Finite Group Databasebeta

← Group #13147880

Character table — Group #13147880

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order12223444466641212121212123366666612121212121212123666121212121212121212121212121212121212121244444444222244446666121212121212121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1111-1-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-111
χ61111111-1-1111-1-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1111111111-1-1-1-1-1-1-1-111-1-1
χ71111111-1-1111-1-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ81111111-1-1111-1-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111-11111-1-1-1-11111-1-1-1-1-1-111
χ911111-1-111111-111-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11-11-1-11-1-111-1-111-1-111-1-111-1-11-11-1
χ1011111-1-111111-111-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-11-11-1-11-1-1-11111-1-111-1-1-1-111-11-11
χ1111111-1-111111-111-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-1-111-11111-1-1-1-111-1-11111-1-1-11-11
χ1211111-1-111111-111-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-111-111-11-1-111-1-111-1-111-1-1111-11-1
χ1311111-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-11-1111-1-1-1-11111-1-1-1-11111-1-1-111-1
χ1411111-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111-11-11-11-111-1-111-1-1-1-111-1-1111-1-11
χ1511111-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1-1-111-1-111-1-11111-1-111-1-11-1-11
χ1611111-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1111-1-11-11-1111-1-1-1-11111-1-1-1-111-111-1
χ1722222222222222222222-12-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000222222000000-1-1-1-100000000-1-1-1-10000
χ1822222222222222222222-12-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-2-2-200000011110000000011110000
χ192222222222222222222-12-122-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000000020020000-1-1-1-1-1-1-1-100000000
χ202222222222222222222-12-122-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-200-200001111111100000000
χ212222222-2-2222-2-2-2-2-2222-12-1-122-122221111-1-1-1-1-1-111-2-2-2-2-1-1-1-11111111100002222-2-2000000111100000000-1-1-1-10000
χ222222222-2-2222-2-2-2-2-2222-12-1-122-122221111-1-1-1-1-1-111-2-2-2-2-1-1-1-1111111110000-2-2-2-222000000-1-1-1-10000000011110000
χ232222222-2-2222-2-2-2-2-222-12-122-1-12-1-1-1-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-11111111122-2-200000000-20020000-1-1-1-1111100000000
χ242222222-2-2222-2-2-2-2-222-12-122-1-12-1-1-1-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-111111111-2-22200000000200-200001111-1-1-1-100000000
χ2522222-2-222222-222-2-2-2-22-12-1-122-1-2-2-2-2-1-1-1-1-1-1-1-1111122-2-21111-1-1-1-11111000022-2-22-2000000-1-11100000000-1-1110000
χ2622222-2-222222-222-2-2-2-22-12-1-122-1-2-2-2-2-1-1-1-1-1-1-1-1111122-2-21111-1-1-1-111110000-2-222-2200000011-1-10000000011-1-10000
