Finite Group Databasebeta

← Group #13151368

Character table — Group #13151368

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222244446666666688999912121212121212121212121218181818181818181818181818182424242424242424363636363636363636363636363636363636363672727272
order1222344666221212336666666644443666666612121212224444444412121212666666121222444466121212121212121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ3111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111
χ4111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ51111111111-1-11111111111-1-111111-1-1-1-1111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ61111111111-1-11111111111-1-111111-1-1-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-11111
χ71111111111-1-11111111111-1-1-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111111111-1-1
χ81111111111-1-11111111111-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-111
χ911111-1-11111-1-1-1111111111-11111111-1-1111-1-1-1-111-1-1-1-1-1-11111111-111-1-1-1-11-11-11-11111-1-1-1-1-1-111-1-11-11-1
χ1011111-1-11111-1-1-1111111111-11111111-1-1111-1-1-1-1-1-111-1-111-1-111111-111-1-1-1-1-111-1-11-1-1-1-111-1-11111-1-1-11-11
χ1111111-1-11111-1-1-1111111111-1-1-1-1-1111-1-1111-1-1-1-111-1-11111-1-1-1-1-1-11-111-1-1-1-1-11-111-111-1-11111-1-1-1-111-111-1
χ1211111-1-11111-1-1-1111111111-1-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-111-1-1-1-11-111-1-1-1-11-1-11-11-1-111-1-11111-1-1111-1-11
χ1311111-1-1111-11-1-111111111-1111111-1-111111-1-1-1-111-1-1-1-1-1-1111111-11-1-111-1-1-11-11-111111-1-1-1-1-1-1-1-111-11-11
χ1411111-1-1111-11-1-111111111-1111111-1-111111-1-1-1-1-1-111-1-111-1-11111-11-1-111-1-11-1-111-1-1-1-1-111-1-111-1-1111-11-1
χ1511111-1-1111-11-1-111111111-11-1-1-1-11-1-111111-1-1-1-111-1-11111-1-1-1-1-1-1-11-1-111-1-11-11-1-1111-1-11111-1-111-1-11-1-11
χ1611111-1-1111-11-1-111111111-11-1-1-1-11-1-111111-1-1-1-1-1-11111-1-111-1-1-1-1-11-1-111-1-1-111-11-1-1-111-1-1111111-1-1-111-1
χ17222222222222222-1-122-1-12220000-12222-1-1-122-1-122220000000000-1-1-1-1-1-1-1-1000022-1-1000000-1-1000000-1-1
χ18222222222222222-1-122-1-12220000-12222-1-1-122-1-1-2-2-2-20000000000-1-1-1-1-1-1-1-10000-2-2110000001100000011
χ1922222222222222-122-1-122-1222222-1-1-1-1-1-1-1-1-1-1220000220000-1-1-1-122-1-1-1-1-1-1002200000000-1-100-1-1-1-10000
χ2022222222222222-122-1-122-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1220000-2-20000111122-1-1-1-1-1-100-2-200000000110011110000
χ212222222222-2-2222-1-122-1-12-2-20000-1-2-2-2-2-1-1-122-1-122220000000000111111-1-10000-2-2-1-1000000-1-100000011
χ222222222222-2-2222-1-122-1-12-2-20000-1-2-2-2-2-1-1-122-1-1-2-2-2-20000000000111111-1-10000221100000011000000-1-1
χ232222222222-2-222-122-1-122-1-2-22222-11111-1-1-1-1-1220000220000-1-1-1-1-2-21111-1-100-2-200000000-1-10011110000
χ242222222222-2-222-122-1-122-1-2-2-2-2-2-2-11111-1-1-1-1-1220000-2-200001111-2-21111-1-10022000000001100-1-1-1-10000
χ2522222-2-22222-2-2-22-1-122-1-122-20000-122-2-2-1-1-1-2-21122-2-20000000000-11-1-1111100002-2-1-100000011000000-11
χ2622222-2-22222-2-2-22-1-122-1-122-20000-122-2-2-1-1-1-2-211-2-2220000000000-11-1-111110000-2211000000-1-10000001-1
χ2722222-2-22222-2-2-2-122-1-122-12-22222-1-1-111-1-1-111-2-20000-2-20000-1-1-1-12-2-1-11111002-2000000001100-1-1110000
