Finite Group Databasebeta

← Group #13146560

Character table — Group #13146560

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size112222222449912121212121212121818181818181824242424363636363636363636363636363636363636363636367272727272727272
order12234461212612223366661212244661212612121244446888888881224242424242424241212121224242424
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111-1-1-1-11-1-1-1-11111111111111-1-1-1-1-1-1-1-1
χ51111-1-11-1-11-111111111-1-11-1-111-1-11-1-1-111-1-11ii−i−iii−i−i-1iiii−i−i−i−i11-1-1ii−i−i
χ61111-1-11-1-11-111111111-1-11-1-111-1-11-1-1-111-1-11−i−iii−i−iii-1−i−i−i−iiiii11-1-1−i−iii
χ71111-1-11-1-11-111111111-1-11-1-111-1-11-1-1-1-1-1111ii−i−i−i−iii-1−i−i−i−iiiii-1-111ii−i−i
χ81111-1-11-1-11-111111111-1-11-1-111-1-11-1-1-1-1-1111−i−iiiii−i−i-1iiii−i−i−i−i-1-111−i−iii
χ911-111-1111-1-1-1-111-1-111-1-111-1-1-1-1-1-111-11-11-11i−ii−ii−ii−i1ii−i−iii−i−i1-11-1i−ii−i
χ1011-111-1111-1-1-1-111-1-111-1-111-1-1-1-1-1-111-11-11-11−ii−ii−ii−ii1−i−iii−i−iii1-11-1−ii−ii
χ1111-111-1111-1-1-1-111-1-111-1-111-1-1-1-1-1-111-1-11-111i−ii−i−ii−ii1−i−iii−i−iii-11-11i−ii−i
χ1211-111-1111-1-1-1-111-1-111-1-111-1-1-1-1-1-111-1-11-111−ii−iii−ii−i1ii−i−iii−i−i-11-11−ii−ii
χ1311-11-111-1-1-11-1-111-1-111111-11-1-111-1-1-111-1-1111-1-111-1-11-111-1-1-1-1111-1-111-1-11
χ1411-11-111-1-1-11-1-111-1-111111-11-1-111-1-1-111-1-111-111-1-111-1-1-1-11111-1-11-1-11-111-1
χ1511-11-111-1-1-11-1-111-1-111111-11-1-111-1-1-11-111-111-1-11-111-1-1-1-11111-1-1-111-11-1-11
χ1611-11-111-1-1-11-1-111-1-111111-11-1-111-1-1-11-111-11-111-11-1-11-111-1-1-1-111-111-1-111-1
χ1722222222222-2-222222222-2-2-2-2-2-2-222220000-200000000-20000000000000000
χ182222-2-22-2-22-2-2-2222222-2-2-222-2-2222-2-2-20000-20000000020000000000000000
χ1922-222-2222-2-22222-2-222-2-2-2-222222-222-20000-200000000-20000000000000000
χ2022-22-222-2-2-222222-2-22222-22-222-2-2-2-2-220000-20000000020000000000000000
χ2144444444444001-211-21-2-20000000-2-2112222000000000000000000-1-1-1-10000
χ2244444444444001-211-21-2-20000000-2-211-2-2-2-200000000000000000011110000
χ234444444444400-21-2-21-211000000011-2-200000222200000000000000000-1-1-1-1
χ244444444444400-21-2-21-211000000011-2-200000-2-2-2-2000000000000000001111
χ254444-4-44-4-44-4001-211-21220000000-22-1-122-2-2000000000000000000-1-1110000
χ264444-4-44-4-44-4001-211-21220000000-22-1-1-2-22200000000000000000011-1-10000
χ274444-4-44-4-44-400-21-2-21-2-1-100000001-122000002i2i−2i−2i00000000000000000−i−iii
χ284444-4-44-4-44-400-21-2-21-2-1-100000001-12200000−2i−2i2i2i00000000000000000ii−i−i
χ2944-444-4444-4-4001-2-1-1-212200000002-21-12-22-2000000000000000000-11-110000
χ3044-444-4444-4-4001-2-1-1-212200000002-21-1-22-220000000000000000001-11-10000
