Finite Group Databasebeta

← Group #72343865

Character table — Group #72343865

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82
size111122446666121212121212121212121212121216161616242424242424242424243232323248484848484848484848484848484848484848484848484864646464646496969696128128128128
order122244882244222244448888882244224444448836662244444444444444888888881212242424244444661212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ311111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ5111111-1-1111111111111-1-1-1-1-1-111-1-111111111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1
χ6111111-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1
χ7111111-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111
χ8111111-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-111
χ91-1-111-1i−i-111-111-1-11-1-11iii−i−i−i1-1i−i1-11-111-1-1i−i1-11-11-1i−ii−ii−i1-11-1ii−i−ii−ii−i11-1-11-1ii−i−i1-1i−i1-1i−i
χ101-1-111-1i−i-111-111-1-11-1-11iii−i−i−i1-1i−i-11-11-1-111i−i1-11-1-11−iii−i−ii1-1-11−i−iii−ii−ii-1-1111-1ii−i−i-11−ii1-1i−i
χ111-1-111-1i−i-111-111-1-11-1-11iii−i−i−i-11−ii1-11-111-1-1i−i1-11-1-11−ii−ii−ii-11-11ii−i−ii−ii−i11-1-11-1ii−i−i-11−ii-11−ii
χ121-1-111-1i−i-111-111-1-11-1-11iii−i−i−i-11−ii-11-11-1-111i−i1-11-11-1i−i−iii−i-111-1−i−iii−ii−ii-1-1111-1ii−i−i1-1i−i-11−ii
χ131-1-111-1−ii-111-111-1-11-1-11−i−i−iiii1-1−ii1-11-111-1-1−ii1-11-11-1−ii−ii−ii1-11-1−i−iii−ii−ii11-1-11-1−i−iii1-1−ii1-1−ii
χ141-1-111-1−ii-111-111-1-11-1-11−i−i−iiii1-1−ii-11-11-1-111−ii1-11-1-11i−i−iii−i1-1-11ii−i−ii−ii−i-1-1111-1−i−iii-11i−i1-1−ii
χ151-1-111-1−ii-111-111-1-11-1-11−i−i−iiii-11i−i1-11-111-1-1−ii1-11-1-11i−ii−ii−i-11-11−i−iii−ii−ii11-1-11-1−i−iii-11i−i-11i−i
χ161-1-111-1−ii-111-111-1-11-1-11−i−i−iiii-11i−i-11-11-1-111−ii1-11-11-1−iii−i−ii-111-1ii−i−ii−ii−i-1-1111-1−i−iii1-1−ii-11i−i
χ172222222222222222222222222222220000000022-1-1-1-1000022002200000000000000-1-1-1-1-1-10000-1-1-1-1
χ1822222222222222222222222222-2-2-2-20000000022-1-1-1-10000-2-200-2-200000000000000-1-1-1-1-1-100001111
χ19222222-2-2222222222222-2-2-2-2-2-222-2-200000000-2-2-1-1-1-10000-2-2002200000000000000-1-111110000-1-111
χ20222222-2-2222222222222-2-2-2-2-2-2-2-22200000000-2-2-1-1-1-100002200-2-200000000000000-1-11111000011-1-1
χ212222-2-20022-2-2-222-2-22-22000000000022-2-22-22-2002222000000000000000000002-22-2-2-2000000000000
χ222222-2-20022-2-2-222-2-22-220000000000-2-222-22-2200222200000000000000000000-22-22-2-2000000000000
χ232-2-222-22i−2i-222-222-2-22-2-222i2i2i−2i−2i−2i2-22i−2i000000002i−2i-11-1100002i−2i002-200000000000000-11−i−iii0000-11−ii
χ242-2-222-22i−2i-222-222-2-22-2-222i2i2i−2i−2i−2i-22−2i2i000000002i−2i-11-110000−2i2i00-2200000000000000-11−i−iii00001-1i−i
χ252-2-222-2−2i2i-222-222-2-22-2-22−2i−2i−2i2i2i2i2-2−2i2i00000000−2i2i-11-110000−2i2i002-200000000000000-11ii−i−i0000-11i−i
χ262-2-222-2−2i2i-222-222-2-22-2-22−2i−2i−2i2i2i2i-222i−2i00000000−2i2i-11-1100002i−2i00-2200000000000000-11ii−i−i00001-1−ii
χ272-2-22-2200-22-22-22-22-2-22200000000002-2-222-2-22002-22-2000000000000000000002-2-22-22000000000000