χ2722222-2-222222-222-2-2-2-2-12-122-1-1211112222-1-1-1-1-2-2-2-2-1-1111111-1-1-1-11111222200000000-200-20000-1-111-1-11100000000
χ2822222-2-222222-222-2-2-2-2-12-122-1-1211112222-1-1-1-1-2-2-2-2-1-1111111-1-1-1-11111-2-2-2-2000000002002000011-1-111-1-100000000
χ2922222-2-2-2-22222-2-222-2-22-12-1-122-1-2-2-2-21111-1-1-1-111-1-1-2-22211111111-1-1-1-1000022-2-2-2200000011-1-100000000-1-1110000
χ3022222-2-2-2-22222-2-222-2-22-12-1-122-1-2-2-2-21111-1-1-1-111-1-1-2-22211111111-1-1-1-10000-2-2222-2000000-1-1110000000011-1-10000
χ3122222-2-2-2-22222-2-222-2-2-12-122-1-121111-2-2-2-2-1-1-1-1-2-22211-1-111111111-1-1-1-122-2-200000000200-20000-1-11111-1-100000000
χ3222222-2-2-2-22222-2-222-2-2-12-122-1-121111-2-2-2-2-1-1-1-1-2-22211-1-111111111-1-1-1-1-2-22200000000-2002000011-1-1-1-11100000000
χ3322-2-22002i−2i2-2-202i−2i000022-22-22-2-200002i2i−2i−2i22-2-200002i−2i0000002i2i−2i−2i00002-22i−2i00000000000000002-2002i−2i0000000000
χ3422-2-22002i−2i2-2-202i−2i000022-22-22-2-200002i2i−2i−2i22-2-200002i−2i0000002i2i−2i−2i0000-22−2i2i0000000000000000-2200−2i2i0000000000
χ3522-2-22002i−2i2-2-202i−2i0000-1212-2-11-233−3−32i2i−2i−2i-1-1110000−ii−i3i333−3−3−i−iii−i3−i3i3i32-22i−2i0000000000000000-113−3−ii−i3i300000000
χ3622-2-22002i−2i2-2-202i−2i0000-1212-2-11-233−3−32i2i−2i−2i-1-1110000−ii−i3i333−3−3−i−iii−i3−i3i3i3-22−2i2i00000000000000001-1−33i−ii3−i300000000
χ3722-2-22002i−2i2-2-202i−2i0000-1212-2-11-2−3−3332i2i−2i−2i-1-1110000−iii3−i3−3−333−i−iiii3i3−i3−i32-22i−2i0000000000000000-11−33−iii3−i300000000
χ3822-2-22002i−2i2-2-202i−2i0000-1212-2-11-2−3−3332i2i−2i−2i-1-1110000−iii3−i3−3−333−i−iiii3i3−i3−i3-22−2i2i00000000000000001-13−3i−i−i3i300000000
χ3922-2-2200−2i2i2-2-20−2i2i000022-22-22-2-20000−2i−2i2i2i22-2-20000−2i2i000000−2i−2i2i2i00002-2−2i2i00000000000000002-200−2i2i0000000000
χ4022-2-2200−2i2i2-2-20−2i2i000022-22-22-2-20000−2i−2i2i2i22-2-20000−2i2i000000−2i−2i2i2i0000-222i−2i0000000000000000-22002i−2i0000000000
χ4122-2-2200−2i2i2-2-20−2i2i0000-1212-2-11-233−3−3−2i−2i2i2i-1-1110000i−ii3−i333−3−3ii−i−ii3i3−i3−i32-2−2i2i0000000000000000-113−3i−ii3−i300000000
χ4222-2-2200−2i2i2-2-20−2i2i0000-1212-2-11-233−3−3−2i−2i2i2i-1-1110000i−ii3−i333−3−3ii−i−ii3i3−i3−i3-222i−2i00000000000000001-1−33−ii−i3i300000000
χ4322-2-2200−2i2i2-2-20−2i2i0000-1212-2-11-2−3−333−2i−2i2i2i-1-1110000i−i−i3i3−3−333ii−i−i−i3−i3i3i32-2−2i2i0000000000000000-11−33i−i−i3i300000000
χ4422-2-2200−2i2i2-2-20−2i2i0000-1212-2-11-2−3−333−2i−2i2i2i-1-1110000i−i−i3i3−3−333ii−i−i−i3−i3i3i3-222i−2i00000000000000001-13−3−iii3−i300000000
χ452-22-222-200-2-22000002-2222-22-2-2-22-22-200002-22-22-20000002-22-20000000000002i−2i2i−2i000000000000000000002i−2i2i−2i0000
χ462-22-222-200-2-22000002-2222-22-2-2-22-22-200002-22-22-20000002-22-2000000000000−2i2i−2i2i00000000000000000000−2i2i−2i2i0000
χ472-22-222-200-2-22000002-22-121-1-2-212-22-23−33−3-11-11-113−30000-11-113−33−33−33−300002i−2i2i−2i00000000−i3i3−i3i300000000−ii−ii0000