χ3144-444-4444-4-400-21221-2-1-10000000-11-22000002i−2i2i−2i00000000000000000−ii−ii
χ3244-444-4444-4-400-21221-2-1-10000000-11-2200000−2i2i−2i2i00000000000000000i−ii−i
χ3344-44-444-4-4-44001-2-1-1-21-2-2000000022-112-2-22000000000000000000-111-10000
χ3444-44-444-4-4-44001-2-1-1-21-2-2000000022-11-222-20000000000000000001-1-110000
χ3544-44-444-4-4-4400-21221-2110000000-1-12-2000002-2-2200000000000000000-111-1
χ3644-44-444-4-4-4400-21221-2110000000-1-12-200000-222-2000000000000000001-1-11
χ374-40400-400004-44400-4-4000004-4000000000000000000000000000000000000
χ384-40400-40000-444400-4-400000-44000000000000000000000000000000000000
χ39666-366-3-3-3-3-32200000000222-1-1-1-100000000-100000000-13−33−33−33−300000000
χ40666-366-3-3-3-3-32200000000222-1-1-1-100000000-100000000-1−33−33−33−3300000000
χ41666-366-3-3-3-3-3-2-200000000-2-2-21111000000001000022221-1-1-1-1-1-1-1-100000000
χ42666-366-3-3-3-3-3-2-200000000-2-2-211110000000010000-2-2-2-211111111100000000
χ43666-3-6-6-333-3322000000002-2-2-1-11100000000-1000000001−i3i3−i3i3i3−i3i3−i300000000
χ44666-3-6-6-333-3322000000002-2-2-1-11100000000-1000000001i3−i3i3−i3−i3i3−i3i300000000
χ45666-3-6-6-333-33-2-200000000-22211-1-100000000100002i2i−2i−2i-1−i−i−i−iiiii00000000
χ46666-3-6-6-333-33-2-200000000-22211-1-10000000010000−2i−2i2i2i-1iiii−i−i−i−i00000000
χ4766-6-36-6-3-3-3332200000000-2-22-1-1-1-100000000100002i−2i2i−2i1−i−iii−i−iii00000000
χ4866-6-36-6-3-3-3332200000000-2-22-1-1-1-10000000010000−2i2i−2i2i1ii−i−iii−i−i00000000
χ4966-6-36-6-3-3-333-2-20000000022-2111100000000-100000000-1−i3i3i3−i3−i3i3i3−i300000000
χ5066-6-36-6-3-3-333-2-20000000022-2111100000000-100000000-1i3−i3−i3i3i3−i3−i3i300000000
χ5166-6-3-66-3333-32200000000-22-2-1-11100000000100002-2-22-1-1-11111-1-100000000
χ5266-6-3-66-3333-32200000000-22-2-1-1110000000010000-222-2-111-1-1-1-11100000000
χ5366-6-3-66-3333-3-2-2000000002-2211-1-100000000-10000000013−3−33−333−300000000
χ5466-6-3-66-3333-3-2-2000000002-2211-1-100000000-1000000001−333−33−3−3300000000
χ558-80800-80000002-46-64-20000000000000000000000000000000000000000000
χ568-80800-80000002-4-664-20000000000000000000000000000000000000000000
χ578-80800-8000000-4200-246i−6i00000000000000000000000000000000000000000
χ588-80800-8000000-4200-24−6i6i00000000000000000000000000000000000000000
χ5912-120-600663−63004-400000000000-2223−230000000000000000000000000000000000
χ6012-120-600663−6300-44000000000002-2−23230000000000000000000000000000000000
χ6112-120-6006−6363004-400000000000-22−23230000000000000000000000000000000000
χ6212-120-6006−636300-44000000000002-223−230000000000000000000000000000000000

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