Finite Group Databasebeta

← Group #13147881

Character table — Group #13147881

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order12223444466612121212412121212336666661212121236661212121212121212121212121212121212121212121244444444222244446666121212121212121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ51111111-1-1111-1-1-1-1-111-1-11111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-111
χ61111111-1-1111-1-1-1-1-111-1-11111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-111111-1-1-1-11111-1-1-1-111-1-1
χ71111111-1-1111-1-1-1-1-111-1-11111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ81111111-1-1111-1-1-1-1-111-1-11111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111-11111-1-1-1-1-1-1-1-11111-1-111
χ911111-1-1111111111-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11-11-1-11-1-111-1-111-1-111-1-111-1-11-11-1
χ1011111-1-1111111111-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-11-11-1-11-1-1-111-1-11111-1-111-1-1-11-11
χ1111111-1-1111111111-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-1-111-11111-1-111-1-1-1-111-1-111-11-11
χ1211111-1-1111111111-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-111-111-11-1-111-1-111-1-111-1-1111-11-1
χ1311111-1-1-1-1111-1-1-1-11-1-11111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-11-1111-1-1-1-11111-1-111-1-1-1-111-111-1
χ1411111-1-1-1-1111-1-1-1-11-1-11111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111-11-11-11-111-1-1-1-11111-1-1-1-1111-1-11
χ1511111-1-1-1-1111-1-1-1-11-1-11111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1-1-111-1-11111-1-1-1-11111-1-11-1-11
χ1611111-1-1-1-1111-1-1-1-11-1-11111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1111-1-11-11-1111-1-1-1-111-1-11111-1-1-111-1
χ172222222222222222222222-12-1-122-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000002202200000000000000000-1-1-1-1
χ182222222222222222222222-12-1-122-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000-2-20-2-2000000000000000001111
χ19222222222222222222222-12-122-1-12-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200000000200200000000-1-1-1-1-1-1-1-10000
χ20222222222222222222222-12-122-1-12-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-200-200000000111111110000
χ212222222-2-2222-2-2-2-2-222-2-22-12-1-122-12222-1-1-1-11111-1-1-2-2-2-2-1-1-1-1111111110000000000220-2-200000000000000000-1-111
χ222222222-2-2222-2-2-2-2-222-2-22-12-1-122-12222-1-1-1-11111-1-1-2-2-2-2-1-1-1-1111111110000000000-2-20220000000000000000011-1-1
χ232222222-2-2222-2-2-2-2-222-2-2-12-122-1-12-1-1-1-1-1-1-1-1-2-2-2-2221111-1-1-1-11111111122-2-200000000-200200000000-1-1-1-111110000
χ242222222-2-2222-2-2-2-2-222-2-2-12-122-1-12-1-1-1-1-1-1-1-1-2-2-2-2221111-1-1-1-111111111-2-22200000000200-2000000001111-1-1-1-10000
χ2522222-2-2222222222-2-2-2-2-22-12-1-122-1-2-2-2-2-1-1-1-1-1-1111122-2-21111-1-1-1-1111100000000002-202-200000000000000000-11-11
