Finite Group Databasebeta

← Group #13136700

Character table — Group #13136700

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size112222222449912121212121212121818181818181824242424363636363636363636363636363636363636363636367272727272727272
order1223446661212223366121212122446666661212444488888888121212121212121212122424242424242424
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111-1-1111-1-1111111-1-1-1-11-1-1111111-1-111-1-1ii−i−iii−i−i-1-11111-1-1-1-1ii−i−iii−i−i
χ61111-1-1111-1-1111111-1-1-1-11-1-1111111-1-111-1-1−i−iii−i−iii-1-11111-1-1-1-1−i−iii−i−iii
χ71111-1-1111-1-1111111-1-1-1-11-1-1111111-1-1-1-111ii−i−i−i−iii-1-1-1-1-1-11111ii−i−i−i−iii
χ81111-1-1111-1-1111111-1-1-1-11-1-1111111-1-1-1-111−i−iiiii−i−i-1-1-1-1-1-11111−i−iiiii−i−i
χ911-111-1-1-111-1-1-1111111-1-111-111-1-1-1-11-1i−ii−i1-11-1i−ii−i1-1ii−i−iii−i−i1-11-1i−ii−i
χ1011-111-1-1-111-1-1-1111111-1-111-111-1-1-1-11-1i−ii−i-11-11−ii−ii1-1ii−i−iii−i−i-11-11−ii−ii
χ1111-111-1-1-111-1-1-1111111-1-111-111-1-1-1-11-1−ii−ii1-11-1−ii−ii1-1−i−iii−i−iii1-11-1−ii−ii
χ1211-111-1-1-111-1-1-1111111-1-111-111-1-1-1-11-1−ii−ii-11-11i−ii−i1-1−i−iii−i−iii-11-11i−ii−i
χ1311-11-11-1-11-11-1-11111-1-1111-1111-1-1-1-1-11i−i−iii−i−ii-111-1-11ii−i−i−i−iiii−i−ii-111-1
χ1411-11-11-1-11-11-1-11111-1-1111-1111-1-1-1-1-11i−i−ii−iii−i1-1-11-11ii−i−i−i−iii−iii−i1-1-11
χ1511-11-11-1-11-11-1-11111-1-1111-1111-1-1-1-1-11−iii−ii−i−ii1-1-11-11−i−iiiii−i−ii−i−ii1-1-11
χ1611-11-11-1-11-11-1-11111-1-1111-1111-1-1-1-1-11−iii−i−iii−i-111-1-11−i−iiiii−i−i−iii−i-111-1
χ1722222222222-2-222222222-2-2-2-2-2-2-22222000000000000-2-20000000000000000
χ182222-2-2222-2-2-2-22222-2-2-2-2-222-2-2-2-222-2-2000000000000220000000000000000
χ1922-222-2-2-222-222222222-2-2-2-22-2-222-2-22-2000000000000-220000000000000000
χ2022-22-22-2-22-22222222-2-222-22-2-2-222-2-2-220000000000002-20000000000000000
χ2144444444444001-21-211-2-200000001-2-210000222200000000000000-1-1-1-10000
χ2244444444444001-21-211-2-200000001-2-210000-2-2-2-20000000000000011110000
χ234444444444400-21-21-2-2110000000-211-200000000222200000000000000-1-1-1-1
χ244444444444400-21-21-2-2110000000-211-200000000-2-2-2-2000000000000001111
χ254444-4-4444-4-4001-21-2-1-12200000001-22-100002i2i−2i−2i00000000000000−i−iii0000
χ264444-4-4444-4-4001-21-2-1-12200000001-22-10000−2i−2i2i2i00000000000000ii−i−i0000
χ274444-4-4444-4-400-21-2122-1-10000000-21-12000000002i2i−2i−2i00000000000000−i−iii
χ284444-4-4444-4-400-21-2122-1-10000000-21-1200000000−2i−2i2i2i00000000000000ii−i−i
χ2944-444-4-4-444-4001-21-211220000000-12-2-100002-22-200000000000000-11-110000
χ3044-444-4-4-444-4001-21-211220000000-12-2-10000-22-22000000000000001-11-10000
