Finite Group Databasebeta

← Group #13136721

Character table — Group #13136721

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size112222222449912121212121212121818181818181824242424363636363636363636363636363636363636363636367272727272727272
order122223666664433666666444121212126666444444448888121224242424242424241212121212121212
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ5111-1-11111-1-1111111-1-1-1-1-1-11111111-1-1ii−i−iii−i−i11-1-1-1-11111-1-1-1-1ii−i−iii−i−i
χ6111-1-11111-1-1111111-1-1-1-1-1-11111111-1-1ii−i−i−i−iii-1-111-1-1-1-1-1-11111ii−i−i−i−iii
χ7111-1-11111-1-1111111-1-1-1-1-1-11111111-1-1−i−iiiii−i−i-1-111-1-1-1-1-1-11111−i−iiiii−i−i
χ8111-1-11111-1-1111111-1-1-1-1-1-11111111-1-1−i−iii−i−iii11-1-1-1-11111-1-1-1-1−i−iii−i−iii
χ911-11-11-1-111-111111111-1-11-1-111-1-1-1-11-11-11-1i−ii−ii−ii−i1-1ii−i−iii−i−i1-11-1i−ii−i
χ1011-11-11-1-111-111111111-1-11-1-111-1-1-1-11-11-11-1−ii−ii−ii−ii1-1−i−iii−i−iii1-11-1−ii−ii
χ1111-11-11-1-111-111111111-1-11-1-111-1-1-1-11-1-11-11i−ii−i−ii−ii1-1−i−iii−i−iii-11-11i−ii−i
χ1211-11-11-1-111-111111111-1-11-1-111-1-1-1-11-1-11-11−ii−iii−ii−i1-1ii−i−iii−i−i-11-11−ii−ii
χ1311-1-111-1-11-11111111-1-111-11-111-1-1-1-1-11i−i−ii1-1-11−iii−i-11−i−iiiii−i−ii−i−ii1-1-11
χ1411-1-111-1-11-11111111-1-111-11-111-1-1-1-1-11i−i−ii-111-1i−i−ii-11ii−i−i−i−iiii−i−ii-111-1
χ1511-1-111-1-11-11111111-1-111-11-111-1-1-1-1-11−iii−i1-1-11i−i−ii-11ii−i−i−i−iii−iii−i1-1-11
χ1611-1-111-1-11-11111111-1-111-11-111-1-1-1-1-11−iii−i-111-1−iii−i-11−i−iiiii−i−i−iii−i-111-1
χ1722222222222-2-222222222-2-2-2-2-2-2-22222000000000000-2-20000000000000000
χ18222-2-22222-2-2-2-22222-2-2-2-222-2-2-2-2-222-2-2000000000000220000000000000000
χ1922-22-22-2-222-2-2-2222222-2-2-222-2-222-2-22-2000000000000-220000000000000000
χ2022-2-222-2-22-22-2-22222-2-2222-22-2-222-2-2-220000000000002-20000000000000000
χ2144444444444001-21-211-2-200000001-2-212222000000000000000000-1-1-1-10000
χ2244444444444001-21-211-2-200000001-2-21-2-2-2-200000000000000000011110000
χ234444444444400-21-21-2-2110000000-211-200002222000000000000000000-1-1-1-1
χ244444444444400-21-21-2-2110000000-211-20000-2-2-2-20000000000000000001111
χ25444-4-44444-4-4001-21-2-1-12200000001-22-12i2i−2i−2i000000000000000000−i−iii0000
χ26444-4-44444-4-4001-21-2-1-12200000001-22-1−2i−2i2i2i000000000000000000ii−i−i0000
χ27444-4-44444-4-400-21-2122-1-10000000-21-1200002i2i−2i−2i000000000000000000−i−iii
χ28444-4-44444-4-400-21-2122-1-10000000-21-120000−2i−2i2i2i000000000000000000ii−i−i
χ2944-44-44-4-444-4001-21-211220000000-12-2-12-22-2000000000000000000-11-110000
χ3044-44-44-4-444-4001-21-211220000000-12-2-1-22-220000000000000000001-11-10000