χ2622222-2-2222222222-2-2-2-2-22-12-1-122-1-2-2-2-2-1-1-1-1-1-1111122-2-21111-1-1-1-111110000000000-220-22000000000000000001-11-1
χ2722222-2-2222222222-2-2-2-2-2-12-122-1-121111-1-1-1-122-2-2-2-2-1-1111111-1-1-1-11111222200000000-200-200000000-1-111-1-1110000
χ2822222-2-2222222222-2-2-2-2-2-12-122-1-121111-1-1-1-122-2-2-2-2-1-1111111-1-1-1-11111-2-2-2-20000000020020000000011-1-111-1-10000
χ2922222-2-2-2-2222-2-2-2-22-2-2222-12-1-122-1-2-2-2-2-1-1-1-111-1-111-2-22211111111-1-1-1-100000000002-20-2200000000000000000-111-1
χ3022222-2-2-2-2222-2-2-2-22-2-2222-12-1-122-1-2-2-2-2-1-1-1-111-1-111-2-22211111111-1-1-1-10000000000-2202-2000000000000000001-1-11
χ3122222-2-2-2-2222-2-2-2-22-2-222-12-122-1-121111-1-1-1-1-2-222-2-211-1-111111111-1-1-1-122-2-200000000200-200000000-1-11111-1-10000
χ3222222-2-2-2-2222-2-2-2-22-2-222-12-122-1-121111-1-1-1-1-2-222-2-211-1-111111111-1-1-1-1-2-22200000000-20020000000011-1-1-1-1110000
χ3322-2-22002i−2i2-2-22i2i−2i−2i0000022-22-22-2-2000022-2-22i−2i00002i−2i0000002i2i−2i−2i00002-22i−2i000000000000000000002-2002i−2i000000
χ3422-2-22002i−2i2-2-22i2i−2i−2i0000022-22-22-2-2000022-2-22i−2i00002i−2i0000002i2i−2i−2i0000-22−2i2i00000000000000000000-2200−2i2i000000
χ3522-2-22002i−2i2-2-22i2i−2i−2i00000-1212-2-11-233−3−3-1-1112i−2i0000−ii−i3i333−3−3−i−iii−i3−i3i3i32-22i−2i00000000000000000000-113−3−ii−i3i30000
χ3622-2-22002i−2i2-2-22i2i−2i−2i00000-1212-2-11-233−3−3-1-1112i−2i0000−ii−i3i333−3−3−i−iii−i3−i3i3i3-22−2i2i000000000000000000001-1−33i−ii3−i30000
χ3722-2-22002i−2i2-2-22i2i−2i−2i00000-1212-2-11-2−3−333-1-1112i−2i0000−iii3−i3−3−333−i−iiii3i3−i3−i32-22i−2i00000000000000000000-11−33−iii3−i30000
χ3822-2-22002i−2i2-2-22i2i−2i−2i00000-1212-2-11-2−3−333-1-1112i−2i0000−iii3−i3−3−333−i−iiii3i3−i3−i3-22−2i2i000000000000000000001-13−3i−i−i3i30000
χ3922-2-2200−2i2i2-2-2−2i−2i2i2i0000022-22-22-2-2000022-2-2−2i2i0000−2i2i000000−2i−2i2i2i00002-2−2i2i000000000000000000002-200−2i2i000000
χ4022-2-2200−2i2i2-2-2−2i−2i2i2i0000022-22-22-2-2000022-2-2−2i2i0000−2i2i000000−2i−2i2i2i0000-222i−2i00000000000000000000-22002i−2i000000
χ4122-2-2200−2i2i2-2-2−2i−2i2i2i00000-1212-2-11-233−3−3-1-111−2i2i0000i−ii3−i333−3−3ii−i−ii3i3−i3−i32-2−2i2i00000000000000000000-113−3i−ii3−i30000
χ4222-2-2200−2i2i2-2-2−2i−2i2i2i00000-1212-2-11-233−3−3-1-111−2i2i0000i−ii3−i333−3−3ii−i−ii3i3−i3−i3-222i−2i000000000000000000001-1−33−ii−i3i30000
χ4322-2-2200−2i2i2-2-2−2i−2i2i2i00000-1212-2-11-2−3−333-1-111−2i2i0000i−i−i3i3−3−333ii−i−i−i3−i3i3i32-2−2i2i00000000000000000000-11−33i−i−i3i30000
χ4422-2-2200−2i2i2-2-2−2i−2i2i2i00000-1212-2-11-2−3−333-1-111−2i2i0000i−i−i3i3−3−333ii−i−i−i3−i3i3i3-222i−2i000000000000000000001-13−3−iii3−i30000
χ452-22-222-200-22-2000002-200222-2-2-2-222-22-22-22-200002-200002-22-20000000000002i−2i2i−2i0000000000002i−2i2i−2i000000000000
χ462-22-222-200-22-2000002-200222-2-2-2-222-22-22-22-200002-200002-22-2000000000000−2i2i−2i2i000000000000−2i2i−2i2i000000000000
χ472-22-22-2200-22-200000-2200222-2-2-2-22-22-222-22-20000-220000-22-220000000000002i−2i−2i2i0000000000002i−2i−2i2i000000000000
