Finite Group Databasebeta

← Group #13151937

Character table — Group #13151937

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size112222244444444466666612121212121212121218181818181824242424242424242424363636363636363636363636363636363636363636727272727272
order1223446246661212121233661212366612121212122244886666612121212122224446688812121212121224242424666122424
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11111111111-1-1-111-111-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111-1-11-1-1
χ41111111111111111111111111111111-1-1-1-1-1-11111111111-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-111
χ51111111-1-11-1-111-1-1111111111111111111111-1-11-1-1-1-11-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-111
χ61111111-1-11-1-111-1-11111111111111111111-1-1-1-11-1-1-1-11-1-1111-1-1111-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ71111111-1-11-1-111-1-1111111111111111-1-1-1-111-1-11-1-1-1-11-1-1-11111-1-1-11-1-1-1-111111111-111-1-1-1
χ81111111-1-11-1-111-1-1111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-11-1-1111-1-1-111-1-11111-1-1-1-11-1-1111
χ911-11-1111-1-1111-1-1-11111-1-11-1-11-1-1-1111-11-11111-111-1-11-1-1-11-11-111-1-11-11-111-1-111-1-1-11-111-1
χ1011-11-1111-1-1111-1-1-11111-1-11-1-11-1-1-1111-11-1-1-111-111-1-11-1-11-111-1-11-11-111-111-1-1-1-1111-11-1-11
χ1111-11-1111-1-1111-1-1-11111-1-11-1-11-1-1-111-11-111111-111-1-11-1-1-1-11-111-11-1-11-11-1-11111-1-1-1-111-11
χ1211-11-1111-1-1111-1-1-11111-1-11-1-11-1-1-111-11-11-1-111-111-1-11-1-111-1-11-1-1111-1-11-1-111-1-11111-1-11-1
χ1311-11-111-11-1-1-11-1111111-1-11-1-11-1-1-1111-11-111-1-1-1-1-1111111-11-11-11-1-11-11-1-1-11111-1-11-11-11-1
χ1411-11-111-11-1-1-11-1111111-1-11-1-11-1-1-1111-11-1-1-1-1-1-1-1-111111-11-1-1111-11-111-1-1-111-1-111-11-11-11
χ1511-11-111-11-1-1-11-1111111-1-11-1-11-1-1-111-11-1111-1-1-1-1-11111111-11-1-1-11-1-11-1111-1-111-1-111-1-1-11
χ1611-11-111-11-1-1-11-1111111-1-11-1-11-1-1-111-11-11-1-1-1-1-1-1-111111-1-111-11-1111-1-1111-1-1-1-111-1-1111-1
χ1722222222222222222-1-1222-12-1-1-1-1-1-120000002-1-1-1-1-12-1-1-10220000002200000000000-1-10-1-1
χ1822222222222222222-1-1222-12-1-1-1-1-1-120000002-1-1-1-1-12-1-1-10-2-2000000-2-20000000000011011
χ192222222222222222-122-1-1-1-1-12-12-1-12-1000022-12-1-1-12-1-1-1-120000200200000000-1-1-1-1-100-100
χ202222222222222222-122-1-1-1-1-12-12-1-12-10000-2-2-12-1-1-12-1-1-1-1-20000-200-2000000001111100100
χ212222222-2-22-2-222-2-22-1-1222-12-1-1-1-1-1-12000000-21-1111-2-111022000000-2-200000000000-1-1011
χ222222222-2-22-2-222-2-22-1-1222-12-1-1-1-1-1-12000000-21-1111-2-1110-2-20000002200000000000110-1-1
χ232222222-2-22-2-222-2-2-122-1-1-1-1-12-12-1-12-10000221-2-111-21-111-20000-200200000000-1-1-1-1100100
χ242222222-2-22-2-222-2-2-122-1-1-1-1-12-12-1-12-10000-2-21-2-111-21-11120000200-2000000001111-100-100
χ252222-2-2200200-2-2002222-2-22222-2-2-2-2-22-2-22000020000-2000000002-2000-2200000000000000
χ262222-2-2200200-2-2002222-2-22222-2-2-2-2-2-222-2000020000-200000000-220002-200000000000000
χ2722-222-2200-200-22002222222-2-22222-2-222-2-20000-20000-20000000022000-2-200000000000000
χ2822-222-2200-200-22002222222-2-22222-2-2-2-2220000-20000-200000000-2-20002200000000000000
χ2922-22-2222-2-2222-2-2-22-1-12-2-2-1-21-1111-120000002-11-1-11-2-11102-20000002-200000000000-110-11
χ3022-22-2222-2-2222-2-2-22-1-12-2-2-1-21-1111-120000002-11-1-11-2-1110-22000000-22000000000001-101-1
χ3122-22-2222-2-2222-2-2-2-122-111-11-2-1-2112-1000022-121-1-1-21-111-20000200-200000000-1-111100-100
χ3222-22-2222-2-2222-2-2-2-122-111-11-2-1-2112-10000-2-2-121-1-1-21-11120000-20020000000011-1-1-100100
χ3322-22-222-22-2-2-22-2222-1-12-2-2-1-21-1111-12000000-21111-12-1-1-102-2000000-2200000000000-1101-1
χ3422-22-222-22-2-2-22-2222-1-12-2-2-1-21-1111-12000000-21111-12-1-1-10-220000002-2000000000001-10-11