χ2822222-2-22222-2-2-2-122-1-122-12-2-2-2-2-2-1-1-111-1-1-111-2-2000022000011112-2-1-1111100-2200000000-1-10011-1-10000
χ2922222-2-2222-22-2-22-1-122-1-12-220000-1-2-222-1-1-1-2-21122-2-200000000001-111-1-1110000-22-1-1000000110000001-1
χ3022222-2-2222-22-2-22-1-122-1-12-220000-1-2-222-1-1-1-2-211-2-22200000000001-111-1-11100002-211000000-1-1000000-11
χ3122222-2-2222-22-2-2-122-1-122-1-222222-111-1-1-1-1-111-2-20000-2-20000-1-1-1-1-2211-1-11100-2200000000110011-1-10000
χ3222222-2-2222-22-2-2-122-1-122-1-22-2-2-2-2-111-1-1-1-1-111-2-200002200001111-2211-1-111002-200000000-1-100-1-1110000
χ3322-2-222-22-2-2002-222-22-22-2-2002i2i−2i−2i20000-2-222-22-200002i−2i00002i2i−2i−2i0000002-20000000000002i−2i0000000000
χ3422-2-222-22-2-2002-222-22-22-2-200−2i−2i2i2i20000-2-222-22-20000−2i2i0000−2i−2i2i2i0000002-2000000000000−2i2i0000000000
χ3522-2-222-22-2-2002-2-12-2-112-21002i2i−2i−2i-1−i3i3−i3i311-1-112-200002i−2i0000−i−iii00−i3i3−i3i3-11000000000000−ii003−33−30000
χ3622-2-222-22-2-2002-2-12-2-112-21002i2i−2i−2i-1i3−i3i3−i311-1-112-200002i−2i0000−i−iii00i3−i3i3−i3-11000000000000−ii00−33−330000
χ3722-2-222-22-2-2002-2-12-2-112-2100−2i−2i2i2i-1−i3i3−i3i311-1-112-20000−2i2i0000ii−i−i00−i3i3−i3i3-11000000000000i−i00−33−330000
χ3822-2-222-22-2-2002-2-12-2-112-2100−2i−2i2i2i-1i3−i3i3−i311-1-112-20000−2i2i0000ii−i−i00i3−i3i3−i3-11000000000000i−i003−33−30000
χ3922-2-22-222-2-200-2222-22-22-2-2002i2i−2i−2i20000-2-22-22-220000−2i2i00002i2i−2i−2i000000-22000000000000−2i2i0000000000
χ4022-2-22-222-2-200-2222-22-22-2-200−2i−2i2i2i20000-2-22-22-2200002i−2i0000−2i−2i2i2i000000-220000000000002i−2i0000000000
χ4122-2-22-222-2-200-22-12-2-112-21002i2i−2i−2i-1−i3i3i3−i311-11-1-220000−2i2i0000−i−iii00−i3i3i3−i31-1000000000000i−i003−3−330000
χ4222-2-22-222-2-200-22-12-2-112-21002i2i−2i−2i-1i3−i3−i3i311-11-1-220000−2i2i0000−i−iii00i3−i3−i3i31-1000000000000i−i00−333−30000
χ4322-2-22-222-2-200-22-12-2-112-2100−2i−2i2i2i-1−i3i3i3−i311-11-1-2200002i−2i0000ii−i−i00−i3i3i3−i31-1000000000000−ii00−333−30000
χ4422-2-22-222-2-200-22-12-2-112-2100−2i−2i2i2i-1i3−i3−i3i311-11-1-2200002i−2i0000ii−i−i00i3−i3−i3i31-1000000000000−ii003−3−330000
χ452-22-2200-22-20000222-22-2-2-2002i−2i2i−2i200002-2-20000002i−2i002-2002i−2i2i−2i0000000000000000002-2002i−2i00000000
χ462-22-2200-22-20000222-22-2-2-2002i−2i2i−2i200002-2-2000000−2i2i00-22002i−2i2i−2i000000000000000000-2200−2i2i00000000
χ472-22-2200-22-20000222-22-2-2-200−2i2i−2i2i200002-2-20000002i−2i00-2200−2i2i−2i2i000000000000000000-22002i−2i00000000
χ482-22-2200-22-20000222-22-2-2-200−2i2i−2i2i200002-2-2000000−2i2i002-200−2i2i−2i2i0000000000000000002-200−2i2i00000000
χ492-2-22200-2-22000022-2-2-2-222002-2-2220000-22-200002-20000002-22-2-22000000000000002-22-200000000000000
χ502-2-22200-2-22000022-2-2-2-222002-2-2220000-22-20000-22000000-222-2-2200000000000000-22-2200000000000000
χ512-2-22200-2-22000022-2-2-2-22200-222-220000-22-200002-2000000-22-222-2000000000000002-2-2200000000000000
χ522-2-22200-2-22000022-2-2-2-22200-222-220000-22-20000-220000002-2-222-200000000000000-222-200000000000000
χ5344444444444444-2-2-2-2-2-2-2-24400001-2-2-2-2111-2-2-2-200000000000000-2-2111111000000000000000000000000
χ544444444444-4-444-2-2-2-2-2-2-2-2-4-4000012222111-2-2-2-20000000000000022-1-1-1-111000000000000000000000000
χ5544444-4-44444-4-4-4-2-2-2-2-2-2-2-24-400001-2-222111222200000000000000-2211-1-1-1-1000000000000000000000000