χ482-22-22-2200-22-200000-2200222-2-2-2-22-22-222-22-20000-220000-22-22000000000000−2i2i2i−2i000000000000−2i2i2i−2i000000000000
χ49444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000
χ504444444-4-4444-4-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-211112222-2-222221111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ5144444-4-4444444444-4-4-4-4-4-2-2-2-2-2-2-2-222221111-2-22222-2-222-1-1-1-11111-1-1-1-1000000000000000000000000000000000000
χ5244444-4-4-4-4444-4-4-4-44-4-444-2-2-2-2-2-2-2-22222111122-2-22222-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000000000
χ5344-4-44004i−4i4-4-44i4i−4i−4i000004-2-4-224-420000-2-222−2i2i00004i−4i000000−2i−2i2i2i0000000000000000000000000000000000000000
χ5444-4-44004i−4i4-4-44i4i−4i−4i00000-2-22-22-2222323−23−2311-1-1−2i2i0000−2i2i−2i32i3−3−333ii−i−ii3i3−i3−i3000000000000000000000000000000000000
χ5544-4-44004i−4i4-4-44i4i−4i−4i00000-2-22-22-222−23−23232311-1-1−2i2i0000−2i2i2i3−2i333−3−3ii−i−i−i3−i3i3i3000000000000000000000000000000000000
χ5644-4-4400−4i4i4-4-4−4i−4i4i4i000004-2-4-224-420000-2-2222i−2i0000−4i4i0000002i2i−2i−2i0000000000000000000000000000000000000000
χ5744-4-4400−4i4i4-4-4−4i−4i4i4i00000-2-22-22-2222323−23−2311-1-12i−2i00002i−2i2i3−2i3−3−333−i−iii−i3−i3i3i3000000000000000000000000000000000000
χ5844-4-4400−4i4i4-4-4−4i−4i4i4i00000-2-22-22-222−23−23232311-1-12i−2i00002i−2i−2i32i333−3−3−i−iiii3i3−i3−i3000000000000000000000000000000000000
χ594-44-444-400-44-4000004-4004-2422-4-4-24-44-4-22-220000-220000-22-2200000000000000000000000000000000000000000000
χ604-44-444-400-44-4000004-400-24-2-4-4224-22-22-22-2200004-40000-22-2200000000000000000000000000000000000000000000
χ614-44-444-400-44-4000004-400-2-2-22222-2-22-221-11-10000-2200001-11-13i−3i3i−3i3i−3i3i−3i000000000000000000000000000000000000
χ624-44-444-400-44-4000004-400-2-2-22222-2-22-221-11-10000-2200001-11-1−3i3i−3i3i−3i3i−3i3i000000000000000000000000000000000000
χ634-44-44-4400-44-400000-44004-2422-4-4-2-44-44-22-2200002-200002-22-200000000000000000000000000000000000000000000
χ644-44-44-4400-44-400000-4400-24-2-4-42242-22-2-22-220000-4400002-22-200000000000000000000000000000000000000000000
χ654-44-44-4400-44-400000-4400-2-2-22222-22-22-21-11-100002-20000-11-113i−3i3i−3i−3i3i−3i3i000000000000000000000000000000000000
χ664-44-44-4400-44-400000-4400-2-2-22222-22-22-21-11-100002-20000-11-11−3i3i−3i3i3i−3i3i−3i000000000000000000000000000000000000
χ674-4-4440000-4-4400000000044-4-44-44-400004-4-440000000000000000000000000000000000000000000000000000000000
χ684-4-4440000-4-440000000004-2-42-2-4420000-222-20023−230000000000000023−23−2323000000000000000000000000000000000000
χ694-4-4440000-4-440000000004-2-42-2-4420000-222-200−232300000000000000−232323−23000000000000000000000000000000000000
χ704-4-4440000-4-44000000000-242-442-2-423−23−2323-222-2000000000023−23−232300000000000000000000000000000000000000000000
