
χ716-66-6-6600002-22-22-2-2-2-2222-2-22204-40-4400002-22-2-220000000000000000000000000000-222-200000000000000
χ726-66-6-6600002-22-22-2-2-2-2222-2-2220-4404-400002-22-2-2200000000000000000000000000002-2-2200000000000000
χ736-66-6-660000-66-6622-222-2-2-22-22-20000000000-222-2-220000000000000000000000-222-200000000000000000000
χ746-66-6-660000-66-6622-2-2-222-22-22-200000000002-2-222-200000000000000000000002-2-2200000000000000000000
χ7588-8-8004i2−4i24i2−4i200000004-44-4000000000000000000000002i2−2i22i2−2i222-2-2000000000000000000000000i2−i2i2−i200000000
χ7688-8-8004i2−4i24i2−4i20000000-44-4400000000000000000000000−2i22i2−2i22i222-2-2000000000000000000000000i2−i2i2−i200000000
χ7788-8-800−4i24i2−4i24i200000004-44-400000000000000000000000−2i22i2−2i22i222-2-2000000000000000000000000−i2i2−i2i200000000
χ7888-8-800−4i24i2−4i24i20000000-44-44000000000000000000000002i2−2i22i2−2i222-2-2000000000000000000000000−i2i2−i2i200000000
χ798-8-880042−42−424200000004-4-440000000000000000000000022−22−22222-2-220000000000000000000000002−2−2200000000
χ808-8-880042−42−42420000000-444-400000000000000000000000−222222−222-2-220000000000000000000000002−2−2200000000
χ818-8-8800−424242−4200000004-4-4400000000000000000000000−222222−222-2-22000000000000000000000000−222−200000000
χ828-8-8800−424242−420000000-444-40000000000000000000000022−22−22222-2-22000000000000000000000000−222−200000000
χ8312121212-12-120000-4-444-4-4-40000-4444400000000000000000000000000000000000000000000000000000000000000
χ8412-1212-12-121200004-44-4-4440000-444-4-400000000000000000000000000000000000000000000000000000000000000
χ851616-16-16008i2−8i28i2−8i200000000000000000000000000000000000000-2-222000000000000000000000000−i2i2−i2i200000000
χ861616-16-1600−8i28i2−8i28i200000000000000000000000000000000000000-2-222000000000000000000000000i2−i2i2−i200000000
χ8716-16-16160082−82−828200000000000000000000000000000000000000-222-2000000000000000000000000−222−200000000
χ8816-16-161600−828282−8200000000000000000000000000000000000000-222-20000000000000000000000002−2−2200000000

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