χ5644444-4-4444-44-4-4-2-2-2-2-2-2-2-2-440000122-2-21112222000000000000002-2-1-111-1-1000000000000000000000000
χ5744-4-444-44-4-4004-44-224-4-22-4000000-2000022-24-4-2200000000000000000000-22000000000000000000000000
χ5844-4-444-44-4-4004-4-2-22-22-2220000001−2i32i3−2i32i3-1-11-22-220000000000000000i3−i3i3−i31-1000000000000000000000000
χ5944-4-444-44-4-4004-4-2-22-22-22200000012i3−2i32i3−2i3-1-11-22-220000000000000000−i3i3−i3i31-1000000000000000000000000
χ6044-4-44-444-4-400-444-224-4-22-4000000-2000022-2-442-2000000000000000000002-2000000000000000000000000
χ6144-4-44-444-4-400-44-2-22-22-2220000001−2i32i32i3−2i3-1-112-22-20000000000000000i3−i3−i3i3-11000000000000000000000000
χ6244-4-44-444-4-400-44-2-22-22-22200000012i3−2i3−2i32i3-1-112-22-20000000000000000−i3i3i3−i3-11000000000000000000000000
χ634-44-4400-44-400004-2-2-4422-4000000-20000-2220000004i−4i00000000000000000000000000000000−2i2i00000000
χ644-44-4400-44-400004-2-2-4422-4000000-20000-222000000−4i4i000000000000000000000000000000002i−2i00000000
χ654-44-4400-44-40000-2442-2-4-42004i−4i4i−4i-20000-22200000000000000−2i2i−2i2i00000000000000000000000000000000
χ664-44-4400-44-40000-2442-2-4-4200−4i4i−4i4i-20000-222000000000000002i−2i2i−2i00000000000000000000000000000000
χ674-4-44400-4-4400004-22-4-42-24000000-200002-2200004-400000000000000000000000000-220000000000000000
χ684-4-44400-4-4400004-22-4-42-24000000-200002-220000-44000000000000000000000000002-20000000000000000
χ694-4-44400-4-440000-24-422-44-2004-4-44-200002-2200000000000000-222-200000000000000000000000000000000
χ704-4-44400-4-440000-24-422-44-200-444-4-200002-22000000000000002-2-2200000000000000000000000000000000
χ716666-366-3-3-366-3-300000000-3-30000000000000000000000222200000000000022000000-1-1-1-100000000-1-100
χ726666-366-3-3-366-3-300000000-3-30000000000000000000000-2-2-2-2000000000000-2-20000001111000000001100
χ736666-366-3-3-3-6-6-3-3000000003300000000000000000000002222000000000000-2-2000000-1-1-1-1000000001100
χ746666-366-3-3-3-6-6-3-300000000330000000000000000000000-2-2-2-200000000000022000000111100000000-1-100
χ756666-3-6-6-3-3-36-63300000000-33000000000000000000000022-2-2000000000000-2200000011-1-1000000001-100
χ766666-3-6-6-3-3-36-63300000000-330000000000000000000000-2-2220000000000002-2000000-1-11100000000-1100
χ776666-3-6-6-3-3-3-6633000000003-3000000000000000000000022-2-20000000000002-200000011-1-100000000-1100
χ786666-3-6-6-3-3-3-6633000000003-30000000000000000000000-2-222000000000000-22000000-1-111000000001-100
χ798-88-8800-88-80000-4-4-44-4444000000200002-2-200000000000000000000000000000000000000000000000000
χ808-8-88800-8-880000-4-44444-4-400000020000-22-200000000000000000000000000000000000000000000000000
χ811212-12-12-612-12-66600-66000000000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-12-6-1212-666006-6000000000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-12-6006-660000000000000000000000000000000000004-4000000000000000000000000-22000000000000
χ8412-1212-12-6006-66000000000000000000000000000000000000-440000000000000000000000002-2000000000000
χ8512-12-1212-60066-6000000000000000000000000000000000000004-400000000000000000000-2200000000000000
χ8612-12-1212-60066-600000000000000000000000000000000000000-44000000000000000000002-200000000000000

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