χ714-4-4440000-4-44000000000-242-442-2-4−232323−23-222-20000000000−232323−2300000000000000000000000000000000000000000000
χ724-4-4440000-4-44000000000-2-222-22-2223−23−23231-1-110023−23000000−333−33-3-33−333−3000000000000000000000000000000000000
χ734-4-4440000-4-44000000000-2-222-22-2223−23−23231-1-1100−2323000000−333−3-333-33−3−33000000000000000000000000000000000000
χ744-4-4440000-4-44000000000-2-222-22-22−232323−231-1-110023−230000003−3−33-333-3−333−3000000000000000000000000000000000000
χ754-4-4440000-4-44000000000-2-222-22-22−232323−231-1-1100−23230000003−3−333-3-333−3−33000000000000000000000000000000000000
χ766666-36666-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000222222000000-1-1-1-1-1-1-1-1000000000000
χ776666-36666-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000-2-2-2-2-2-200000011111111000000000000
χ786666-366-6-6-3-3-33333-6-3-3330000000000000000000000000000000000000000002222-2-20000001111-1-1-1-1000000000000
χ796666-366-6-6-3-3-33333-6-3-333000000000000000000000000000000000000000000-2-2-2-222000000-1-1-1-11111000000000000
χ806666-3-6-666-3-3-3-3-3-3-3-6333300000000000000000000000000000000000000000022-2-22-2000000-1-111-1-111000000000000
χ816666-3-6-666-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000-2-222-2200000011-1-111-1-1000000000000
χ826666-3-6-6-6-6-3-3-33333633-3-300000000000000000000000000000000000000000022-2-2-2200000011-1-1-1-111000000000000
χ836666-3-6-6-6-6-3-3-33333633-3-3000000000000000000000000000000000000000000-2-2222-2000000-1-11111-1-1000000000000
χ846-66-6-36-6003-3333−3333−330-3333−330000000000000000000000000000000000000000002i−2i2i−2i00000000−i3i3−i3i3−ii−ii000000000000
χ856-66-6-36-6003-3333−3333−330-3333−33000000000000000000000000000000000000000000−2i2i−2i2i00000000i3−i3i3−i3i−ii−i000000000000
χ866-66-6-36-6003-33−3333−33330-33−33330000000000000000000000000000000000000000002i−2i2i−2i00000000i3−i3i3−i3−ii−ii000000000000
χ876-66-6-36-6003-33−3333−33330-33−3333000000000000000000000000000000000000000000−2i2i−2i2i00000000−i3i3−i3i3i−ii−i000000000000
χ886-66-6-3-66003-3333−3333−3303-3−33330000000000000000000000000000000000000000002i−2i−2i2i00000000−i3i3i3−i3−iii−i000000000000
χ896-66-6-3-66003-3333−3333−3303-3−3333000000000000000000000000000000000000000000−2i2i2i−2i00000000i3−i3−i3i3i−i−ii000000000000
χ906-66-6-3-66003-33−3333−333303-333−330000000000000000000000000000000000000000002i−2i−2i2i00000000i3−i3−i3i3−iii−i000000000000
χ916-66-6-3-66003-33−3333−333303-333−33000000000000000000000000000000000000000000−2i2i2i−2i00000000−i3i3i3−i3i−i−ii000000000000
χ921212-12-12-60012i−12i-666−6i−6i6i6i0000000000000000000000000000000000000000000000000000000000000000000000000000000
χ931212-12-12-600−12i12i-6666i6i−6i−6i0000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-1212-6000066-6−6i36i36i3−6i30000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-1212-6000066-66i3−6i3−6i36i30000000000000000000000000000000000000000000000000000000000000000000000000000000

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