χ482-22-222-200-2-22000002-22-121-1-2-212-22-23−33−3-11-11-113−30000-11-113−33−33−33−30000−2i2i−2i2i00000000i3−i3i3−i300000000i−ii−i0000
χ492-22-222-200-2-22000002-22-121-1-2-212-22-2−33−33-11-11-11−330000-11-11−33−33−33−3300002i−2i2i−2i00000000i3−i3i3−i300000000−ii−ii0000
χ502-22-222-200-2-22000002-22-121-1-2-212-22-2−33−33-11-11-11−330000-11-11−33−33−33−330000−2i2i−2i2i00000000−i3i3−i3i300000000i−ii−i0000
χ512-22-22-2200-2-2200000-22222-22-2-2-2-22-2200002-22-2-22000000-22-220000000000002i−2i−2i2i000000000000000000002i−2i−2i2i0000
χ522-22-22-2200-2-2200000-22222-22-2-2-2-22-2200002-22-2-22000000-22-22000000000000−2i2i2i−2i00000000000000000000−2i2i2i−2i0000
χ532-22-22-2200-2-2200000-222-121-1-2-21-22-223−33−3-11-111-1−3300001-11-13−33−3−33−3300002i−2i−2i2i00000000−i3i3i3−i300000000−iii−i0000
χ542-22-22-2200-2-2200000-222-121-1-2-21-22-223−33−3-11-111-1−3300001-11-13−33−3−33−330000−2i2i2i−2i00000000i3−i3−i3i300000000i−i−ii0000
χ552-22-22-2200-2-2200000-222-121-1-2-21-22-22−33−33-11-111-13−300001-11-1−33−333−33−300002i−2i−2i2i00000000i3−i3−i3i300000000−iii−i0000
χ562-22-22-2200-2-2200000-222-121-1-2-21-22-22−33−33-11-111-13−300001-11-1−33−333−33−30000−2i2i2i−2i00000000−i3i3i3−i300000000i−i−ii0000
χ574444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000
χ584444444-4-4444-4-4-4-4-444-2-2-2-2-2-2-2-2-2-2-2-222221111-2-22222221111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ5944444-4-444444-444-4-4-4-4-2-2-2-2-2-2-2-22222-2-2-2-211112222-2-222-1-1-1-11111-1-1-1-1000000000000000000000000000000000000
χ6044444-4-4-4-44444-4-444-4-4-2-2-2-2-2-2-2-222222222111122-2-222-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000000000
χ6144-4-44004i−4i4-4-404i−4i00004-2-4-224-420000−2i−2i2i2i-2-22200004i−4i000000−2i−2i2i2i0000000000000000000000000000000000000000
χ6244-4-44004i−4i4-4-404i−4i0000-2-22-22-2222323−23−23−2i−2i2i2i11-1-10000−2i2i−2i32i3−3−333ii−i−ii3i3−i3−i3000000000000000000000000000000000000
χ6344-4-44004i−4i4-4-404i−4i0000-2-22-22-222−23−232323−2i−2i2i2i11-1-10000−2i2i2i3−2i333−3−3ii−i−i−i3−i3i3i3000000000000000000000000000000000000
χ6444-4-4400−4i4i4-4-40−4i4i00004-2-4-224-4200002i2i−2i−2i-2-2220000−4i4i0000002i2i−2i−2i0000000000000000000000000000000000000000
χ6544-4-4400−4i4i4-4-40−4i4i0000-2-22-22-2222323−23−232i2i−2i−2i11-1-100002i−2i2i3−2i3−3−333−i−iii−i3−i3i3i3000000000000000000000000000000000000
χ6644-4-4400−4i4i4-4-40−4i4i0000-2-22-22-222−23−2323232i2i−2i−2i11-1-100002i−2i−2i32i333−3−3−i−iiii3i3−i3−i3000000000000000000000000000000000000
χ674-44-444-400-4-44000004-4-24-2-4422-4-22-220000-22-224-4000000-22-2200000000000000000000000000000000000000000000
χ684-44-444-400-4-44000004-4-2-2-22-2222-22-2223−2323−231-11-1-2223−2300001-11-1−33−33−33−33000000000000000000000000000000000000
χ694-44-444-400-4-44000004-4-2-2-22-2222-22-22−2323−23231-11-1-22−232300001-11-13−33−33−33−3000000000000000000000000000000000000
χ704-44-44-4400-4-4400000-44-24-2-4422-42-22-20000-22-22-440000002-22-200000000000000000000000000000000000000000000
