Finite Group Databasebeta

← Group #13146562

Character table — Group #13146562

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size112222222449912121212121212121818181818181824242424363636363636363636363636363636363636363636367272727272727272
order122344612126124433666612122246612126121212224444446888812242424242424242466121212121212
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ51111-1-11-1-11-111111111-1-1-1-11-1-1111-1-1-11-11-111-1-1-111-1-111111-1-1-1-11-11-111-1-1
χ61111-1-11-1-11-111111111-1-1-1-11-1-1111-1-1-11-11-1-1-111-1-1-1111-1-1-1-111111-11-1-1-111
χ71111-1-11-1-11-111111111-1-1-1-11-1-1111-1-1-1-11-1111-1-1-1-1-1111-1-1-1-11111-11-1111-1-1
χ81111-1-11-1-11-111111111-1-1-1-11-1-1111-1-1-1-11-11-1-111-111-1-111111-1-1-1-1-11-11-1-111
χ911-111-1111-1-1-1-111-111-1-1-11-11-1-1-1-1-11-1111-1-1i−ii−i1i−ii−i1ii−i−iii−i−i11-1-1i−ii−i
χ1011-111-1111-1-1-1-111-111-1-1-11-11-1-1-1-1-11-1111-1-1−ii−ii1−ii−ii1−i−iii−i−iii11-1-1−ii−ii
χ1111-111-1111-1-1-1-111-111-1-1-11-11-1-1-1-1-11-11-1-111i−ii−i1−ii−ii1−i−iii−i−iii-1-111i−ii−i
χ1211-111-1111-1-1-1-111-111-1-1-11-11-1-1-1-1-11-11-1-111−ii−ii1i−ii−i1ii−i−iii−i−i-1-111−ii−ii
χ1311-11-111-1-1-11-1-111-111-111-11111-1-1-1-11-11-1-11i−i−ii-1i−i−ii1ii−i−i−i−iii1-1-11i−i−ii
χ1411-11-111-1-1-11-1-111-111-111-11111-1-1-1-11-11-1-11−iii−i-1−iii−i1−i−iiiii−i−i1-1-11−iii−i
χ1511-11-111-1-1-11-1-111-111-111-11111-1-1-1-11-1-111-1i−i−ii-1−iii−i1−i−iiiii−i−i-111-1i−i−ii
χ1611-11-111-1-1-11-1-111-111-111-11111-1-1-1-11-1-111-1−iii−i-1i−i−ii1ii−i−i−i−iii-111-1−iii−i
χ1722222222222-2-222222222-2-2-2-2-2-2-2222200000000-20000-20000000000000000
χ182222-2-22-2-22-2-2-2222222-2-222-222-2-22-2-2-20000000020000-20000000000000000
χ1922-222-2222-2-22222-222-2-2-2-22-22222-22-2200000000-20000-20000000000000000
χ2022-22-222-2-2-222222-222-2222-2-2-2-222-2-22-20000000020000-20000000000000000
χ2144444444444001-211-21-2-20000000-211-200002222000000000000000000-1-1-1-1
χ2244444444444001-211-21-2-20000000-211-20000-2-2-2-20000000000000000001111
χ234444444444400-21-2-21-21100000001-2-212222000000000000000000-1-1-1-10000
χ244444444444400-21-2-21-21100000001-2-21-2-2-2-200000000000000000011110000
χ254444-4-44-4-44-4001-211-21220000000-2-1-12000022-2-2000000000000000000-1-111
χ264444-4-44-4-44-4001-211-21220000000-2-1-120000-2-22200000000000000000011-1-1
χ274444-4-44-4-44-400-21-2-21-2-1-10000000122-12-22-2000000000000000000-11-110000
χ284444-4-44-4-44-400-21-2-21-2-1-10000000122-1-22-220000000000000000001-11-10000
χ2944-444-4444-4-4001-2-11-2-122000000021-1-200002i−2i2i−2i000000000000000000−ii−ii
χ3044-444-4444-4-4001-2-11-2-122000000021-1-20000−2i2i−2i2i000000000000000000i−ii−i