χ3144-444-4-4-444-400-21-21-2-2-1-100000002-112000000002i−2i2i−2i00000000000000−ii−ii
χ3244-444-4-4-444-400-21-21-2-2-1-100000002-11200000000−2i2i−2i2i00000000000000i−ii−i
χ3344-44-44-4-44-44001-21-2-1-1-2-20000000-122100002i−2i−2i2i00000000000000−iii−i0000
χ3444-44-44-4-44-44001-21-2-1-1-2-20000000-12210000−2i2i2i−2i00000000000000i−i−ii0000
χ3544-44-44-4-44-4400-21-21221100000002-1-1-2000000002-2-2200000000000000-111-1
χ3644-44-44-4-44-4400-21-21221100000002-1-1-200000000-222-2000000000000001-1-11
χ374-4040000-4004-444-4-40000000004-40000000000000000000000000000000000
χ384-4040000-400-4444-4-4000000000-440000000000000000000000000000000000
χ39666-366-3-3-3-3-32200000000222-1-1-1-10000000000000000-1-13−33−33−33−300000000
χ40666-366-3-3-3-3-32200000000222-1-1-1-10000000000000000-1-1−33−33−33−3300000000
χ41666-366-3-3-3-3-3-2-200000000-2-2-21111000022220000000011-1-1-1-1-1-1-1-100000000
χ42666-366-3-3-3-3-3-2-200000000-2-2-211110000-2-2-2-200000000111111111100000000
χ43666-3-6-6-3-3-33322000000002-2-2-1-1-1-10000000000000000113−33−3−33−3300000000
χ44666-3-6-6-3-3-33322000000002-2-2-1-1-1-1000000000000000011−33−333−33−300000000
χ45666-3-6-6-3-3-333-2-200000000-2221111000022-2-200000000-1-1-1-1-1-1111100000000
χ46666-3-6-6-3-3-333-2-200000000-22211110000-2-22200000000-1-11111-1-1-1-100000000
χ4766-6-36-633-3-332200000000-2-2211-1-100002i−2i2i−2i000000001-1−i−iii−i−iii00000000
χ4866-6-36-633-3-332200000000-2-2211-1-10000−2i2i−2i2i000000001-1ii−i−iii−i−i00000000
χ4966-6-36-633-3-33-2-20000000022-2-1-1110000000000000000-11−i3i3i3−i3−i3i3i3−i300000000
χ5066-6-36-633-3-33-2-20000000022-2-1-1110000000000000000-11i3−i3−i3i3i3−i3−i3i300000000
χ5166-6-3-6633-33-32200000000-22-211-1-100002i−2i−2i2i00000000-11−i−iiiii−i−i00000000
χ5266-6-3-6633-33-32200000000-22-211-1-10000−2i2i2i−2i00000000-11ii−i−i−i−iii00000000
χ5366-6-3-6633-33-3-2-2000000002-22-1-11100000000000000001-1−i3i3i3−i3i3−i3−i3i300000000
χ5466-6-3-6633-33-3-2-2000000002-22-1-11100000000000000001-1i3−i3−i3i3−i3i3i3−i300000000
χ558-8080000-800002-4-246i−6i0000000000000000000000000000000000000000000
χ568-8080000-800002-4-24−6i6i0000000000000000000000000000000000000000000
χ578-8080000-80000-424-2006i−6i00000000000000000000000000000000000000000
χ588-8080000-80000-424-200−6i6i00000000000000000000000000000000000000000
χ5912-120-600−6i36i36004-400000000000−2i32i3-220000000000000000000000000000000000
χ6012-120-600−6i36i3600-44000000000002i3−2i32-20000000000000000000000000000000000
χ6112-120-6006i3−6i36004-4000000000002i3−2i3-220000000000000000000000000000000000
χ6212-120-6006i3−6i3600-4400000000000−2i32i32-20000000000000000000000000000000000

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