χ3144-44-44-4-444-400-21-21-2-2-1-100000002-11200002i−2i2i−2i000000000000000000−ii−ii
χ3244-44-44-4-444-400-21-21-2-2-1-100000002-1120000−2i2i−2i2i000000000000000000i−ii−i
χ3344-4-444-4-44-44001-21-2-1-1-2-20000000-12212i−2i−2i2i000000000000000000−iii−i0000
χ3444-4-444-4-44-44001-21-2-1-1-2-20000000-1221−2i2i2i−2i000000000000000000i−i−ii0000
χ3544-4-444-4-44-4400-21-21221100000002-1-1-200002-2-22000000000000000000-111-1
χ3644-4-444-4-44-4400-21-21221100000002-1-1-20000-222-20000000000000000001-1-11
χ374-4000400-4004i−4i44-4-400000004i−4i000000000000000000000000000000000000
χ384-4000400-400−4i4i44-4-40000000−4i4i000000000000000000000000000000000000
χ3966666-3-3-3-3-3-32200000000222-1-1-1-10000000000000000-1-13−33−33−33−300000000
χ4066666-3-3-3-3-3-32200000000222-1-1-1-10000000000000000-1-1−33−33−33−3300000000
χ4166666-3-3-3-3-3-3-2-200000000-2-2-21111000000000000222211-1-1-1-1-1-1-1-100000000
χ4266666-3-3-3-3-3-3-2-200000000-2-2-21111000000000000-2-2-2-2111111111100000000
χ43666-6-6-3-3-3-3332200000000-2-22-1-1-1-10000000000000000113−33−3−33−3300000000
χ44666-6-6-3-3-3-3332200000000-2-22-1-1-1-1000000000000000011−33−333−33−300000000
χ45666-6-6-3-3-3-333-2-20000000022-2111100000000000022-2-2-1-1-1-1-1-1111100000000
χ46666-6-6-3-3-3-333-2-20000000022-21111000000000000-2-222-1-11111-1-1-1-100000000
χ4766-66-6-333-3-3322000000002-2-2-1-1110000000000000000-11−i3i3i3−i3−i3i3i3−i300000000
χ4866-66-6-333-3-3322000000002-2-2-1-1110000000000000000-11i3−i3−i3i3i3−i3−i3i300000000
χ4966-66-6-333-3-33-2-200000000-22211-1-10000000000002i−2i2i−2i1-1−i−iii−i−iii00000000
χ5066-66-6-333-3-33-2-200000000-22211-1-1000000000000−2i2i−2i2i1-1ii−i−iii−i−i00000000
χ5166-6-66-333-33-32200000000-22-2-1-11100000000000000001-1−i3i3i3−i3i3−i3−i3i300000000
χ5266-6-66-333-33-32200000000-22-2-1-11100000000000000001-1i3−i3−i3i3−i3i3i3−i300000000
χ5366-6-66-333-33-3-2-2000000002-2211-1-10000000000002i−2i−2i2i-11−i−iiiii−i−i00000000
χ5466-6-66-333-33-3-2-2000000002-2211-1-1000000000000−2i2i2i−2i-11ii−i−i−i−iii00000000
χ558-8000800-800002-4-246-60000000000000000000000000000000000000000000
χ568-8000800-800002-4-24-660000000000000000000000000000000000000000000
χ578-8000800-80000-424-2006-600000000000000000000000000000000000000000
χ588-8000800-80000-424-200-6600000000000000000000000000000000000000000
χ5912-12000-6−6i36i36004i−4i00000000000−2i2i23−230000000000000000000000000000000000
χ6012-12000-6−6i36i3600−4i4i000000000002i−2i−23230000000000000000000000000000000000
χ6112-12000-66i3−6i36004i−4i00000000000−2i2i−23230000000000000000000000000000000000
χ6212-12000-66i3−6i3600−4i4i000000000002i−2i23−230000000000000000000000000000000000

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