χ282-2-22-2200-22-22-22-22-2-2220000000000-222-2-222-2002-22-200000000000000000000-222-2-22000000000000
χ29333333333333-1-1-1-1-1-1-1-13-1-13-1-1333311111111-1-100001111-1-111-1-111-1-1-1-11111-1-1-1-1000000-1-1-1-10000
χ30333333333333-1-1-1-1-1-1-1-13-1-13-1-13333-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111100000011110000
χ31333333333333-1-1-1-1-1-1-1-13-1-13-1-1-3-3-3-311111111-1-10000-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-100000011110000
χ32333333333333-1-1-1-1-1-1-1-13-1-13-1-1-3-3-3-3-1-1-1-1-1-1-1-1-1-100001111111111111111-1-1-1-11111000000-1-1-1-10000
χ33333333-3-33333-1-1-1-1-1-1-1-1-311-31133-3-31111111111000011-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1000000-1-1110000
χ34333333-3-33333-1-1-1-1-1-1-1-1-311-31133-3-3-1-1-1-1-1-1-1-1110000-1-1111111-1-1-1-1-1-1-1-11111111100000011-1-10000
χ35333333-3-33333-1-1-1-1-1-1-1-1-311-311-3-33311111111110000-1-111-1-11111-1-11111-1-1-1-1-1-1-1-100000011-1-10000
χ36333333-3-33333-1-1-1-1-1-1-1-1-311-311-3-333-1-1-1-1-1-1-1-111000011-1-1-1-1-1-11111-1-1-1-111111111000000-1-1110000
χ373-3-333-33i−3i-333-3-1-111-111-13i−i−i−3iii3-33i−3i1-11-111-1-1−ii00001-1i−i−iii−i-111-1−i−iiii−ii−i-1-111000000-11−ii0000
χ383-3-333-33i−3i-333-3-1-111-111-13i−i−i−3iii3-33i−3i-11-11-1-111−ii0000-11−ii−ii−ii-11-11ii−i−i−ii−ii11-1-10000001-1i−i0000
χ393-3-333-33i−3i-333-3-1-111-111-13i−i−i−3iii-33−3i3i1-11-111-1-1−ii0000-11−iii−i−ii1-1-11−i−iiii−ii−i-1-1110000001-1i−i0000
χ403-3-333-33i−3i-333-3-1-111-111-13i−i−i−3iii-33−3i3i-11-11-1-111−ii00001-1i−ii−ii−i1-11-1ii−i−i−ii−ii11-1-1000000-11−ii0000
χ413-3-333-3−3i3i-333-3-1-111-111-1−3iii3i−i−i3-3−3i3i1-11-111-1-1i−i00001-1−iii−i−ii-111-1ii−i−i−ii−ii-1-111000000-11i−i0000
χ423-3-333-3−3i3i-333-3-1-111-111-1−3iii3i−i−i3-3−3i3i-11-11-1-111i−i0000-11i−ii−ii−i-11-11−i−iiii−ii−i11-1-10000001-1−ii0000
χ433-3-333-3−3i3i-333-3-1-111-111-1−3iii3i−i−i-333i−3i1-11-111-1-1i−i0000-11i−i−iii−i1-1-11ii−i−i−ii−ii-1-1110000001-1−ii0000
χ443-3-333-3−3i3i-333-3-1-111-111-1−3iii3i−i−i-333i−3i-11-11-1-111i−i00001-1−ii−ii−ii1-11-1−i−iiii−ii−i11-1-1000000-11i−i0000
χ454444-4-40044-4-4-444-4-44-4400000000000000000000-2-2-2-200000000000000000000000022000000000000
χ464-4-44-4400-44-44-44-44-4-44400000000000000000000-22-220000000000000000000000002-2000000000000
χ4766666666-2-2-2-22-2-22-22-22-222-22200002222-2-2-2-2-2-20000000000000000000022-2-2000000000000000000
χ4866666666-2-2-2-22-2-22-22-22-222-2220000-2-2-2-22222-2-200000000000000000000-2-222000000000000000000
χ4966666666-2-2-2-2-222-22-22-2-2-2-2-2-2-2000000000000220000222200-2-200-2-200000000000000000000000000
χ5066666666-2-2-2-2-222-22-22-2-2-2-2-2-2-2000000000000220000-2-2-2-20022002200000000000000000000000000
χ51666666-6-6-2-2-2-22-2-22-22-222-2-22-2-200002222-2-2-2-22200000000000000000000-2-222000000000000000000
χ52666666-6-6-2-2-2-22-2-22-22-222-2-22-2-20000-2-2-2-22222220000000000000000000022-2-2000000000000000000
χ53666666-6-6-2-2-2-2-222-22-22-2222222000000000000-2-2000022-2-2002200-2-200000000000000000000000000
χ54666666-6-6-2-2-2-2-222-22-22-2222222000000000000-2-20000-2-22200-2-2002200000000000000000000000000