χ3522-22-222-22-2-2-22-222-122-111-11-2-1-2112-10000221-21112-1-1-1-120000-200-200000000-1-111-100100
χ3622-22-222-22-2-2-22-222-122-111-11-2-1-2112-10000-2-21-21112-1-1-1-1-2000020020000000011-1-1100-100
χ374444444444444444-2-2-2-2-2-21-2-21-211-2-2000000-2-2111-2-2111000000000000000000000000000
χ384444444-4-44-4-444-4-4-2-2-2-2-2-21-2-21-211-2-2000000221-1-1221-1-1000000000000000000000000000
χ394444-4-4400400-4-4004-2-24-4-4-24-2-22222-400000000-20000200000000000000000000000000000
χ404444-4-4400400-4-400-244-222-2-24-2-422-4200000000-20000200000000000000000000000000000
χ414444-4-4400400-4-400-2-2-2-2221-2-212-1-1220000000013-300-13-3000000000000000000000000000
χ424444-4-4400400-4-400-2-2-2-2221-2-212-1-122000000001-3300-1-33000000000000000000000000000
χ4344-444-4400-400-44004-2-2444-2-42-2-2-2-22-40000000020000200000000000000000000000000000
χ4444-444-4400-400-4400-244-2-2-2-22-4-24-2-2-420000000020000200000000000000000000000000000
χ4544-444-4400-400-4400-2-2-2-2-2-21221-2112200000000-13-300-1-33000000000000000000000000000
χ4644-444-4400-400-4400-2-2-2-2-2-21221-2112200000000-1-3300-13-3000000000000000000000000000
χ4744-44-4444-4-4444-4-4-4-2-2-2-22212212-1-1-2-2000000-2-2-111221-1-1000000000000000000000000000
χ4844-44-444-44-4-4-44-444-2-2-2-22212212-1-1-2-200000022-1-1-1-2-2111000000000000000000000000000
χ494-40400-400000000044-4-400400-4000000000−2i22i2000000000000000000000000000−2i22i200000000
χ504-40400-400000000044-4-400400-40000000002i2−2i20000000000000000000000000002i2−2i200000000
χ514-40400-4000000000-24-4223−23-2002023−23000000−2i22i2000000000000000000000000000i2−i2i6−i6000000
χ524-40400-4000000000-24-4223−23-2002023−230000002i2−2i2000000000000000000000000000−i2i2−i6i6000000
χ534-40400-4000000000-24-42−2323-20020−2323000000−2i22i2000000000000000000000000000i2−i2−i6i6000000
χ544-40400-4000000000-24-42−2323-20020−23230000002i2−2i2000000000000000000000000000−i2i2i6−i6000000
χ55666-366-366-3-3-3-3-3-3-30000000000000002222000000000000000220-1-1000-1-1-1-1-1-10000000000
χ56666-366-366-3-3-3-3-3-3-3000000000000000-2-2-2-2000000000000000-2-20110001111110000000000
χ57666-366-3-6-6-333-3-3330000000000000002222000000000000000-2-20-1-1000-1-111110000000000
χ58666-366-3-6-6-333-3-333000000000000000-2-2-2-20000000000000002201100011-1-1-1-10000000000
χ59666-3-6-6-300-3−3i33i333−3i33i30000000000000002-2-22000000000000000000-110001-1−i3i3−i3i30000000000
χ60666-3-6-6-300-3−3i33i333−3i33i3000000000000000-222-20000000000000000001-1000-11i3−i3i3−i30000000000
χ61666-3-6-6-300-33i3−3i3333i3−3i30000000000000002-2-22000000000000000000-110001-1i3−i3i3−i30000000000
χ62666-3-6-6-300-33i3−3i3333i3−3i3000000000000000-222-20000000000000000001-1000-11−i3i3−i3i30000000000
χ6366-6-36-6-3003−3i33i33-33i3−3i300000000000000022-2-2000000000000000000-1-100011−i3i3i3−i30000000000
χ6466-6-36-6-3003−3i33i33-33i3−3i3000000000000000-2-22200000000000000000011000-1-1i3−i3−i3i30000000000
χ6566-6-36-6-30033i3−3i33-3−3i33i300000000000000022-2-2000000000000000000-1-100011i3−i3−i3i30000000000
χ6666-6-36-6-30033i3−3i33-3−3i33i3000000000000000-2-22200000000000000000011000-1-1−i3i3i3−i30000000000
χ6766-6-3-66-36-63-3-3-33330000000000000002-22-20000000000000002-20-11000-11-1-1110000000000
χ6866-6-3-66-36-63-3-3-3333000000000000000-22-22000000000000000-2201-10001-111-1-10000000000
χ6966-6-3-66-3-66333-33-3-30000000000000002-22-2000000000000000-220-11000-1111-1-10000000000
χ7066-6-3-66-3-66333-33-3-3000000000000000-22-220000000000000002-201-10001-1-1-1110000000000
χ718-80800-80000000008-44-800-4004000000000000000000000000000000000000000000000000
χ728-80800-8000000000-4-44443−43200-20−2323000000000000000000000000000000000000000000000
χ738-80800-8000000000-4-444−4343200-2023−23000000000000000000000000000000000000000000000
χ7424-240-1200120000000000000000000000000000000000000000000000000000000000000000000

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