χ714-44-44-4400-4-4400000-44-2-2-22-22222-22-223−2323−231-11-12-2−23230000-11-11−33−333−33−3000000000000000000000000000000000000
χ724-44-44-4400-4-4400000-44-2-2-22-22222-22-2−2323−23231-11-12-223−230000-11-113−33−3−33−33000000000000000000000000000000000000
χ734-4-4440000-44-4000000044-4-4-4-444000000004-4-4400000000000000000000000000000000000000000000000000000000
χ744-4-4440000-44-400000004-2-422-44-20000−2i32i32i3−2i3-222-2000000000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ754-4-4440000-44-400000004-2-422-44-200002i3−2i3−2i32i3-222-20000000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ764-4-4440000-44-40000000-242-4-42-2423−23−23230000-222-20000000023−23−232300000000000000000000000000000000000000000000
χ774-4-4440000-44-40000000-242-4-42-24−232323−230000-222-200000000−232323−2300000000000000000000000000000000000000000000
χ784-4-4440000-44-40000000-2-22222-2-223−23−2323−2i32i32i3−2i31-1-1100000000−333−3i3−i3−i3i33i−3i−3i3i000000000000000000000000000000000000
χ794-4-4440000-44-40000000-2-22222-2-223−23−23232i3−2i3−2i32i31-1-1100000000−333−3−i3i3i3−i3−3i3i3i−3i000000000000000000000000000000000000
χ804-4-4440000-44-40000000-2-22222-2-2−232323−23−2i32i32i3−2i31-1-11000000003−3−33i3−i3−i3i3−3i3i3i−3i000000000000000000000000000000000000
χ814-4-4440000-44-40000000-2-22222-2-2−232323−232i3−2i3−2i32i31-1-11000000003−3−33−i3i3i3−i33i−3i−3i3i000000000000000000000000000000000000
χ826666-36666-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000002202200000000000000000-1-1-1-1
χ836666-36666-3-3-36-3-3-3-3-3-300000000000000000000000000000000000000000000000000-2-20-2-2000000000000000001111
χ846666-366-6-6-3-3-3-63333-3-300000000000000000000000000000000000000000000000000220-2-200000000000000000-1-111
χ856666-366-6-6-3-3-3-63333-3-300000000000000000000000000000000000000000000000000-2-20220000000000000000011-1-1
χ866666-3-6-666-3-3-3-6-3-33333000000000000000000000000000000000000000000000000002-202-200000000000000000-11-11
χ876666-3-6-666-3-3-3-6-3-3333300000000000000000000000000000000000000000000000000-220-22000000000000000001-11-1
χ886666-3-6-6-6-6-3-3-3633-3-333000000000000000000000000000000000000000000000000002-20-2200000000000000000-111-1
χ896666-3-6-6-6-6-3-3-3633-3-33300000000000000000000000000000000000000000000000000-2202-2000000000000000001-1-11
χ901212-12-12-60012i−12i-6660−6i6i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ911212-12-12-600−12i12i-66606i−6i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9212-1212-12-612-120066-600000-660000000000000000000000000000000000000000000000000000000000000000000000000000
χ9312-1212-12-6-12120066-6000006-60000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-1212-600006-6600063−63000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-1212-600006-66000−6363000000000000000000000000000000000000000000000000000000000000000000000000000000

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