χ556666-6-60066-6-62-2-222-22-2000000000022-2-22-22-200000000000000000000000000-22-2200000000000000
χ566666-6-60066-6-62-2-222-22-20000000000-2-222-22-22000000000000000000000000002-22-200000000000000
χ576666-6-600-2-222-2-2-2-2222204i−4i04i−4i000022-2-2-22-220000000000000000002i−2i2i−2i0000000000000000000000
χ586666-6-600-2-222-2-2-2-2222204i−4i04i−4i0000-2-2222-22-2000000000000000000−2i2i−2i2i0000000000000000000000
χ596666-6-600-2-222-2-2-2-222220−4i4i0−4i4i000022-2-2-22-22000000000000000000−2i2i−2i2i0000000000000000000000
χ606666-6-600-2-222-2-2-2-222220−4i4i0−4i4i0000-2-2222-22-20000000000000000002i−2i2i−2i0000000000000000000000
χ616-6-666-66i−6i2-2-222-22-2-2-222−2i2i2i2i−2i−2i00002-22-2-2-222−2i2i000000000000000000002i−2i−2i2i000000000000000000
χ626-6-666-66i−6i2-2-222-22-2-2-222−2i2i2i2i−2i−2i0000-22-2222-2-2−2i2i00000000000000000000−2i2i2i−2i000000000000000000
χ636-6-666-66i−6i2-2-22-22-2222-2-2−2i−2i−2i2i2i2i0000000000002i−2i00002-22i−2i00−2i2i00-2200000000000000000000000000
χ646-6-666-66i−6i2-2-22-22-2222-2-2−2i−2i−2i2i2i2i0000000000002i−2i0000-22−2i2i002i−2i002-200000000000000000000000000
χ656-6-666-6−6i6i2-2-222-22-2-2-2222i−2i−2i−2i2i2i00002-22-2-2-2222i−2i00000000000000000000−2i2i2i−2i000000000000000000
χ666-6-666-6−6i6i2-2-222-22-2-2-2222i−2i−2i−2i2i2i0000-22-2222-2-22i−2i000000000000000000002i−2i−2i2i000000000000000000
χ676-6-666-6−6i6i2-2-22-22-2222-2-22i2i2i−2i−2i−2i000000000000−2i2i00002-2−2i2i002i−2i00-2200000000000000000000000000
χ686-6-666-6−6i6i2-2-22-22-2222-2-22i2i2i−2i−2i−2i000000000000−2i2i0000-222i−2i00−2i2i002-200000000000000000000000000
χ696-6-66-66002-22-2-2-2222-2-2204-40-4400002-2-22-222-20000000000000000002-2-220000000000000000000000
χ706-6-66-66002-22-2-2-2222-2-2204-40-440000-222-22-2-22000000000000000000-222-20000000000000000000000
χ716-6-66-66002-22-2-2-2222-2-220-4404-400002-2-22-222-2000000000000000000-222-20000000000000000000000
χ726-6-66-66002-22-2-2-2222-2-220-4404-40000-222-22-2-220000000000000000002-2-220000000000000000000000
χ736-6-66-6600-66-662-22-222-2-200000000002-2-222-2-2200000000000000000000000000-222-200000000000000
χ746-6-66-6600-66-662-22-222-2-20000000000-222-2-222-2000000000000000000000000002-2-2200000000000000
χ7512121212-12-1200-4-4444444-4-4-4-400000000000000000000000000000000000000000000000000000000000000
χ7612-12-1212-1212004-44-444-4-4-444-400000000000000000000000000000000000000000000000000000000000000
χ771616-16-160000000000000000000000000000000000004-4-4400000000000000000000000000000000000000
χ781616-16-16000000000000000000000000000000000000-222-200000000000000000000000000i6−i6i6−i600000000
χ791616-16-16000000000000000000000000000000000000-222-200000000000000000000000000−i6i6−i6i600000000
χ8016-1616-1600000000000000000000000000000000000044-4-400000000000000000000000000000000000000
χ8116-1616-16000000000000000000000000000000000000-2-222000000000000000000000000006−6−6600000000
χ8216-1616-16000000000000000000000000000000000000-2-22200000000000000000000000000−666−600000000

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