χ3144-444-4444-4-400-212-212-1-10000000-1-22122-2-2000000000000000000-1-1110000
χ3244-444-4444-4-400-212-212-1-10000000-1-221-2-22200000000000000000011-1-10000
χ3344-44-444-4-4-44001-2-11-2-1-2-200000002-11200002i−2i−2i2i000000000000000000−iii−i
χ3444-44-444-4-4-44001-2-11-2-1-2-200000002-1120000−2i2i2i−2i000000000000000000i−i−ii
χ3544-44-444-4-4-4400-212-212110000000-12-2-12-2-22000000000000000000-111-10000
χ3644-44-444-4-4-4400-212-212110000000-12-2-1-222-20000000000000000001-1-110000
χ374-40400-400004i−4i440-4-4000000004i−4i0000000000000000000000000000000000
χ384-40400-40000−4i4i440-4-400000000−4i4i0000000000000000000000000000000000
χ39666-366-3-3-3-3-32200000000222-1-1-1-1000000000000-10000-13−33−33−33−300000000
χ40666-366-3-3-3-3-32200000000222-1-1-1-1000000000000-10000-1−33−33−33−3300000000
χ41666-366-3-3-3-3-3-2-200000000-2-2-21111000000000000122221-1-1-1-1-1-1-1-100000000
χ42666-366-3-3-3-3-3-2-200000000-2-2-211110000000000001-2-2-2-211111111100000000
χ43666-3-6-6-333-332200000000-2-2211-1-100000000000010000-13−33−3−33−3300000000
χ44666-3-6-6-333-332200000000-2-2211-1-100000000000010000-1−33−333−33−300000000
χ45666-3-6-6-333-33-2-20000000022-2-1-111000000000000-122-2-21-1-1-1-1111100000000
χ46666-3-6-6-333-33-2-20000000022-2-1-111000000000000-1-2-22211111-1-1-1-100000000
χ4766-6-36-6-3-3-3332200000000-22-2-1-1-1-100000000000012i−2i2i−2i1−i−iii−i−iii00000000
χ4866-6-36-6-3-3-3332200000000-22-2-1-1-1-10000000000001−2i2i−2i2i1ii−i−iii−i−i00000000
χ4966-6-36-6-3-3-333-2-2000000002-221111000000000000-10000-1−i3i3i3−i3−i3i3i3−i300000000
χ5066-6-36-6-3-3-333-2-2000000002-221111000000000000-10000-1i3−i3−i3i3i3−i3−i3i300000000
χ5166-6-3-66-3333-322000000002-2-211-1-1000000000000-12i−2i−2i2i1−i−iiiii−i−i00000000
χ5266-6-3-66-3333-322000000002-2-211-1-1000000000000-1−2i2i2i−2i1ii−i−i−i−iii00000000
χ5366-6-3-66-3333-3-2-200000000-222-1-11100000000000010000-1−i3i3i3−i3i3−i3−i3i300000000
χ5466-6-3-66-3333-3-2-200000000-222-1-11100000000000010000-1i3−i3−i3i3−i3i3i3−i300000000
χ558-80800-80000002-46-24-60000000000000000000000000000000000000000000
χ568-80800-80000002-4-6-2460000000000000000000000000000000000000000000
χ578-80800-8000000-4204-206i−6i00000000000000000000000000000000000000000
χ588-80800-8000000-4204-20−6i6i00000000000000000000000000000000000000000
χ5912-120-600663−63004i−4i00000000000−2i32i3−2i2i0000000000000000000000000000000000
χ6012-120-600663−6300−4i4i000000000002i3−2i32i−2i0000000000000000000000000000000000
χ6112-120-6006−6363004i−4i000000000002i3−2i3−2i2i0000000000000000000000000000000000
χ6212-120-6006−636300−4i4i00000000000−2i32i32i−2i0000000000000000000000000000000000

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